ISSN 2188-5001
MATERIALS DESIGN AND
CHARACTERIZATION LABORATORYSUPERCOMPUTER CENTERACTIVITY REPORT

2021

THE UNIVERSITY OF TOKYO

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Materials Design and Characterization Laboratory (MDCL)
The MDCL was established as the third research facility of the Institute for Solid
State Physics (ISSP) when the latter was reorganized in May 1996. Its aim is to promotematerial science with an emphasis on the “DSC cycle”, where DSC stands for design,synthesis and characterization, three processes for developing new materials.
The MDCL consists of two sections, Materials Design (MD) section and Materials
Synthesis and Characterization (MSC) section. The Supercomputer Center of the ISSP
(SCC-ISSP) is placed in the MD section, while in the MSC section there are seven laboratories for joint use; Materials Synthesis Laboratory, Chemical Analysis Laboratory, X-ray
Diﬀraction Laboratory, Electron Microscope Laboratory, Electromagnetic Measurement
Laboratory, Spectroscopy Laboratory, and High-Pressure Synthesis Laboratory.
Almost all the facilities of the MDCL are open to scientists in Japan through the User
Programs conducted by two steering committees of the MDCL. One is the steering committee of the SCC-ISSP, under which the Supercomputer Project Advisory Committee isplaced for reviewing proposals. The other is the steering committee of the MSC facilities.
More than half of the members of these committees are from the outside of ISSP.

COVER FIGURE
Stable 6x6 surface structure obtained by Bayesian optimization. Brown, blue and whiteatoms correspond to Ga, N and H, respectively.
See Page 42–44, A. Oshiyama, ”Clariﬁcation of Microscopic Mechanisms of Semiconductor Epitaxial Growth and Device-Interface Formation by Large-Scale Quantum-TheoryBased Computations”.

iiActivity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

PREFACEThe Supercomputer Center (SCC) is a part of the Materials Design and Characterization
Laboratory (MDCL) of ISSP. Its mission is to serve the whole community of computationalcondensed-matter physics of Japan providing it with high performance computing environment.
In particular, the SCC selectively promotes and supports large-scale computations. For thispurpose, the SCC invites proposals for supercomputer-aided research projects and hosts theSteering Committee, as mentioned below, that evaluates the proposals.
The ISSP supercomputer system consists of two subsystems: System B, which was last replacedin Oct. 2020, is intended for larger total computational power and has more nodes withrelatively loose connections whereas System C is intended for higher communication speed
among nodes. System B (ohtaka) consists of 1680 CPU nodes of AMD EPYC 7702 (64 cores)
and 8 FAT nodes of Intel Xeon Platinum 8280 (28 cores) with total theoretical performance of
6.881 PFlops. System C (enaga) consists of 252 nodes of HPE SGI 8600 with 0.77 PFLOPS,
which stopped operation in Dec. 2021 for replacement. The new machine (kugui), which
consists of 128 nodes of AMD EPYC 7763 (128 cores) and 8 nodes of AMD EPYC 7763 (64cores) with total theoretical performance of 0.973 PFLOPS, will start operation in June 2022.
In addition to the hardware administration, the SCC puts increasing effort on the software
support. Since 2015, the SCC has been conducting “Project for advancement of software
usability in materials science (PASUMS).”In this project, for enhancing the usability of the
ISSP supercomputer system, we conduct several software-advancement activities: developing
new application software that runs efficiently on the ISSP supercomputer system, adding new
functions to existing codes, help releasing private codes for public use, creating/improving
manuals for public codes, etc. Three target programs were selected in fiscal year 2021 anddeveloped or enhanced the ustablity of software were released as (1) ESM-RISM (proposal
made by M. Otani (AIST)), and (2) 2DMAT (proposal made by T. Hoshi (Tottori Univ.)). In
2021, we also started the data repository service for storing results of numerical calculation andenhancing their reusability.
All staff members of university faculties or public research institutes in Japan are invited topropose research projects (called User Program). The proposals are evaluated by the Steering
Committee of SCC. Pre-reviewing is done by the Supercomputer Project Advisory Committee.
In fiscal year 2021, totally 321 projects were approved including the ones under the frameworkof Supercomputing Consortium for Computational Materials Science (SCCMS), which
specially supports FUGAKU and other major projects in computational materials science.
The research projects are roughly classified into the following three (the number of projects
approved):
First-Principles Calculation of Materials Properties (142)
Strongly Correlated Quantum Systems (29)
Cooperative Phenomena in Complex, Macroscopic Systems (128)
In all the three categories, most proposals involve both methodology and applications. The
results of the projects are reported in 'Activity Report 2021' of the SCC. Every year 3-4 projects
are selected for “invited papers” and published at the beginning of the Activity Report. In the
Activity Report 2021, the following three invited papers are included:iii

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo"Theory, practice, and application of the van der Waals density functional",
Ikutaro HAMADA (Osaka Univ.)"Development of permanent magnet materials—from the view point of first-principles
calculation”,
Hisazumi AKAI (ISSP) and Shinji TSUNEYUKI (Univ. Tokyo)"Development of Bayesian optimization tool and its applications in materials science",
Ryo TAMURA (NIMS), Yuichi MOTOYAMA (ISSP), and Kazuyoshi YOSHIMI (ISSP)
June 2, 2022
Naoki Kawashima(Chairman of the steering committee, SCC, ISSP)

iv

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

CONTENTSPREFACE
1 OUTLINE1

1.1 Supercomputer System
1.2 Project Proposals
1.3 Committees
1.4 Staﬀ

1
2
4
7

2 STATISTICS (SCHOOL YEAR 2021)
2.1 System and User Statistics
2.2 Queue and Job Statistics
2.3 Project for Advancement of Software Usability
in Materials Science
2.4 ISSP Data Repository
3 RESEARCH REPORTS

8
8
8
11
13
14

3.1 Invited Articles
3.2 First-Principles Calculation of Material Properties
3.3 Strongly Correlated Quantum Systems
3.4 Cooperative Phenomena in Complex Macroscopic
Systems
3.5 SCCMS Projects
3.6 Software Advancement Projects
and Workshop Support
4 PUBLICATION LIST

14
41
171
205
324
341

348

ISSP Joint Research Projects
SCCMS Projects
Doctor Theses
Master Theses

349
394
400
402

v

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

1

OUTLINE

1.1

Supercomputer System

In School year 2021 (SY 2021), the ISSP supercomputer center provided users with
System B - Dell PowerEdge C6525/R940 system named “ohtaka” and System
C - HPE SGI 8600 system named “enaga”. System B is a massively-parallel
supercomputer with two types of compute nodes: 8 “Fat” nodes and 1680 “CPU”
nodes. “Fat” nodes are each comprised of four Intel Xeon Platinum 8280 CPUs
(28 cores/CPU) and 3 TB of memory per node. “CPU” nodes have two AMD
EPYC 7702 CPUs (64 cores/CPU) and 256 GB of memory per node. System B
achieves about 6.881 PFLOPS in theoretical peak performance with high powereﬃciency. The subsystem comprised of only CPU nodes ranks 87st in the Nov.
2020 Top 500 List, which is a ranking based on total performance measured by
the HPL benchmark. The compute nodes communicate to each other throughHDR100 Inﬁniband and are connected in fat tree topology. SY 2021 was the second
year of the operation of the current System B. System C is a massively-parallel
supercomputer with 252 “CPU” nodes, which have two Intel Xeon Gold 6148
CPUs (20 cores/CPU) and 192 GB of memory. System C achieves 774 TFLOPS
in theoretical peak performance. SY 2021 was the last year of the operation of thecurrent System C. For further details, please contact ISSP Supercomputer Center(SCC-ISSP).
[Correspondence: center@issp.u-tokyo.ac.jp]

Figure 1: Supercomputer System at the SCC-ISSP

1

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

1.2

Project Proposals

The ISSP supercomputer system provides computation resources for scientists
working on condensed matter sciences in Japan. All scientiﬁc staﬀ members (including post-docs) at universities or public research institutes in Japan can submit
proposals for projects related to research activities on materials and condensed
matter sciences. These proposals are peer-reviewed by the Advisory Committee
members (see Sec. 1.3), and then the computation resources are allocated basedon the review reports. The leader of an approved project can set up user accounts
for collaborators. Other types of scientists, including graduate students, may also
be added. Proposal submissions, peer-review processes, and user registration are
all managed via a web system.
The computation resources are distributed in a unit called “point”, determined
as a function of available CPU utilization time and consumed disk resources. There
were calls for six classes of research projects in SY 2021. The number of projects
and the total number of points that were applied for and approved in this school
year are listed in Table 1.
• Class A is for trial use by new users; proposals for Class A projects are
accepted throughout the year.
• Proposals for projects in Classes B (small), C (mid-size), E (large-scale), andS (exceptional) can be submitted twice a year. Approved projects in Classes
A, B, C, and E continue to the end of the school year.
• In Class D, projects can be proposed on rapidly-developing studies that needto perform urgent and relatively large calculations. An approved projectcontinues for 6 months from its approval.
• Class S is for projects that are considered extremely important for the ﬁeldof condensed matter physics and requires extremely large-scale computation.
The project may be carried out either by one research group or cooperatively
by several investigators at diﬀerent institutions. A project of this class should
be applied with at least 10,000 points; there is no maximum. We requiregroup leaders applying for Class S to give a presentation on the proposal to
the Steering Committee of the SCC-ISSP. Class S projects are carried out
within one year from its approval.
• Project leaders can apply for points so that the points for each system do
not exceed the maximum point shown in this table.
In addition, from SY 2016, ISSP Supercomputer has been providing 20% of
its computational resources for Supercomputing Consortium for Computational
Materials Science (SCCMS), which aims at advancing parallel computations incondensed matter, molecular, and materials sciences on the 10-PFlops K Computer
and the exascale post-K project. From SY 2020, about 10% of the computational
resources have been provided for SCCMS. Computational resources have also beenallotted to Computational Materials Design (CMD) workshops, as well as CCMS
hands-on workshops.

2Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 1: Classes of research projects in SY 2021. Total points listed in this table
are rounded. In Class D, we collect information about the projects ended in eachsemester. Note that the maximum points of Classes A and D in the ﬁrst semester
had been changed to those listed in the second semester since May 2021.

Class

A
B
C
D
E
S
SCCMS
Total

Class

A
B
C
D
E
S
SCCMS
Total

Maximum
PointsSys–B Sys–C
100
50
800
100
8k
1k
10k
1k
24k
3k
–
–

Maximum
PointsSys–B Sys–C
40
100
800
40
8k
400
10k
400
24k
1.2k
–
–

First semester (Apr.-Sep.)
Application # ofTotal points
Proj.
AppliedApproved
Sys–B Sys–C Sys–B Sys–C
any time
12
1.2k
0.5k
1.2k
0.5k
twice a year
58
40.9k
4.5k
23.2k
3.4k
twice a year
116 725.7k
71.1k 372.6k 50.8k
any time
00000
twice a year
8 187.0k
24.0k 110.0k 17.3k
twice a year
0
0
0
0
0
11
26.1k
5.0k
26.1k
5.0k
205 980.9k 105.1k 533.1k 77.0k

Second semester (Oct.-Mar.)
Application # ofTotal points
Proj.
AppliedApproved
Sys–B Sys–C Sys–B Sys–C
any time
5
0.5k
0.2k
0.5k
0.2k
twice a year
38
27.2k
0.8k
14.7k
0.7k
twice a year
53 327.6k
8.5k 159.8k
6.6k
any time
3
16.0k
0
13.5k
0
twice a year
6 136.0k
7.2k
83.0k
5.5k
twice a year
0
0
0
0
0
11
28.0k
2.4k
28.0k
2.4k
116 535.2k
19.1k 299.5k 15.3k

3Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

1.3

Committees

In order to fairly manage the projects and to smoothly determine the system
operation policies, the Materials Design and Characterization Laboratory (MDCL)of the ISSP has organized the Steering Committee of the MDCL and the Steering
Committee of the SCC-ISSP, under which the Supercomputer Project Advisory
Committee (SPAC) is formed to review proposals. The members of the committees
in SY 2021 were as follows:

Steering Committee of the MDCLKAWASHIMA, Naoki
HIROI, Zenji
OZAKI, Taisuke
NOGUCHI, Hiroshi
UWATOKO, Yoshiya
SUGINO, Osamu
KUBO, Momoji
ONO, Tomoya
YAMAURA, Jun-ichi
TAKAHASHI, Hiroki
MOTOME, Yukitoshi
HOSHI, Takeo
ISHIWATA, Shintaro
HASEGAWA, Masashi
NAKATSUJI, Satoru

ISSP (Chair person)
ISSP
ISSP
ISSP
ISSP
ISSP
Tohoku Univ.
Kobe Univ.
Tokyo Tech.
Nihon Univ.
Univ. of Tokyo
Tottori Univ.
Osaka Univ.
Nagoya Univ.
ISSP

Steering Committee of the SCC-ISSP
KAWASHIMA, Naoki
NOGUCHI, Hiroshi
OZAKI, Taisuke
SUGINO, Osamu
TSUNETSUGU, Hirokazu
KATO, Takeo
YAMASHITA, Minoru
MORITA, Satoshi
HIGUCHI, Yuji
FUKUDA, Masahiro
IDO, Kota
KAWAMURA, Mitsuaki
NAKAJIMA, Kengo
HATANO, Naomichi
MOTOME, Yukitoshi
ONO, Tomoya

ISSP (Chair person)
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
Univ. of Tokyo
Univ. of Tokyo
Univ. of Tokyo
Kobe Univ.

4

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

TODO, Synge
KUBO, Momoji
OBA, Fumiyasu
WATANABE, Hiroshi
YOSHINO, Hajime
OKUMURA, Hisashi
HOSHI, Takeo
YOSHIMI, Kazuyoshi
YATA, Hiroyuki
FUKUDA, Takaki

Univ. of Tokyo
Tohoku Univ.
Tokyo Tech.
Keio Univ.
Osaka Univ.
NINS-RSCS
Tottori Univ.
ISSP
ISSP
ISSP

Supercomputer Project Advisory Committee
KAWASHIMA, Naoki
OZAKI, Taisuke
NOGUCHI, Hiroshi
SUGINO, Osamu
TSUNETSUGU, Hirokazu
YAMASHITA, Minoru
KATO, Takeo
MORITA, Satoshi
HIGUCHI, Yuji
FUKUDA, Masahiro
IDO, Kota
KAWAMURA, Mitsuaki
NAKAJIMA, Kengo
HATANO, Naomichi
MOTOME, Yukitoshi
ONO, Tomoya
TODO, Synge
KUBO, Momoji
OBA, Fumiyasu
WATANABE, Hiroshi
YOSHINO, Hajime
OKUMURA, Hisashi
HOSHI, Takeo
TSUNEYUKI, Shinji
SUZUKI, Takafumi
YOSHIMOTO, Yoshihide
TOHYAMA, Takami
KITAO, Akio
ARITA, Ryotaro
IKUHARA, Yuichi
SHIBATA, Naokazu
AKAGI, Kazuto

ISSP (Chair person)
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
Univ. of Tokyo
Univ. of Tokyo
Univ. of Tokyo
Univ. of Tsukuba
Univ. of Tokyo
Tohoku Univ.
Tokyo Tech.
Keio Univ.
Osaka Univ.
NINS-RSCS
Tottori Univ.
Univ. of Tokyo
Univ. of Hyogo
Univ. of Tokyo
Tokyo Univ. of Sci.
Tokyo Tech.
Univ. of Tokyo
Univ. of Tokyo
Tohoku Univ.
Tohoku Univ.

5

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoYANASE, Yoichi
HATSUGAI, Yasuhiro
OKADA, Susumu
KOBAYASHI, Nobuhiko
NAKAYAMA, Takashi
HOTTA, Takashi
MATSUKAWA, Hiroshi
YAMAUCHI, Jun
HAGITA, Katsumi
KONTANI, Hiroshi
SAITO, Mineo
KAWAKAMI, Norio
YUKAWA, Satoshi
SUGA, Seiichiro
TATENO, Masaru
YASUDA, Chitoshi
OGATA, Masao
WATANABE, Satoshi
HUKUSHIMA, Koji
NEMOTO, Koji
YABANA, Kazuhiro
FURUKAWA, Nobuo
KUROKI, Kazuhiko
YASUOKA, Kenji
TANAKA, Yukio
MASUBUCHI, Yuichi
KUSAKABE, Koichi
SHIRAI, Koun
SAKAI, Toru
ISHIBASHI, ShojiOTANI, Minoru
TOMITA, Yusuke
SHIRAISHI, Kenji
OGUCHI, Tamio
KAWAKATSU, Toshihiro
KOBAYASHI, Kazuaki
TATEYAMA, Yoshitaka
KIM, KangOTSUKI, TomiMORIKAWA, Yoshitada
ODA, Tatsuki
OTSUKI, Junya
KOGA, Akihisa
SHIMOJO, Fuyuki
TAKETSUGU, Tetsuya

Kyoto Univ.
Univ. of Tsukuba
Univ. of Tsukuba
Univ. of Tsukuba
Chiba Univ.
Tokyo Metropolitan Univ.
Aoyama Gakuin Univ.
Keio Univ.
National Defense Academy
Nagoya Univ.
Kanazawa Univ.
Kyoto Univ.
Osaka Univ.
Univ. of Hyogo
Univ. of Hyogo
Univ. of the Ryukyus
Univ. of Tokyo
Univ. of Tokyo
Univ. of Tokyo
Hokkaido Univ.
Univ. of Tsukuba
Aoyama Gakuin Univ.
Osaka Univ.
Keio Univ.
Nagoya Univ.
Nagoya Univ.
Osaka Univ.
Osaka Univ.
Univ. of Hyogo
AIST
AIST
Shibaura Inst. Tech.
Nagoya Univ.
Osaka Univ.
Tohoku Univ.
NIMS
NIMS
Osaka Univ.
Sophia Univ.
Osaka Univ.
Kanazawa Univ.
Okayama Univ.
Tokyo Tech.
Kumamoto Univ.
Hokkaido Univ.

6

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

TSURUTA, Kenji
Okayama Univ.
HAMAGUCHI, Satoshi
Osaka Univ.
NISHIDATE, Kazume
Iwate Univ.
KAGESHIMA, Hiroyuki
Shimane Univ.
ISHII, Fumiyuki
Kanazawa Univ.
TATETSU, Yasutomi
Meio Univ.
YANAGISAWA, Susumu Univ. of the Ryukyus
SHUDO, Ken-ichi
Yokohama Natl. Univ.
OHMURA, Satoshi
Hiroshima Inst. Tech.
NOGUCHI, Yoshifumi
Shizuoka Univ.
NAKAMURA, Kazuma
Kyushu Inst. Tech.
GOHDA, Yoshihiro
Tokyo Tech.
HAMADA, Ikutaro
Osaka Univ.
RAEBIGER, Hannes
Yokohama Natl. Univ.
KAWARABAYASHI, Tohru Toho Univ.
KATO, Yusuke
Univ. of Tokyo
NASU, Joji
Tohoku Univ.
HOTTA, Chisa
Univ. of Tokyo
ISOBE, Masaharu
Nagoya Inst. Tech.
HARADA, Ryuhei
Univ. of Tsukuba
TAMURA, Ryo
NIMS
TANAKA, Shu
Keio Univ.
TADA, Tomofumi
Kyushu Univ.

1.4

Staﬀ

The following staﬀ members of the SCC-ISSP usually administrate the ISSP Supercomputer.
KAWASHIMA, Naoki
NOGUCHI, Hiroshi
OZAKI, Taisuke
SUGINO, Osamu
IDO, Kota
FUKUDA, Masahiro
HIGUCHI, Yuji
KAWAMURA, Mitsuaki
MORITA, Satoshi
YOSHIMI, Kazuyoshi
MOTOYAMA, Yuichi
YATA, Hiroyuki
FUKUDA, Takaki
ARAKI, Shigeyuki

Professor (Chair person)
Associate Professor
Professor
Professor
Research Associate
Research Associate
Research Associate
Research Associate
Research Associate
Project Researcher
Project Researcher
Technical Specialist
Technical Specialist
Project Academic Specialist

7Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

2

STATISTICS (SCHOOL YEAR 2021)

2.1

System and User Statistics

In the following, we present statistics for operation time taken in the period from
April 2021 to March 2022 (SY 2021). In Table 2, we show general statistics of thesupercomputer system in SY 2021. The total numbers of compute nodes in System
B “ohtaka” and System C “enaga” are 1688 and 252, respectively. Consumed disk
points amount to about a few percent of the total consumed points in both System
B and System C.
Table 2: Overall statistics of SY 2021

total service time (×103 node·hours)
number of executed jobs
total consumed points (×103 point)
CPU points (×103 point)
disk points (×103 point)
total exec. time (×103 node·hours)
availability
utilization rate

System B
ohtaka14396
456984
498
480
18
12980
97.34%
90.14%

System C
enaga
1601
46166
30
29
2
1367
96.23%
85.47%In Fig. 2, availabilities, utilization rates, and consumed points in Systems B
and C are plotted for each month. Throughout the school year, the availability
and the utilization rates were very high : the availability and the utilization rates
exceed about 90% and 80% throughout most of the year, respectively.
The user statistics are shown in Fig. 3. The horizontal axis shows the rank of theuser/group arranged in the descending order of the execution time (hour×nodes).
The execution time of the user/group of the ﬁrst rank is the longest. The verticalaxis shows the sum of the execution time up to the rank. From the saturation
points of the graphs, the numbers of “active” users of Systems B and C are around
400 and 100, respectively. The maximum ranks in the graphs correspond to thenumber of the users/groups that submitted at least one job.

2.2

Queue and Job Statistics

Queue structures of Systems B and C in SY2021 are shown in Tables 3 and 4,
respectively. In System B “ohtaka”, users can choose from two types of computenodes; jobs submitted to queues with “cpu” and “fat” at the end of their queue
names are submitted to CPU and Fat nodes, respectively, while only CPU nodes
are available in System C “enaga”. See Sec. 1.1 for a description of each type ofcompute node. The user then has to choose the queue according to the number

8Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 3: Queue structures of System B in SY 2021

queue
name
F1cpu
L1cpu
F4cpu
L4cpu
F16cpuL16cpuF36cpuL36cpuF72cpuL72cpuF144cpu
L144cpu
i8cpu
F2fat
L2fat
i1fat

Elapsed time
limit (hr)
24
120
24
120
24
120
24
120
24
120
24
120
0.5
24
120
0.5

System B, ohtaka# of nodes # of nodes/job/queue
1
600
1
300
2–4
216
2–4
108
5–16
288
5–16
144
17–36
72
17–36
36
72
576
72
288
144
432
144
144
1–8
72
1–2
7
1–2
3
1
1

Memorylimit (GB)230/node
230/node
230/node
230/node
230/node
230/node
230/node
230/node
230/node
230/node
230/node
230/node
230/node
2900/node2900/node2900/nodejob points/(node·day)
1
1
1
1
1
1
1
1
1
1
1
1
1
4
4
4

of nodes to use and the duration of their calculation jobs. Queue names startingwith “F” are for jobs taking 24 hours or less, while those starting with “L” canrun much longer up to 120 hours. More nodes are allotted to “F” queues in orderto maximize the turnaround time of user jobs. The queue names starting with“i” are used for interactive debugging of user programs and the elapsed time limit
is 30 minutes. The number following “F”, “L”, or “i” correspond to the numberof nodes that can be used by one user job. Although we do not mention here indetail, to promote utilization of the massively parallel supercomputer, backgroundqueues (queue name starting with “B”) for Systems B and C which charge nopoints for the jobs have also been open.
To prevent overuse of the storage, points are charged also for usage of disk
quota in the three systems, as shown in Table 5. Disk points are revised often for
optimal usage of the resources by examining usage tendencies each year.
The number of jobs, average waiting time, and total execution time in eachqueue are shown in Tables 6 and 7. In System B, a large portion of jobs havebeen executed in “F” queues. The largest amount of the execution time has been
consumed in the large-scale “F72cpu” queues for ohtaka, respectively. However,substantial number of jobs were run in every queue, suggesting that a wide variety
of user needs are met by this queuing scheme. In most of these queues, the queue
settings meet the user’s tendencies in that the waiting times are on the order ofthe elapsed-time limit.

9

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

System B

System C
Availability, Utilization [%]

100

90
80
Availability
Utilization

70

90
80

60

60

80

8

60
40
20
0
04

05

06

07

08

09 10
Month

11

12

01

02

6
4
2
0
04

03

Availability
Utilization

70

Point consumption[×103 points]

Point consumption[×103 points]

Availability, Utilization [%]

100

05

06

07

08
Month

09

10

11

12

Figure 2: Availabilities, utilization rates and point consumptions of each month
during SY 2021.

System B

System C
1.4

12
1.2
10

8

106 node·hours

106 node·hours

1.0

6

0.8

0.6
4
user exec. timegroup exec. time2

user exec. timegroup exec. time

0.4

0.2
0

100

200
300
400
Rank of user/group

500

600

0

20

40

60
80 100 120
Rank of user/group

140

160

Figure 3: User statistics. The horizontal axis shows the rank of the user/grouparranged in the descending order of the execution time (hour×nodes). The verticalaxis shows the sum of the execution time up to the rank.

10Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 4: Queue structures of System C in SY 2021

queue
name
F4cpu
L4cpu
i4cpu
F9cpu
L9cpu
F36cpuL36cpu∗Elapsed time
limit (hr)
24
120
0.5
24
120
24
120

System C, enaga# of nodes # of nodes/job/queue
1–4
54
1–4
18
1–4
18
5–9
36
5–9
18
10–36
144
10–36
36

Memorylimit (GB)170/node
170/node
170/node
170/node
170/node
170/node
170/node

job points/(node·day)
1
1
1
1
1
18(36)/(# of nodes)∗18(36)/(# of nodes)∗For F/L36cpu queue, the number of occupied node increases in increments of 18 nodes.

Table 5: Disk points of Systems B and C

System B ohtaka
System C enaga

∗
∗

/home
/work
/home
/work

point/day
0.001 × θ(q − 600)
0.0001 × θ(q − 6000)
0.001 × θ(q − 150)
0.0001 × θ(q − 1500)

q is denoted in unit of GB.
θ(x) is equal to the Heaviside step function H(x) multiplied by x, i.e., xH(x).

2.3

Project for Advancement of Software Usability in Materials Science

From School Year 2015, the supercomputer center (SCC) has started “Project
for advancement of software usability in materials science”. In this project, forenhancing the usability of the supercomputer system in ISSP, we perform some
software-advancement activity such as implementing a new function to an existing
code, releasing a private code on Web, writing manuals. Target programs are
publicly oﬀered in December and selected in the review by the Steering Committeeof SCC. The projects are carried out by the software development team composedof three members in ISSP. In SY 2021, three projects were selected as listed inTable 8.

11

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 6: Number of jobs, average waiting time, total execution time, and average
number of used nodes per job in each queue of System B.

queue# of Jobs

F1cpu
L1cpu
F4cpu
L4cpu
F16cpuL16cpuF36cpuL36cpuF72cpuL72cpuF144cpu
L144cpu
i8cpu
F2fat
L2fat
i1fat

211125
10781
73536
5619
21718
1621
1633
87
7773
133
3023
134
91096
3673
282
522

System B, ohtaka
Waiting Time
Exec. Time # of nodes(hour) (×103 node·hour)
16.62
320.551.00
60.45
289.72
1.00
11.69
1175.58
2.87
17.66
400.572.53
15.21
1505.98
10.18
79.48
663.189.93
67.66
315.88
27.74
51.37
93.18
21.63
33.00
3494.1072.00
68.15
373.0472.00
144.0017.02
2062.21141.08677.79144.00
0.09
42.54
3.23
28.21
24.77
1.10
39.31
15.96
1.23
0.50
0.06
1.00

Table 7: Number of jobs, average waiting time, total execution time, and average
number of used nodes per job in each queue of System C.

queue# of Jobs

F4cpu
L4cpu
i4cpu
F9cpu
L9cpu
F36cpuL36cpu

23663
727
7775
1434
77
1551
62

System C, enaga
Waiting Time
Exec. Time # of nodes(hour) (×103 node·hour)
5.24
185.74
1.78
50.21
80.59
1.59
0.05
2.64
2.33
6.11
68.23
7.22
11.94
22.05
6.68
8.13
301.11
29.58
10.02
28.94
20.32

12

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 8: List of Project for advancement of software usability in materials science
for SY 2021.
Project Proposer
Minoru Otani
AIST CD-FMat
Takeo Hoshi
Tottori University

2.4

Project Name
Improvement of Quantum ESPRESSO
implementing the ESM RISM method
Uniﬁed platform of experiment-data analysis
for 2D material structure

ISSP Data Repository

From School Year 2021, the supercomputer center (SCC) has started to operate
ISSP Data Repository (ISSP-DR) for accumulating and utilizing research data inmaterials science. GitLab is used as the data management system, and a portalsite is provided as a data registration and search system for the registered data.
By using ISSP-DR, it is possible to store and publish research data used in papers and datasets useful in the ﬁeld of condensed matter science. Users of ISSP
Supercomputer are welcome to apply for and use ISSP-DR.

Acknowledgments
The staﬀs would like to thank Prof. Takafumi Suzuki (now at University of Hyogo)
for developing WWW-based system (SCM: SuperComputer Management System)
for management of project proposals, peer-review reports by the SPAC committee,
and user accounts. We also thank Ms. Reiko Iwafune for creating and maintaining
a new WWW page of the ISSP Supercomputer Center.

13

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

3
3.1

RESEARCH REPORTS
Invited Articles

Theory, practice, and applicationof the van der Waals density functional

15

Ikutaro HAMADA

Development of permanent magnet materials–from the view point of ﬁrst-principles calculation

24

Hisazumi AKAI and Shinji TSUNEYUKI

Development of Bayesian optimization tooland its applications in materials science
Ryo TAMURA, Yuichi MOTOYAMA, and Kazuyoshi YOSHIMI

14

32

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theory, practice, and application of the van der
Waals density functional
Ikutaro HAMADA
Department of Precision Engineering, Graduate School of Engineering, Osaka University
2-1 Yamadaoka, Suita, Osaka 565-0871, Japan

Abstract
The van der Waals density functional is a classof the density functional, which enables the description of the dispersion forces within theframework of density functional theory. In
this article, theory and practice of the van der
Waals density functional are reviewed, and applicability of a high-accuracy van der Waals
density functional to various systems is demonstrated.

1

Introduction

Density functional theory (DFT) [1, 2] within
the local density (LDA) and semilocal (GGA)
approximations has been proven to be accurate in describing covalent, ionic, and metallic bondings, but has also been known to beunable to describe the dispersion forces (or often referred to as the van der Waals forces)[3] properly. This is because the dispersion
forces originate from the instantaneous dipoleinduced dipole interaction due to the electron
fluctuation or the dynamic and nonlocal electron correlation, which are inherently missingin LDA and GGA. Wave function based theory and many body perturbation theory are
shown to describe the dispersion interaction
very accurately, but the computational cost is
prohibitively large, hindering their application
to complex systems, such as surfaces and interfaces.
There have been several proposals to correct the missing dispersion forces by adding
the term proportional to 1/r6 (and higherorder terms) to the total energy within semilocal DFT, where r is the interatomic or inter-fragment distance. This type of approach was
initiated in the field of the quantum chemistry(QC) [4], and has been established [5] and improved over the years by introducing accurate
dispersion coefficients [6] and damping functions [7], as well as the environmental effects
on the dispersion coefficients through the local
electron density [8, 9] or coordination numbers[6]. Furthermore, accuracy of such pair-wisecorrection methods have been improved by introducing the three-body term[6] or the manybody dispersion[10]. See Refs. [11, 12, 13] forrecent reviews.

The van der Waals density functional (vdWDF) [14, 15, 16, 17, 18] is a versatile methodthat allows one to describe different interactions including the dispersion forces within the
DFT framework. It is grounded on the electron
gas tradition and the many-body perturbation
theory as other constraint-based exchangecorrelation (XC) functionals, and formally has
no empirical or fitting parameters to reproduce
the results of experiments or accurate theoretical calculations. The physical foundation of
vdW-DF has been established [19], and theoretical and algorithmic improvements make ita method of choice in theoretical studies of materials and molecules.

In this article, I give a brief overview of thetheory of vdW-DF and discuss a technical issue related to the use of pseudopotentials withapplications. The Hartree atomic unit is usedthroughout unless otherwise specified.

15

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

2

Method2.1

TheoryThe XC energy, which is responsible for thequantum-mechanical electron-electron interaction, can be expressed exactly by using the adiabatic connection fluctuation dissipation theorem (ACFDT) [20, 21] as
Z 1

dλ
λ

Z ∞

i
du h λtr χ (iu)V λ − Eself ,
2π
0
0
(1)
where λ is the adiabatic parameter, whichscales the electron-electron Coulomb interaction as V λ (r, r′ ) = λ/|r − r′ |, χλ (iu) is the
reducible density-density response function at
the adiabatic parameter λ and imaginary frequency u = −iω, and Eself is the electronelectorn self-energy defined by Eself = tr [nV ]with V = V λ=1
the trace is defined
RR . Here,′as tr[AB] =drdr A(r, r′ )B(r′ , r) for arbitrary operators Â and B̂. χλ (ω) is definedby δn(ω) = χλ (ω)δvext (ω), where δn(ω) andδvext (ω) are the induced electron density andthe external potential at the frequency ω, respectively.
The vdW-DF is constructed based on
ACFDT as follows: Exc may be split as
Exc = −

0
Exc = Exc
+ Ecnl ,(2)0 and E nl are the semilocal exchangewhere Excccorrelation and the nonlocal correlation energyfunctionals, respectively, and in vdW-DF, a
tractable form of Ecnl has been developed basedon several physical constraints.
We first introduce χ̃λ , which is defined byλ (ω) with δV λ (ω) being theδn(ω) = χ̃λ (ω)δVscr
scr
screened potential. χλ (ω) and χ̃λ (ω) are related via the Dyson-like equation χλ = χ̃λ +χ̃λ V λ χλ . Then, the full-potential approximation (FPA) is introduced, which sets χ̃λ =χ̃λ=1 and is exact at the van der Waals asymptote (|r − r′ | → ∞). This enables the analytic
integration over λ and leads to Exc in FPA as
Z ∞io
du n hExc =tr ln 1 − χ̃λ=1 (iu)V− Eself .
2π
0(3)This expression has a formal similarity withthat obtained within the random phase ap-

proximation (RPA):Z ∞
du  
tr ln 1 − χ0 (iu)V − Eself ,
Exc =
2π
0
(4)
0
where χ is the irreducible density-density response function, which is connected to χλ via
a Dyson equation χλ = χ0 + χ0 V λ χλ within
RPA. Exc within FPA can also be expressed
as
Z ∞
du
Exc =
tr {ln [∇ · ε(iu)∇G]} − Eself ,2π
0(5)where ε is the dielectric function and G is the
Coulomb Green’s function, i.e., G = −4πV .
0 is approximated with
To extract Ecnl , Exc
that of homogeneous electron gas within FPA,
which is also called the internal XC energy, as
Z ∞
du
in
Exc =
tr {ln [ε(iu)]} − Eself ,(6)2π0
to obtainZ ∞dunl
tr {ln [∇ · ε(iu)∇G] − ln [ε(iu)]} .
Ec =
2π
0
(7)
nl
It is apparent that by construction, Ec vanishes in the uniform electron-gas limit.
The thus obtained Ecnl is expanded in termsof a response function S = ln ε ≈ 1 − ε−1 upto the second order as
Z ∞o
du n 2nl
Ec =tr S (iu) − [∇S(iu) · ∇G]24π
0(8)and in the plane-wave representation as
Z ∞
Z
Z
 i
du
dq
dq′ h
′ 2
Ecnl =
1
−
q̂
·
q̂
2π
(2π)3
(2π)3
0
× Sq,q′ (iu)Sq′ ,q (iu),(9)
where q̂ = q/|q| andS(ω) = S(r, r′ , ω)ZZdq′ −iq·r
dq
′ ′
=
e
Sq,q′ (ω)eiq ·r
3
3
(2π)
(2π)
(10)
This Ecnl is made tractable by applying
theplasmon-poleapproximation to Sq,q′ (ω), which is expressed as

16

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyoih
Sq,q′ (ω) = 12 S̃q,q′ (ω) + S̃−q,−q′ (ω) andZ
S̃q,q′ (ω) =×with the GGA exchange enhancement factor
for the internal XC functional given by′

dre−i(q−q )·r

ωp (r)
.
[ω + ωq (r)] −ω + ωq′ (r)Fxin (s) = 1 −(11)Here, ωp (r) = 4πn(r) is the plasma frequency,
where n(r) is the electron density, and ωq (r)is the plasmon dispersion. The specific form of
the response function S has been determinedto satisfy the following constraints: (i) thetime-reversal symmetry, (ii) the f -sum rule,(iii) cancellation of the self-energy, and (iv)charge conservation.
By writing the internal XC energy as
Z
in
(12)
Exc
= drϵinxc (r)n(r),the internal XC energy per electron ϵin
xc reads


Z
dq
1
2
ϵin
(r)
=
π
,
(13)
−
xc
(2π)3 ωq (r) q 2
where q = |q| and the second term in theright-hand side is obtained by evaluating theself-energy term explicitly. The local plasmon
dispersion is modeled byωq (r) =q2
2h[q/q0 (r)](14)

with h being the switching function which controls the behavior of the plasmon depending on
the wave vector and q0 (r), an inverse lengthscale which depends on the electron density
and its gradient |∇n(r)|. The functional formof h is determined in such a way that ωq (r) satisfies the small- and large-q cases (see below).
By imposingZ ∞3dy [h(y) − 1] = ,(15)
40
q0 is related to ϵin
xc as
ϵin
xc (r) = −3q0 (r).
4π(16)

In vdW-DF, ϵin
xc is made to be the GGA exchange plus LDA correlation functionals as
in
LDA
ϵin
(r) + ϵLDA,
xc (r) = Fx (s)ϵx
c

(17)

Zab 2
s ,
9

(18)

= −3/4πkF with kF = (3π 2 n)1/3
where ϵLDAxand s = |∇n|/kF n. By this choice, q0 canbe interpreted as kF modulated by the enLDA . In the first version ofergy ratio ϵin
xc /ϵx
vdW-DF (vdW-DF1), Zab = −0.8491 basedon the second-order gradient expansion for the
slowly varying electron gas [22, 23], while inthe second version of vdW-DF (vdW-DF2),
Zab = −1.887 based on the second-order largeN expansion for the neutral atom [17].
The switching function h for the plasmon
dispersion is determined to satisfy Eq. (15) andthe following constraints. (i) h(y) ≈ γy 2 + · · ·in the small-y limit, where γ is an arbitrary
constant to ensure h(0) = 0, which corresponds to the charge conservation of the spherical XC hole model of the internal XC energy.
(ii) h(y) → 1 in the large-y limit, which corresponds to ωq → q 2 /2 in the large q-limit. This
constraint ensures the cancellation of the divergent term of Eself in the q → 0 limit in ϵin
xc .
In Refs. [15, 17], the following form for h wasused
h(y) = 1 − exp(−γy 2 )(19)with γ = 4π/9, implying that the Gaussian
form of the XC hole is used in ϵinxc [19]. Thereis a freedom in the functional form of h and it
is not limited to Eq. (19). Indeed, Berland etal. [24] proposed a functional form, which can
improve the asymptotic behavior (and the socalled C6 coefficient) of vdW-DF . To improve
the accuracy of Ecnl as a part of the development of the third version of vdW-DF (vdWDF3), Chakraborty et al. [25] proposed thefollowing functional form
1h(y) = 1 −.
(20)
2
1 + γy + γ 2 y 4 + αy 8
See Table 1 in Ref. [25] for the parameters γ
and α. Note however, in the development of
vdW-DF3, parameters in the functionals were
optimized to the reference high-accuracy QC
results of a large molecular data set. These
parameters may vary when a plane-wave pseduopotential program is used in the optimization, depending on the pseudopotentials used.

17

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo
2.0

After tedious but straightfoward calculations, one arrives at the following form of thenonlocal correlation functional
ZZ
1
nl
Ec =
drdr′ n(r)ϕ(d, d′ )n(r′ ),
(21)
2

δ=0.0
δ=0.5
δ=0.9

1.0
0.5

2

D φ (arb. unit)

1.5

where d = q0 (r)|r − r′ | and d′ = q0 (r′ )|r − r′ |.
The kernel function is given by
Z ∞
Z ∞
2
′
2
ϕ(d, d ) = 2
dbb2 W (a, b)
daa
π 0
(22)
0
′
′
× T [ν(a), ν(b), ν (a), ν (b)],where
W (a, b) =2 (3 − a2 )b sin a cos b+ (3 − b2 )a cos a sin b
2

2+ (a + b − 3) sin a sin b(23)−3ab cos a cos b]

-0.5
-1.0
0

2

4
D

6

but in practice, it results in less accurate results. By allowing crossover in the exchange
functional and letting
0
in
GGA
Exc
= Exc
+ ∆Ex = Exc+ EcLDA ,(24)

with ν(y) = y 2 /2h(y/d) and ν ′ (y) =y 2 /2h(y/d′ ) (d and d′ are defined above). Calculating the ϕ on the fly is impractical, as thetime-consuming double integral over the variables a and b is included. In practice, ϕ iscalculated and tabulated in advance as a function of D = (d + d′ )/2 and δ = (d − d′ )/(d + d′ )(0 ≤ D < ∞ and 0 ≤ |δ| < 1) and the ϕvalue is calculated on demand by interpolation. This approach works quite well, thankto the fact that ϕ is a smooth function of Dand δ (See Fig. 1). Note that ϕ should berecalculated when different switching function
h is employed, although the shapes of the hfunctions look similar, but y 2 /h(y), which isrelevant to the plasmon dispersion, differs significantly [24, 25].
Remaining task in the development of vdWDF is to determine the semilocal XC funcin as E 0 is the most consistenttional. Using Exc
xc
approach within the framework of vdW-DF,

8

Figure 1: The kernel ϕ times D2 as a functionof D at various δ’s obtained using an in-house
kernel generation code [26].

and


1
1
1
+
T (w, x, y, z) =2 w+x y+z1
×(w + y)(x + z)1+,
(w + z)(y + x)

0.0

(25)

the local correlation energy can be consistentin , and the semilocal exchangewith that of Exc
energy has been investigated.
In vdW-DF for layered materials [14] andgeneral geometry vdW-DF (vdW-DF1) [15],the revised Perdew-Burke-Ernzherof (PBE)[27] exchange (revPBE) of Zhang and Yang[28] was employed because it does not show
spurious binding of rare gas dimers from exchange only. However, it turns out that the
revPBE exchange tends to overestimate thePauli repulsion, leading to a too large separation between the fragments. In searching for more accurate exchange energy functional, Klimeš et al. [29] proposed a set of
exchange functionals, leading to optPBE-vdW
and optB88-vdW, based on the optimization
to the reference QC results. Cooper [30] proposed an exchange functional (C09) which satisfies the following constraint: (i) The gradient expansion approximation (GEA) form inthe slowly varying electron density (small-s)
limit, i.e., Fx (s) = 1 + µs2 with µ = 0.0864[31], which is mainly responsible for the covalent interaction. (ii) The revPBE behavior
in the homogeneous electron density (large-s)
limit which is relevant to the vdW bonding.
Although the µ value is not exactly the sameas that of GEA for the slowly varying electron

18

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Although the precise performance of the
vdW-DF functional depends on the combination of exchange and nonlocal correlation functionals, newly proposed functionals are shown
to be more accurate than the original one,

2.5

2.0
Fx

gas (µGEA = 10/81 [32]), this work demonstrated the importance of GEA in predicting
accurate interaction energies and atomic geometries. Murray et al. [33] showed that theexchange enhancement factor should be proportional to s2/5 in the large-s limit. Theydeveloped the revised PW86 [31] functional(PW86R), which obeys GEA in the small-s
limit and has the s2/5 behavior in the large-s
limit for the exchange enhancement factor, andpaired with a new Ecnl , to propose vdW-DF2[17]. Klimeš et al.[34] developed the optB86b
exchange functional (and optB86b-vdW) in
which the exchange enhancement factor obeys
the gradient expansion approximation (GEA)in the slowly varying density (small-s) limit
with µGEA and has the s2/5 behavior in thelarge s-limit. Berland and Hyldgaard [35] proposed an exchange functional (LV-PW86R),
which is exactly the same as that of the internal exchange-correlation functional in thesmall-s region, while it reproduces the PW86R
behavior in the large-s region. This semilocal exchange functional is the most consistent
with that of the internal XC functional (consistent exchange), and thus the resulting vdWDF functional is named vdW-DF-cx. Hamada[37] proposed an alternative one (B86R) basedon the B86b [36] exchange functional, whose
enhancement factor obeys GEA in the small-s
limit and reproduces the original B86b behavior (proportional to s2/5 ) in the large-s region.
The B86R exchange is paired with Ecnl of vdWDF2 and dubbed rev-vdW-DF2. In the latest
development of vdW-DF (vdW-DF3) [25], B88[38] and B86b [36] forms of the exchange enhancement factors are used. They are bothdesigned to obey GEA in the small-s limit,
and the remaining parameters are optimized to
the reference QC results. The proposed GGA
enhancement factors for vdW-DF are shownin Fig. 2, along with those for Perdew-BurkeErnzerhof (PBE) [27] and PBEsol [39], the latter of which also obeys GEA in the slowlyvarying density limit.

PBE
PBEsolrevPBE
optB88
optB86b
PW86R
LV-PW86R
B86R
C09

1.5

1.0
0

1

2

3

4

5
s

6

7

8

9

10

Figure 2: GGA enhancement factors (Fx ) proposed for various exchange-correlation functionals as a function of reduced density gradient (s).
and are versatile tools for accurate prediction of structures and energetics of materials,
molecules, and interfaces. See Refs. [24, 25,
40, 41, 42, 43] for assessments of the different
vdW-DF functionals on various materials andmolecules.

2.2

Pseudopotentials

In electronic structure calculations, the pseudopotential and projector augmented wave
(PAW) [44] methods are often used, in which(pseudo)potentials generated using certain XC
functionals are used. As a rule of thumb, the
XC functional used to generate pseudopotentials should be consistent with that for the
calculations of materials and molecules, but
this issue has not been discussed in vdWDF calculations. This is presumably because
the appropriate XC functionals for atomic systems have not known nor been discussed forthe vdW-DF calculations. However, it should
not be overlooked, given that the vdW-DF
employs different exchange and nonlocal correlation functionals and is not a simple dispersion correction to a semilocal XC functional. Callsen and Hamada [45] proved that
Ecnl vanishes in an isotropic system and showedthat the XC functional to be used to generate(pseudo)potentials for specific vdW-DF functional is uniquely determined. For instance,
the B86R exchange plus LDA correlation functional should be used to generate potentials

19Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo40

exchange
revPBE
PW86R
optB88
optB86b
C09
LV-PW86R
B86R

correlation
LDA
LDA
LDA
LDA
LDA
LDA
LDA

for the rev-vdW-DF2 calculations of molecular/extended systems. See Table 1 for the exchange and correlation functionals to be usedin the pseudo- and PAW-potential generationfor vdW-DF calculations.

3

Application

In the following, applications of rev-vdW-DF2
to selected systems are presented. Emphasis is put onto the comparison of the results
obtained using (psuedo)potentials generated
with different XC functionals, i.e., the PBE
and the B86R exchange plus LDA correlation(B86Rx+LDAc), the latter of which is compatible with rev-vdW-DF2. All the calculations were based on the PAW method and selfconsistent vdW-DF as implemented [23, 46] inthe Quantum-ESPRESSO [47] code. The
proper extension of vdW-DF to the spin polarized system [48, 49] was adopted when necessary. The PAW potentials were generatedusing the input files supplied in the PSLIBRARY [50].
I first calculated the interaction energies for
the S22 dataset [51], a set of 22 noncovalently bonded molecular duplexes. The calculations were performed at the S22 geometries[51] without any further optimization. Figure 3 depicts the deviations of the binding energies obtained using PBE and B86Rx+LDA
potentials, with respect to the reference results
obtained by the coupled cluster calculations
with singlet, doublet, and perturbative triplet
excitations [CCSD(T)] [52], along with the difference between the deviations obtained using

20

rev-vdW-DF2 (B86Rx+LDAc)
rev-vdW-DF2 (PBE)

0
-20
-40

∆Eb (B86Rx+LDAc) - ∆Eb (PBE) (meV)

vdW-DF functional
vdW-DF1
vdW-DF2
optB88-vdW
optB86b-vdW
vdW-DFC09x
vdW-DF-cx
rev-vdW-DF2∆Eb (meV)

Table 1: vdW-DF functional and corresponding exchange and correlation functionals to be
used in the atomic calculation and pseudo- andPAW-potential generation.

-60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

2.0
1.5
1.0
0.5
0.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
S22 index

Figure 3: Deviations of the binding energies
obtained using rev-vdW-DF2 with different
PAW potentials with respect to the reference
CCSD(T) results (∆Eb , upper panel) and difference between the ∆Eb ’s obtained with different potentials (lower panel).
different potentials. The binding energies obtained with PBE and B86Rx+LDA potentials
are virtually the same (within the difference of
2 meV), and the mean absolute deviations are
20.5 and 20.8 meV for the former and the latter, respectively, validating the use of the PBE
potentials in the vdW-DF calculations.
I then calculated the interlayer binding energy of graphite as a function of interlayer
distance, as shown in Fig. 4. The equilibrium in-plane lattice constant is 2.46 Å, andinterlayer distance and binding energy are
3.33 Å and 59.4 meV/atom, respectively, using both potentials. The interlayer binding
energy is slightly overestimated as comparedwith quantum Monte-Carlo (56±5 meV/atom[53]), ACFDT-RPA (48 meV/atom [54]), andexperiment (52±5 meV/atom [55]) but is inreasonable agreement with them.
I also performed the calculations of a benzene crystal. Figure 5 shows the binding
energy of the benzene crystal in the Pbca
symmetry as a function of the unit cell volume. The calculated equilibrium volume is
460 Å3 with both potentials, and the binding energies are 532 and 531 meV/moleculewith B86Rx+LDAc and PBE potentials, respectively, which are in reasonable agreementwith the most recent experimental estimate of
573±23 meV/molecule [56]. Optimized cellparameters are a = 7.273 Å, b = 9.418 Å,

20

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo
50

30

rev-vdW-DF2 (B86Rx+LDAc)
rev-vdW-DF2 (PBE)
ACFDT-RPA
Expt.

20
0

0
Eb (meV)Eb (meV/atom)

10

rev-vdW-DF2
PBE
ACFDT-RPA

-10
-20
-30

-50

-40
-50
-60
2.0

2.5

3.0

3.5

4.0

4.5

-100

5.0

2

Figure 4: Binding energy of graphite (Eb )as a function of interlayer distance (d) using rev-vdW-DF2 with different potentials,
along with the equilibrium energy and distancefrom ACFDT-RPA (Ref. [54]) and experiment(Ref. [55])and c = 6.723 Å, which are also in reasonable agreement with the experimental valuesof a = 7.36 Å, b = 9.37 Å, and c = 6.70 Å [57].
These results suggest that the effect of using the potentials generated using the PBE
functional is minor in vdW-DF calculations,at least with rev-vdW-DF2, although benchmark calculations on a larger set of materials
and molecules need to be done.
-470
-480

3

4

5

d (Å)

d (Å)

rev-vdW-DF2 (B86Rx+LDAc)
rev-vdW-DF2 (PBE)

Eb (meV/molecule)

-490
-500
-510

Figure 6: Binding energy of graphene onNi(111) (Eb ) as a function of distance fromthe surface (d) using rev-vdW-DF2 and PBE,
along with the ACFDT-RPA results from
Refs. [58, 59].
used but the result obtained using PBE potentials was found to be virtually identical. I also
confirmed that present result is consistent withthe one reported in Ref. [37] but with a different code. Figure. 6 shows the binding energy
as a function of graphene-Ni surface distanceby using PBE and rev-vdW-DF2 functionals(PBE potentials were used for the PBE calculations). It was found that the rev-vdWDF2 slightly overestimates the binding energies, but is able to reproduce the binding energy curve with two local minima obtained using the ACFDT-RPA [58, 59], which is suggested to be a result of competing chemicaland physical interactions. This demonstrates
the accuracy of rev-vdW-DF2 in describing theadsorption system.

-520
-530
-540
440

4
460

480

500
3
V (Å )

520

540

Figure 5: Binding energy of benzene crystal in
the P bca symmetry (Eb ) as a function of unit
cell volume (V ) obtained using rev-vdW-DF2
and different potentials.
Finally, as a critical assessment of rev-vdWDF2, I chose to calculate graphene adsorbedon Ni(111) in the atop-fcc configuration. In
this calculation, B86Rx+LDAc potentials wereSummary

I give a brief review of the theory of vdWDF, present recent theoretical advancements
and some applications based on a variant of
vdW-DF, rev-vdW-DF2. I discuss the properchoice of the XC functional to be used in
the pseudo- and PAW-potential generation for
vdW-DF calculations. It was found that theuse of PBE potentials in rev-vdW-DF2 calculations has a minor impact on the calculated
results, which may assure vdW-DF calculations in the literature. The accuracy of rev-

21

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

vdW-DF2 in describing the adsorption system
is also demonstrated, and it is anticipated thatits applicability is further broadened by introducing a fraction of the unscreened/screened
Fock exchange, i.e., nonempirical hybrid vdWDF [60, 61, 62].

Acknowledgements
The present work has been supported partly
by Grants in Aid for Scientific Researchon Innovative Areas ”Hydrogenomics” (No.
JP18H05519). Numerical calculations were inpart performed using the super computers in
Institute for Solid State Physics (ISSP), theUniversity of Tokyo.

References[1] P. Hohenberg and W. Kohn, Phys. Rev.
136, B864 (1964).
[2] W. Kohn and L. J. Sham, Phys. Rev. 140,
A1133 (1965).

[12] J. Hermann, R. A. DiStasio, and A.
Tkatchenko, Chem. Rev. 117, 4714
(2017).
[13] E. Caldeweyher and J. G. Brandenburg,
J. Phys. Condens. Matter 30, 213001(2018).
[14] H. Rydberg, et al., Phys. Rev. Lett. 91,
126402 (2003).
[15] M. Dion, et al., Phys. Rev. Lett. 92,
246401 (2004).
[16] M. Dion, et al., Phys. Rev. Lett. 95,
109902 (2005)[17] K. Lee, et al., Phys. Rev. B 82, 081101(2010).
[18] K. Berland, et al., Rep. Prog. Phys. 78,
066501 (2015).
[19] P. Hyldgaard, K. Berland and E.
Schröder, Phys. Rev. B 90, 075148 (2014).
[20] O. Gunnarsson and B. I. Lundqvist, Phys.
Rev. B 13, 4274 (1976).

[3] F. London, Z. Physik 63, 245 (1930).
[4] J. Hepburn, G. Scoles, and R. Penco,Chem. Phys. Lett. 36, 451 (1975).
[5] S. Grimme, J. Comput. Chem. 27, 1787
(2006).
[6] S. Grimme, J. Antony, S. Ehrlich, and
H. Krieg, J. Chem. Phys. 132, 154104(2010).
[7] A. D. Becke and E. R. Johnson, J. Chem.
Phys. 123, 154101 (2005).
[8] A. Tkatchenko and M. Scheffler, Phys.
Rev. Lett. 102, 073005 (2009).
[9] T. Sato and H. Nakai, J. Chem. Phys.
131, 224104 (2009).
[10] A. Tkatchenko, R. A. DiStasio, R. Car,and M. Scheffler, Phys. Rev. Lett. 108,236402 (2012).
[11] S. Grimme, A. Hansen, J. G. Brandenburg, and C. Bannwarth, Chem. Rev.
116, 5105 (2016).

[21] D. C. Langreth and J. P. Perdew, Phys.
Rev. B 15, 2884 (1977).
[22] D. C. Langreth and S. Vosko, Adv. Quantum Chem. 21, 175 (1990).
[23] T. Thonhauser, et al., Phys. Rev. B 76,
125112 (2007).
[24] K. Berland, D. Chakraborty, and T.
Thonhauser, Phys. Rev. B 99, 195418(2019).
[25] D. Chakraborty, K. Berland, and T.
Thonhauser, J. Chem. Theory Comput.
16, 5893 (2020).
[26] I. Hamada, vdwphi drsll:
A codeto calculate the kernel function of
the van der waals density functional,
https://github.com/ikuhamada/vdwphi drsll.
[27] J. P. Perdew, K. Burke, and M. Ernzerhof,
Phys. Rev. Lett. 77, 3865 (1996).
[28] Y. Zhang and W. Yang, Phys. Rev. Lett.
80, 890 (1998).

22

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo[29] J. Klimeš, D. R. Bowler, and A.
Michaelides, J. Phys. Condens. Matter
22, 022201 (2009).
[30] V. R. Cooper, Phys. Rev. B 81, 161104(2010).
[31] J. P. Perdew and W. Yue, Phys. Rev. B
33, 8800 (1986).
[32] P. R. Antoniewicz and L. Kleinman, Phys.
Rev. B 31, 6779 (1985).
[33] É. D. Murray, K. Lee, and D. C. Langreth,J. Chem. Theory Comput. 5, 2754 (2009).
[34] J. Klimeš, D. R. Bowler, and A.
Michaelides, Phys. Rev. B 83, 195131(2011).
[35] K. Berland and P. Hyldgaard, Phys. Rev.
B 89, 035412 (2014).
[36] A. D. Becke, J. Chem. Phys. 85, 7184
(1986).
[37] I. Hamada, Phys. Rev. B 89, 121103(2014).
[38] A. D. Becke, Phys. Rev. A 38, 3098
(1988).

[46] R. Sabatini et al. J. Phys. Condens. Matter 24, 424209 (2012).
[47] P. Giannozzi, et al. J. Phys. Condens.
Matter 21, 395502 (2009).
[48] T. Thonhauser, et al., Phys. Rev. Lett.
115, 136402 (2015).
[49] C. M. Frostenson, et al., Electron. Struct.
4, 014001 (2022).
[50] A. Dal Corso, Comput. Mater. Sci. 95,
337 (2014).
[51] P. Jurečka, J. Sp̌oner, J. Cěrný, and P.
Hobza, Phys. Chem. Chem. Phys. 8, 1985
(2006).
[52] T. Takatani, et al., J. Chem. Phys. 132,
144104 (2010).
[53] L. Spanu, S. Sorella, and G. Galli, Phys.
Rev. Lett. 103, 196401 (2009).
[54] S. Lebégue, et al., Phys. Rev. Lett. 105,
196401 (2010).
[55] R. Zacharia, H. Ulbricht, and T. Hertel,
Phys. Rev. B 69, 155406 (2004).
[56] J. Yang, et al., Science 345, 640 (2014).

[39] J. P. Perdew, et al., Phys. Rev. Lett. 100,
136406 (2008).

[57] W. David, R. Ibberson, G. Jeffrey, and J.
Ruble, Physica B 180-181, 597 (1992).

[40] T. Björkman, J. Chem. Phys. 141, 074708(2014).

[58] F. Mittendorfer, et al., Phys. Rev. B 84,
201401 (2011).

[41] T. Rangel, et al., Phys. Rev. B 93, 115206(2016).

[59] T. Olsen and K. S. Thygesen, Phys. Rev.
B 87, 075111 (2013).

[42] F. Tran, et al., Phys. Rev. Materials 3,063602 (2019).

[60] Y. Jiao, E. Schröder, and P. Hyldgaard,
J. Chem. Phys. 148, 194115 (2018).

[43] S. Yanagisawa and I. Hamada in Theoretical Chemistry for Advanced Nanomaterials: Functional Analysis by Computation and Experiment, edited by T. Onishi(Springer Singapore, Singapore, 2020).

[61] V. Shukla, Y. Jiao, C. M. Frostenson, P.
Hyldgaard, J. Phys. Condens. Matter 34,
025902 (2022).
[62] V. Shukla et al., arXiv:2203.06682.

[44] P. E. Blöchl, Phys. Rev. B 50, 17953(1994).
[45] M. Callsen and I. Hamada, Phys. Rev. B
91, 195103 (2015).

23

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of permanent magnet materials—from the view
point of ﬁrst-principles calculation
Hisazumi AKAI1 and Shinji TSUNEYUKI2
1 The Institute for Solid State Physics, The University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581, Japan
2 Graduate School of Science, The University of Tokyo
Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

Abstract
Theoretical approaches investigating the intrinsic
properties of permanent magnet materials are reviewed. Three topics, namely, possible maximum performance of magnetic materials, highthroughput calculation surveying candidates forthe high-performance magnetic materials, and theﬁnite temperature magnetic properties, are discussed. Emphasis is put on the importance of large
scale ﬁrst-principles as well as high-throughput calculations.

1

Introduction

The properties featuring high-performance permanent magnets such as Nd2 Fe14 B originate from
subtle combination of micro, macro and metallographic structures. This means that intrinsic
properties of permanent magnet materials are notdirectly reﬂected to the properties of permanent
magnets. On the other hand, it is also true that theperformance of a permanent magnet as a whole isseverely limited by the intrinsic properties of constituent materials. For example, the upper bound of
coercivity is the magnetocrystalline anisotropy—
reality is that it is usually only 20∼30% of thelatter. Among those intrinsic properties, important ones are, in addition to the magnetocrystalline
anisotropy, the magnetic moment and Curie temperature. The higher the values, the better the
performance expected. The importance of ﬁrst-

principle calculation arises here: although predicting the properties of permanent magnets is very
diﬃcult task, it would be still possible to predict
better materials for permanent magnets on the basisof ﬁrst-principles calculation. Also, the approachis powerful to analyze the mechanism inherent tocertain speciﬁc electronic and magnetic properties.
In the past decade, many works based on ﬁrstprinciples calculation have been done from theabove point of view [1]. There are two aspects
existing in those works: the ﬁrst one is the accumulation of results of ﬁrst-principles calculations
and their analyses. The second is the developmentof methodology that enables us to perform such attempts. In this paper, we will present some of ourresults as examples of the former, putting emphasis
upon the importance of the latter.
We ﬁrst will discuss the possible maximum performance of permanent magnet on the basis of theﬁrst principles calculation [2]. In spite of the intensive eﬀorts, no essentially novel magnet showing better performance than Nd2 Fe14 B magnet has
been so far invented. Then, one might question if
there exists any permanent magnet materials at allsuperior to the already known ones. Or, might it bebetter to proceed to other directions such as pursuing magnets less expensive but with reasonable performance, and hence, replacing ferrite magnets? In
answering this, we will show that there exists a possible maximum performance that we can expect forpermanent magnets. Fortunately, this maximum
has not be reached by currently used permanent24Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

magnet materials and it is worthwhile seeking further possibilities.
One of ways to seek such possibilities may be
performing ﬁrst-principles calculation over a wide
range of composition space of magnetic materials. Since most of those materials contain morethan several elements, in many cases as solid solutions, the procedure inevitably becomes a highdimensional search requiring high-throughput calculations. A machinery based on the Korringa–
Kohn–Rostoker Green’s function method combined with the coherent potential approximation(KKR-CPA) is quite eﬃcient for this purpose [3] .
For the high throughput calculations, it is desirable to perform calculations for many systems with
diﬀerent compositions in parallel. We have devised
such a system, called HOFMAN, which realizes
this procedure for KKR-CPA eﬃciently and havebeen applied to various systems. Some examples
will be given in a later section.
The problem arising in ﬁrst-principles calculations of rare-earth permanent magnets is a treatment of 𝑓 -states playing a main role in provoking the magnetocrystalline anisotropy. In the local
density approximation (LDA), or the generalized
gradient approximation (GGA), the strongly localized 𝑓 -states cannot be treated properly. So far, noreal solution for this problem exists. As a compromise, one may use the exact-exchange [4] insteadof the LDA/GGA exchange. Since the 𝑓 -statesin rare-earth elements are suﬃciently localized,
the exchange energy for 𝑓 -states may be replacedwith that of local 𝑓 -orbitals. This can be simply done by subtracting self-interaction from theHartree energy—self-interaction correction (SIC)[5]—because the exchange in the present case ismostly the self-exchange.
The permanent magnets in electric vehicles andwind turbines are used mostly at temperatures 100∼200◦ higher than the room temperature. Therefore,
the importance is on the performance at rather hightemperatures. Although ﬁnite temperature magnetic properties of materials is out of the scopeof Kohn–Sham scheme, we can still access thisproblem through perturbative ways. Namely, we

can estimate the eﬀects of low lying excitation by
constructing a low energy eﬀective Hamiltonian
through DFT as a problem of the ground state ofconstrained systems [6]. The results of such calculations give rise to a set of parameters for the effective Hamiltonian, from which we can obtain theﬁnite temperature electronic and magnetic properties.
There are several kinds of excitations that haveto be taken into account when discussing ﬁnite
temperature magnetic properties of magnetic materials. Among them are phonons and magnons[7, 8, 9]. Usually, single electron excitations at
the Fermi surfaces do not contribute signiﬁcantly
to the magnetic properties at the temperature range
below the Curie temperature. In the following we
neglect such excitations. The treatment of phonons
is the following: We apply a static approximation
for phonons and treat them as external ﬁeld acting on electrons. This problem can be treated in
the framework of DFT. The statistical average canbe taken, in principle, by performing a functional
integral with suitable probability weights. However, this being practically impossible, we further
introduce an approximation to make it tractable.
We employ a single-site approximation, where thefunctional integral is reduced to a conﬁguration
average using CPA. In this scheme, the eﬀects ofphonons are nothing but those of random displacements of atoms around their equilibrium positions.
The average displacements are estimated from either the Debye model or ﬁrst-principles phonon calculations: no noticeaable diﬀerence between them
was found.
The treatment of magnons is somewhat subtle
because the motion of the magnetic moments has tobe separated from the electron degrees of freedom.
We rely on the fact that the time scale of local spin
ﬂuctuations is much slower than that of remaining dynamics. Then we can expand the magnetic
energy into the local spin ﬂuctuations as∬
1
𝐸 mag [𝑺(𝒓)] = −𝑑 𝒓𝑑 𝒓 ′2
𝑺(𝒓) 𝜒(𝒓) −1 𝜒(𝒓, 𝒓 ′) 𝜒(𝒓 ′) −1 𝑺(𝒓 ′), (1)where 𝑺(𝒓) is the spin density, 𝜒(𝒓) and 𝜒(𝒓, 𝒓 ′)25

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

are the local and non-local susceptibilities, respectively. Such an expansion can be performed in
the framework of constrained DFT as long as theabove separation of degrees of freedom and thestatic approximation are employed. This provides
us with a low energy eﬀective Hamiltonian of thesystem, as is already mentioned. If the longitudinal
ﬂuctuations neglected, it is nothing but the Heisenberg Hamiltonian. Now, we can take the same
approach as used for phonons: instead of random
displacement of atoms, random ﬂipping of the local magnetic moments with probability determined
self-consistently at each temperature is consideredwithin KKR-CPA.
We have studied the eﬀects of phonons andmagnons on ﬁnite temperature magnetism, targeting at permanent magnet materials.
We discuss the possible maximum performanceof permanent magnets in Sec. 2. Several examples of high-throughput calculation are presented
in Sec. 3. Section 4 is devoted for the ﬁnite temperature properties of magnetic materials under the
existences of phonons and magnons. We summarize in Sec. 5.

2against the lattice constant 𝑎 and atomic number
𝑍. The crystal structure is ﬁxed to bcc. Here,the fractional atomic number of a ﬁctitious atom
is used: 𝑍 = 25, 26, and 27 corresponds to Mn,
Fe, and Co atoms, respectively. Whereas 𝑀 is adecreasing function of 𝑍 for a large lattice constant(𝑎 ∼ 3.2 Å), it shows a usual Slater-Pauling type behavior [11] for a lattice constant of bcc Fe (2.867 Å
at room temperature): it takes the maximum valueof 2.35 𝜇B /atom at 𝑍 = 26.2 and decreases to bothsides. The peak position shifts towards larger 𝑍
with decreasing lattice constant. Meanwhile, thepeak height decreases rapidly. These behaviors
are the results of the facts: (1) the position where
the transition from strong to weak ferromagnetism
takes place is shifted, and (2) the position where theinstability of ferromagnetism against volume collapse takes place is shifted, both occurring whenatomic number decreases.

Maximum performance of permanent magnet materials

We assume that 3𝑑 magnetic ions are the main origin of magnetic polarization (magnetization). On
the other hand, 4 𝑓 ions are of main concern forthe magnetic anisotropy energy (MAE) although
3𝑑–5𝑑 transition metal ions partly contribute to it,in particular, at high temperature. For this reason,
we will discuss MAE in a somewhat diﬀerent way
than we do for the magnetic polarization 𝐽S andCurie temperature 𝑇C . The discussions are basedon all-electron ﬁrst-principles electronic structure
calculations performed within the framework of thelocal density approximation (LDA/GGA) of density functional theory (DFT). We used a KKR-CPA
package (AkaiKKR) [3], and for the calculation of
𝑇C , Liechtenstein’s method [10] was exploited.
Figure 1 shows the overall behavior of magnetic
moment 𝑀 (𝑎, 𝑍) per atom of 3𝑑 elements plotted

Figure 1: Magnetic moment per atom 𝑀 against
the lattice constant 𝑎(Å) and the atomic number 𝑍
of a ﬁctitious atom
The behavior of saturation magnetic polarization 𝐽S shown in Fig. 2 does not obey that of themagnetic moment. The most prominent feature isthat it has a dome-like structure appearing around𝑎 = 2.65 Å and 𝑧=26.4, where 𝐽S takes the maximum value of 2.66 T. Such a feature is not seen in
𝑀. We point out, not going into details, that this isrelated to the fact that in the bcc structure, the interatomic distance between nearest neighbor pairs
is rather small, forming a considerable bonding–26

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

antibonding splitting and the associated pseudogap. Unfortunately, the lattice constant 𝑎 = 2.65 Å
is 7 % too small compared with the equilibrium
lattice constant of bcc Fe. It should be noticed that,
contrary to the behavior of the magnetic moment,
the magnetic polarization increases with decreasing 𝑎 up to the point where the magnetic state starts
to rapidly collapse.

Figure 2: Saturation magnetic polarization 𝐽S ofthe system against the lattice constant 𝑎 (Å) andthe atomic number 𝑍 of a fictitious atom. The
ferromagnetic state is unstable in the region to theleft of the dashed line.
Magnetic polarization takes on a large value at
one of the corner points in the 𝑍-𝑎 plane, 𝑍 = 25
and 𝑎 = 3.2 Å, but this is not real. The truthis that in a broad region of the 𝑍-𝑎 plane—the
region to the left of the dashed line in Fig. 2—
the ferromagnetic state is unstable as will be seen
below. If we combine this fact with the information
given by Fig. 2, we may conclude that a large 𝐽S
is expected only in the vicinity of the dome-likestructure seen in Fig. 2, and the upper limit of 𝐽S
would not exceed ∼ 2.7 T.
Figure 3 shows the overall behavior of magnetictransition temperature 𝑇C . Here, we again see adome-like structure near 𝑍 = 26.5 and 𝑎 = 2.9 Å.
This position approximately coincides with the position of the similar dome-like structure in 𝐽S . This
indicates that if 𝑍 = 26.5 and 𝑎 = 2.9 Å is forcedby some means (crystal structure, chemical composition, pressure, temperature, etc.), 𝐽S ∼ 2.7 T

is achieved. 𝑇C drops rapidly toward the corner in
the 𝑍-𝑎 plane, 𝑍 = 25 and 𝑎 = 3.2 Å, where 𝑇C
becomes negative, meaning that the antiferromagnetic state should be the ground state. Although theregion of stable ferromagnetism does not appear to
be extensive, there is hope in the fact that, in mostof the region where the ferromagnetism is stable,
𝑇C is well above 1000 K, which is much higher
than the usual working temperature range. Now,
we may say that the upper limit of 𝑇C is ∼ 2000
K (if fcc structure were assumed, the upper limit
would be ∼ 1500 K).

Figure 3: Magnetic transition temperature 𝑇C
against the lattice constant 𝑎 (Å) and atomic number 𝑍 of a fictitious atom. The negative value of
𝑇C means that the antiferromagnetic state is morestable than the ferromagnetic state.
There are two origins of MAE: one is spin
orbit coupling and the other is magnetic shapeanisotropy. The magnetic shape anisotropy iscaused by the dipole interactions between two magnetic moments. In the case of rare earths, the former is the main origin of MAE and is well describedwithin each 𝐿𝑆 multiplet by the effective Hamiltonian given by 𝐻so = 𝜆𝑳 · 𝑺, where 𝜆 = ±𝜁/𝑛 is the
spin-orbit coupling constant for the ground state
𝐿𝑆 multiplet. The plus sign is for the less-thanhalf-filled 𝑓 shell and vice versa; 𝜁 is the single
electron spin-orbit coupling constant, 𝑛 the number of unpaired electrons. For the 3𝑑–5𝑑 cases,
we use the single electron spin-orbit interactions
given by 𝐻so = 𝑖 𝜁𝑖 ℓ 𝑖 · 𝒔𝑖 , where the sum is over27

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo     

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all electrons. Table 1 shows the values of the spinorbit coupling constant 𝜁 for some representative
elements.
Assuming that the orbitals are ﬁrmly boundto the lattice, the upper limit of the magnetic
anisotropy constant 𝐾1 for Sm (Sm3+ in Sm-type
Sm element) estimated from the value of 𝜁, together
with the values of ⟨𝐿⟩, is as large as ∼ 1000 MJm−3 .
The upper limit of 𝐾1 for other lanthanides, if scaledby the value of 𝐿, also would be similar to the Sm
case. This value obtained under the assumptionthat the 4 𝑓 orbitals are ﬁrmly bound to the lattice,
however, seems too large: one order of magnitude
smaller, i.e., ∼100 MJm−3 would be realistic.



Table 1: Absolute values of the single electron
spin-orbit coupling 𝜁 (eV) of element materials Fe,
Sm, and Pt. 𝜁 at the Fermi energy are given.



f
0.001
0.163
0.001

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d
0.068
0.218
0.762

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p
0.231
1.36
2.72

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Fe
Sm
Pt

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8.18
10.0
44.2

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𝜁 (eV)

scheme is not implemented in the present version of
KKR-CPA—full-potential KKR-CPA codes (FPKKR) exist but they do not suit the high-throughput
calculation because of the heavy computational demands. On the other hand, the pseudo-potential
codes can calculate the ordered system quite eﬃciently although their accuracy has to be checkedfrom time to time through comparisons with theresults obtained by other reliable method such as
FPKKR and FLAPW. Considering the above, oneof the practical ways to do is to combine KKR-CPA
and pseudo-potential codes: use pseudo-potential
codes for the end points, i.e., ordered alloys, ofcomposition space and use KKR-CPA to interpolate whole the region of composition space. A
computational system HOFMAN constructed under such a strategy is now running.



3



High-throughput calculation

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The purpose of high-throughput calculation in thepresent context is to generate data of intrinsic
properties of magnetic materials spreading overmulti-dimensional composition space. This enable us to construct permanent magnet materials
databases that might be used to ﬁnd new candidates of high-performance permanent magnet
materials. Given a structure and a set of components, e.g., Sm(Fe1−𝑥 Co 𝑥 )12 (N1−𝑦 S 𝑦 ), we typically need calculations for 100∼1000 diﬀerent systems. Since these systems are compositionally disordered, usual band structure calculation is not sensible. An eﬃcient way to manage this problem is
to use the KKR-CPA method [3] , which can takea conﬁgurational average of disordered systems
rather accurately. Unfortunately, the full-potential








       

Figure 4: Magnetic polarization (T) (top) and 𝑇C(K) (bottom) of Sm(Fe1−𝑥 Co 𝑥 )12 (N1−𝑦 S 𝑦 ).
An example of the usage of HOFMAN system is seen in Fig. 4, where a new alloy system

28

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Sm(Fe1−𝑥 Co 𝑥 )12 (N1−𝑦 S 𝑦 ) is examined. The results show that the Curie temperature rises by replacing Fe with Co by ∼40% whereas it decreases
the magnetic polarization. On the other hand, replacing N with S turned out not to be promising as
for the magnetic properties.
1.0

Co concentration x

0.8

0.7
Sm2(Fe1-xCox)17Ny
JS (T)

0.75
0.8

4

0.85
0.9

0.6

0.95
1.05
1.1
1.15
1.2

0.0
0.0

0.5

1.0
1.5
2.0
N contents y

2.5

3.0

1320

1300

1.0

0.8

0.6

0.4

0.2

0.0

Sm2(Fe1-xCox)17Ny
TC(K)01282601 0124
1220
120080111160 1140
1120
1100
1060 1080
1040

0.0
1.0

0.5

10
00 10
20

Co concentration x

Finite temperature properties ofpermanent magnet materials

1
0.4

0.2

1.0
1.5
2.0
N contents y

2.5

3.0

Sm2(Fe1-xCox)17Ny
3

K1 (MJ/m )

6
7.5

-3

0.4

4.5

3

0

0.6

1.5

-1.5

0.8
Co concentration x

where the content of N 𝑦 takes 0 ≤ 𝑦 ≤ 3 (Fig.
5). Here the magnetic anisotropy constant 𝐾1 wasalso calculated. In this case, 𝑇C monotonicallyincreases as the concentration of Co increases. Although the addition of N lowers 𝑇C , it enhances
the uniaxial magnetic anisotropy 𝐾1 . This fact was
already known for Sm2 Fe17 N 𝑦 but addition of Co
further enhances this tendency is a new ﬁnding.

10 9
.5

0.2

0.0
0.0

0.5

1.0
1.5
2.0
N contents y

2.5

3.0

Figure 5: Magnetic polarization (T) (top) and𝑇C (K) (middle), and 𝐾1 (MJ/m3 ) (bottom) of
Sm(Fe1−𝑥 Co 𝑥 )12 N 𝑦 .
Another example is for Sm2 (Fe1−𝑥 Co 𝑥 )17 N 𝑦 ,There are many cases that there exist experimental
data of magnetic polarization 𝐽S at several diﬀerent
temperatures around the room temperature. What
we would like to do is to estimate the temperaturedependence of 𝐽S in whole the range of temperature below 𝑇𝐶 from these rather restricted data.
One of the ways to do this is the following: First,
the Curie temperatures, which are not necessarily known experimentally, are estimated by ﬁtting
the temperature dependence of magnetic moment
by Kuz’min’s empirical formula [12]. Meanwhile,the theoretical Curie temperature and 0K magnetic
moment are obtained by ﬁrst-principles calculation
using KKR-CPA. Then theoretical temperature dependence of magnetization is obtained again using
Kuz’min’s formula. Finally, the temperatures are
scaled using experimentally estimated Curie temperatures. Examples of such estimation of temperature dependence of 𝐽S are depicted in Fig. 6 for
SmFe12 family with several diﬀerent compositions.
The theoretical estimations reasonably ﬁt the experimental data and also provide the extrapolation to
the whole range of temperature.
Before entering the discussion of the temperature dependence of magnetic properties including the eﬀects of phonons and magnons,
it might be useful to see the eﬀects ofmagnon excitations to the Curie temperature.
Sucheﬀects comes in through the parameters∬𝑑 𝒓𝑑 𝒓 ′ 𝑺(𝒓) 𝜒(𝒓) −1 𝜒(𝒓, 𝒓 ′) 𝜒(𝒓 ′) −1 𝑺(𝒓 ′) = 𝐽𝑖 𝑗
in eq. (1). Here the integral are performed withineach atomic cell surrounding 𝑖-th or 𝑗-th atom.
There are two limiting cases in the calculations of29

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo
Calc.
Calc. lmd
Expt.

R2Fe14B
1000
TC (K)𝐽𝑖 𝑗 : one is the calculation at the ground state andanother is the calculation above 𝑇C where the directions of local moments align randomly without any
short-range order. Which is more realistic depends
on the characteristic of the spin-ﬂuctuations. The
former is realistic for the system where the local
ﬂuctuation of the magnetic moments does not playa role. The latter is suitable for the opposite cases.

500

0

La

Ce

th]

Pr

Nd Sm Gd Tb Dy Ho Er
Rare-earth elements

Tm Yb

Lu

Y

Figure 7: Calculated 𝑇C of 𝑅2 Fe14 B compared withexperiments.

2.0(R1-xZrx)(Fe0.75Co0.25)11+yTi1-y

1.5

1000

1.0
SmFe11Ti
Sm(Fe0.75Co0.25)11Ti
Sm(Fe0.75Co0.25)11.5Ti0.5(Sm0.8Zr0.2)(Fe0.75Co0.25)11.5Ti0.5
Nd2Fe14B
SmFe11Ti
Sm(Fe0.75Co0.25)11Ti
Sm(Fe0.75Co0.25)11.5Ti0.5(Sm0.8Zr0.2)(Fe0.75Co0.25)11.5Ti0.5
Nd2Fe14B

0.5

0.0

Calc.
Calc. lmd
Expt.

0

200

400
600
Temperature (K)TC (K)JS (T)

R2Co14B

500

0

800

1000

th]

La

Pr Nd Sm Gd Tb
Rare-earth elements

Y

Figure 8: Calculated 𝑇C of 𝑅2 Co14 B compared withexperiments.
Figure 6: Temperature dependence of magnetization of various systems of SmFe12 family.
Figures 7 and 8 show the results of calculation of
𝑇C of 𝑅2 (Fe,Co)14 B (𝑅 = La, Ce,. . . , Lu, Y). The
results under the above two options are comparedwith the experiments. For the Fe based cases, thecalculation assuming that the local ﬂuctuation isdominant (red) gives good agreement with the experiments (blue) whereas the assumption that thelong range ﬂuctuation determined 𝑇C (green) seems
very reasonable for Co cases.
The above discussion is only for 𝑇C withmagnons excitations. For the ﬁnite temperature
properties below 𝑇C and also with not only magnons
but also phonons need more elaobrate treatment as
mentioned in Sec. 1.
Table 2: Calculated 𝑇C of Nd2 Fe14 B
phonons only plus magnons
0K
500K

1062K
1198K

561K
548K

It was fond that, in the case of bcc Fe, there is asigniﬁcant eﬀect of electron–phonon scattering on
the Curie temperature 𝑇C , while that of magnons is
not prominent (not shown). On the other hand, theeﬀect of magnons, becomes remarkable in the caseof Nd2 Fe14 B permanent magnet materials. Some
examples of calculated 𝑇C of Nd2 Fe14 B are given
in Table 2. The ﬁrst column indicates the temperature in which the average displacement due tophonons is calculated. The experimental value of
𝑇C is 585K.
Figure 9 shows the calculated magnetic polarization of Nd2 Fe14 B. Both the eﬀects of phononsand magnons are included. The theoretical curveshows a weak ﬁrst-order transition at the magnetictransition temperature, which occurs as a resultof electron–phonon coupling. The temperature isscaled so that 𝑇C reproduces the experimental valueof 585K although the scaling factor is close to 1.
The calculated results are fairly consistent with experiments, is concluded.

30

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References40

M (T) (µB/f.u.)

Nd2Fe14B M(T)30

[1] See, e.g., T. Miyake, Y. Harashima,
T. Fukazawaa, and H. Akai, Sci. Tech. Adv.
Mater.Sci. Tech. Adv. Mater. 22, 543 (2021)

20
thoeryexperiment
Kuz'min

10

0

0

100

200

[2] H. Akai, Scr. Mater. 154, 300 (2018).
300

400

500

600

[3] H. Akai, AkaiKKR,
http://kkr.issp.u-tokyo.ac.jp/(2002).

Temperature (K)Figure 9: Calculated and experimental magnetic
polarization vs. temperature of Nd2 Fe14 B[4] T. Kotani, Phys. Rev. B 50, 14816 (1994).

5[5] A. Filippetti, C.D. Pemmaraju, S. Sanvito,
P. Delugas, D. Puggioni, and V. Fiorentini,
Phys. Rev. B 84, 195127 (2011) andreferences therein.

Summary

We discuss the theoretical approached to investigate the intrinsic properties of permanent magnet materials, focusing on three subjects: possible maximum performance of magnetic materials,
high-throughput calculation to survey the candidate of the high-performance magnetic materials
in multi-dimensional composition space, and the ﬁnite temperature magnetic properties. Admittedly,
we have not yet succeeded in inventing any new
permanent magnet materials that realize the performance exceeding that of Nd2 Fe14 B, the best permanent magnet materials so far known. However, we
put emphasis on the fact that the remaining composition space not yet searched is immensely large
and we still have much chance to get a leap. For
this, large scale ﬁrst-principle calculation such as
reviewed here is one of most powerful approaches.
In addition, it is clear that schemes fully equippedwith machine learning technique provide us witha complementary approach for the development of
new permanent magnet materials[6] P.H. Dederichs, S. Blügel, R. Zeller, and
H. Akai, Phys. Rev. Lett. 53, 2512 (1984).
[7] N. H. Long, M. Ogura, and H. Akai, Phys.
Rev. B 85, 224437 (2012).
[8] S. Kou and H. Akai, Solid State Commun.
296, 1 (2018).
[9] H. Shinya, S. Kou, T. Fukushima,
A. Masago, K. Sato, H. Katayama-Yoshida,and H. Akai, Appl. Phys. Lett. 117, 042402(2020).
[10] A. I. Liechtenstein, M. Katsnelson,
V. Antropov, V. Gubanov, J. Magn. Magn.
Mater. 67, 65 (1987).
[11] P.H. Dederichs, R. Zeller, H. Akai, andH. Ebert J. Magn. Magn. Mater. 100, 241(1991).
[12] M. D. Kuz’min, Phys. Rev. Lett. 94, 107204(2005).

31

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of Bayesian optimization tool and its
applications in materials science
Ryo Tamuraa,b , Yuichi Motoyamac , and Kazuyoshi YoshimicaInternational Center for Materials Nanoarchitectonics (WPI-MANA)
National Institute for Materials Science
1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japanb
Graduate School of Frontier Sciences, The University of Tokyo
5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561, Japanc
Institute for Solid State Physics, University of Tokyo, Chiba 277-8581, Japan

1

Introduction

Recently, materials informatics has establishedan important position in materials science [1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. As a feature of materials science, it is not always easy to obtainmaterials data whether by experiments or simulations. In contrast, when general machinelearning and artiﬁcial intelligence techniques
are applied to materials data, it is necessary
to use a large amount of data to gather meaningful results. Therefore, to achieve success inmaterials informatics research, it is necessary
to use some ingenuities in treating small-data
problems. One strategy to overcome smalldata problems is to start with a small amountof data and gradually increase the amount ofdata with the help of machine learning. Thisis called black-box optimization. One of thetypical techniques is Bayesian optimization.
In this paper, we introduce a Bayesian optimization method that can eﬀectively select thenext candidate for an experiment or simulation
with the help of machine learning. We also
give examples of its application in materials informatics. In Bayesian optimization, Gaussian
processes are used as a machine-learning surrogate model, which is constructed to predict
the target material properties using alreadyobtained materials data. Based on the predic-

tions, the next candidate for the experimentor simulation is selected to improve the materials properties. By repeating these processes,
training and selection using machine learning,materials with better properties can be foundusing the fewest number of experiments or simulations. Recently, many successful examplesof Bayesian optimization have been reported
in materials science [12, 13, 14, 15, 16].

2

Algorithm of Bayesian optimization

2.1

Problem setting

Let us explain an algorithm for Bayesian optimization. In materials research, the variables that describe materials are called descriptors, and include compositions, structures,processes, and simulation parameters. A descriptor vector with dimension d is denoted byx ∈ Red . Additionally, the materials property
is expressed as y which is obtained through experiments or simulations when x is given. Evidently, the relationship between x and y cannot be explicitly expressed as a simple function in materials science. Thus, in materials
informatics, we replace this relationship witha machine learning surrogate model. That is,
the machine-learning surrogate model fML (x)32Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

is introduced, and y for any x is approximately
obtained as follows:y  fML (x).

(1)

Using such a machine learning surrogate
model, Bayesian optimization can find x withthe better material properties y among themany candidates of x. For example, a problem may be set up for Bayesian optimization
as follows:• There are N candidate materials expressed by {xi }i=1,...,N .
• Among {xi }i=1,...,N , we search for materials with a better material property valuey. In addition, the number of experiments
or simulations to obtain y is minimized asmuch as possible.
• Experiments or simulations for M candidate materials have been completed,and M material properties have been obtained. Currently, we have dataset D ={xk , yk }k=1,...,M .
• We select the next candidate material expressed by xM +1 using fML (x). That is,
the surrogate model is trained using thetraining data D, and the potential of amaterial is evaluated by using the trainedmodel. To evaluate the potential, the acquisition function is introduced. Here,the Bayesian optimization uses a Gaussian
process as a surrogate model.
• After evaluating the value of yM +1 on
the selected material xM +1 by experiments or simulations, the M + 1-th pair(xM +1 , yM +1 ) is added to D. Then, thenext candidate material is selected by using the updated surrogate model.
The Bayesian optimization cycle is shown in
Fig. 1.

Figure 1: Flow of Bayesian optimization. In
step 2, the Gaussian process (GP) regression istrained by the already obtained data and thenext point is selected based on the acquisition
functions. In step 3, the materials propertyof the selected material is evaluated by experiments or simulations. By repeating of steps 2
and 3, we select better materials.

2.2

Gaussian process

In the Gaussian process which is used as
the surrogate model in Bayesian optimization,
when the training data D are given, the conditional probability distribution for y at x is
given byP (y|D) = N (µ(x), σ(x)).

(2)

Here, µ(x) is the mean of the predicted value
by the Gaussian process regression when x is
the input, and the variance σ(x) is the uncertainty, when D = {xk , yk }k=1,...,M . These aredefined as follows:µ(x) = k (K + λI)−1 y,(3)σ(x) = k(x, x) + λ − k (K + λI)−1 k,(4)where λ is the hyperparameter, I is the identity matrix, and y = (y1 · · · yM ) . In addition,

33

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyok and K are deﬁned as follows:
(
)⊤
k =
(5)
k(x1 , x) · · · k(xM , x) ,k(x1 , x1 ) · · · k(x1 , xM )


..
..
..
K = 
,
.
.
.
k(xM , x1 ) · · ·k(xM , xM )(6)

where k(xi , xj ) is a Gaussian kernel function,][
1
2
k(xi , xj ) = exp − 2 ∥xi − xj ∥ . (7)2γHere, γ is a hyperparameter.

2.3

Acquisition functions

To evaluate the potential of the material,acquisition functions are introduced. There
are many types of acquisition functions, suchas the probability of improvement (PI) [17],the expected improvement (EI) [18], and theThompson sampling [19]. Firstly, the PI represents the probability of exceeding the current maximum value of the already obtained
y: ymax = maxk yk . This score is deﬁned asfollows:
PI(x) = P [y(x) > ymax ]= F (t(x)) ,(8)

where F (·) is the cumulative distribution function of N (0, 1) and t(x) = (µ(x) − ymax )/σ(x).
Here, µ(x) and σ(x) are obtained using theGaussian process.
Next, the EI is the expected value of how
much ymax updates when x is observed. Thisis deﬁned as

Here, a coeﬃcient vector w∗ was sampled according to the posterior distribution in theGaussian process. ϕ(x) is a random feature
map and ϕ(x)⊤ ϕ(x) expresses the Gaussian
kernel, approximately.
In Bayesian optimization, the material expressed by x with the largest value of the acquisition function is selected as the next candidate for the experiment or simulation. By
using these acquisition functions, we can incorporate into the selection process not only
the predicted value µ(x) but also informationon the uncertainty of the prediction σ(x). This
makes the selection more eﬀective than if thenext candidate is randomly selected.

3

PHYSBO package

To realize fast and scalable Bayesian optimization, we developed PHYSBO (optimization tools for PHYSics based on Bayesian Optimization) [20, 21] which is a Python librarydeveloped under the support of the “Project
for advancement of software usability in materials science” by the Institute for Solid State
Physics, University of Tokyo. In PHYSBO, arandom feature map, Cholesky decomposition,
and Thompson sampling are used to accelerate the calculations required for Bayesian optimization. Note that PHYSBO is an updated
version of COMBO [22] and includes some newfunctions.
The following are the features of PHYSBO.
• PHYSBO can be used to ﬁnd better solutions for both single and multi-objective
optimization problems.

EI(x) = E [max(y(x) − ymax , 0)]= σ(x) [t(x)F (t(x)) + f (t(x))] ,• At each cycle in Bayesian optimization, asingle proposal or multiple proposals canbe selected.

(9)where f (·) denotes the probability density ofN (0, 1).
Finally, we consider Thompson sampling,
and the acquisition function using Thompson
sampling is as follows:
TS(x) = w∗ ⊤ ϕ(x).

• Parallel calculation can be performed.
The results of parallelization performanceare shown in Fig. 2.
• Detailed manual is provided.

(10)

34

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

PHYSBO is available from https://github.
com/issp-center-dev/PHYSBO.

Figure 2: Selection time as a function of thenumber of candidate data values for different scores depending on the number of cores.
As the number of cores increases, the selection times steadily decrease. Computing timeis measured using CPU: 2.3 GHz Quad Corei7. Panels reproduced with permission from
Ref. [20].

4

Examples in materials science

In this section, some results obtained by performing Bayesian optimization in materials science are introduced. In Secs. 4.1-4.3, singleobjective problems are the focus for discussion.
Sections 4.1 and 4.2 consider the cases where
Bayesian optimization is combined with experiments, and in Sec. 4.3, the results where simulation data is used are introduced. In addition, the multi-objective optimization results
are presented in Sec. 4.4.

4.1

Composition optimization for Li
ion conductivity

Li-ion conductive oxides are attractive electrolytes for Li-ion secondary batteries owing totheir stability and low toxicity. To increase theLi-ion conductivity of a material, doping of additives or mixing heterogeneous materials havebeen considered. However, it is difficult to determine the optimal chemical compositions us-

ing experimental methods. This is because itis practically impossible to cover all compositions because of the large number of possibilities in the search space. Thus, to reduce thenumber of experiments, Bayesian optimization
is a useful tool.
To investigate the efficiency of Bayesian optimization, we attempted to optimize the composition of the ternary oxide solid electrolyte
Li3 PO4 -Li3 BO3 -Li2 SO4 [23, 24]. The mixedmaterial was stable under atmospheric conditions and could be combined by sinteringwith both positive and negative electrode materials. As the initial traial, we prepared 15
samples with a composition ratio interval of
25%. Using these 15 data points, a ternarycomponent heat map of Li-ion conductivity
was drawn by the Gaussian process regression,
which is shown in Fig. 3 (a). We can see thatin samples 7 and 8, the Li-ion conductivity increased. Bayesian optimization was performed
using this as the initial state, and 10 samples
were further synthesized. Using all data, theternary component heat map is shown in Fig. 3(b). We obtained an optimum polycrystalline
material with a composition of 25:14:61 (mol%) for Li3 PO4 -Li3 BO3 -Li2 SO4 , which is threetimes the Li-ion conductivity (4.9 × 10−4 S/cm
at 300 ◦ C) compared with the highest case inbinary compounds.

4.2

Process optimization for gas atomization

The use of metal 3D printing is rapidly advancing in aerospace engines, and low-cost production and a ready supply of superalloy powders
have become essential in the industry. In particular, for high-pressure turbine disks, which
are important components of engines, it is necessary to produce high-quality superalloy powders with a high sphericity, uniform structure,high yield, and low cost. Most of these powders are produced by gas atomization, and thedesired powder is produced using the industrial
equipment used in the manufacturing process.

35

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 3: Heat maps of the Li-ion conductivity interpolated by the Gaussian process for (a)initial 15 data and (b) 25 data after Bayesian
optimization. Panels reproduced with permission from Ref. [23].
To do this it is necessary to optimize multiple
process conditions such as the melting temperature of the metal and gas pressure. Even withthe expertise of specialists, this optimization
task requires enormous cost, time, and humanresources.
In this study, Bayesian optimization wasused to optimize the gas atomization process
without the use of expert knowledge or historical data (Fig. 4 (a)) [25]. A Ni-Co based
superalloy for high-pressure turbine disks withexcellent heat resistance was chosen for investigation. The target powder specifications area size of 53 µm or less, which is suitable forturbine disk fabrication. The process of maximizing the yield of these powers was explored.
Melting temperature of the metal and gas pressure were chosen from the various gas atomization processes as a focus for the optimization.
First, as initial data, superalloy powders
were produced by three different processes, andthe yield under 53 µm was evaluated by sieveclassification. Using these data as the training data, a Gaussian process was trained to
predict the yields of the candidate processes
and estimate the errors. Here, in the candidates processes, the melting temperature is
T = 50 × i + 1400 [◦ C] (i = 1, ..., 5) and thegas pressure is P = i + 4 [MPa] (i = 1, ..., 5).
Based on the results of the prediction, we selected the process with the highest acquisition
function and conducted powder production using the selected process. By repeating this optimization loop thrice, we succeeded in determining the process conditions to obtain thetarget powder finer than 53 µm in approximately 78% yield, when it is typically a 10-30%
yield. The yields obtained from these six trials
and unit costs of the raw materials are shownin Fig. 4 (b). By performing Bayesian optimization, the yield was improved, and the unit
cost of the raw material was cheaper. The superalloy powder produced by the process foundby Bayesian optimization succeeded in reducing the cost by approximately 72% comparedwith commercially available powder (values estimated from the unit cost of raw materials).

4.3

Model parameter estimation

In condensed matter physics, knowing the effective model of a material is one method used
to understand the target material [27, 28].
Bayesian statistics are useful for solving inverse problems [29], in which an effectivemodel is derived that explains the given simulation results or experimental results. Basedon Bayesian statistics, plausible model parameters in the effective model that explain
the given physical quantity are determined by36

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

distribution that expresses prior knowledge ofthe model parameters x. To estimate an effective model, the maximizer of the posterior
distribution should be determined. This problem can be solved using Bayesian optimization,
where the value of y is generated from the posterior distribution.
As a sample problem, the estimation of magnetic interactions of the spin-1/2 Heisenberg
chain model at 12 sites from a magnetization
curve was set as a challenge. Here, three
types of magnetic interactions that need tobe estimated are considered: nearest neighbor
J1 , next-nearest neighbor J2 , and 3rd-nearest
neighbor J3 . Thus, the Hamiltonian can be
written as
H =

12

i=1

J1 Si · Si+1

+J2 Si · Si+2 + J3 Si · Si+3 , (13)Figure 4: (a) Cycle of Bayesian optimizationin process optimization of gas atomization. (b)Yields and the unit cost depending on the cycles. Values obtained for commercial gas atomized powders prepared by Company A andCompany B [26] are also plotted. Panels reproduced with permission from Ref. [25].
maximizing the posterior distribution, which isdefined as
P (x|y target ) ∝ exp[−E(x)],(11)

where the energy function E(x) as a functionof model parameters x is given by
2

E(x) = 1/(2σ )(ytarget

−y

cal

(x))

2

− log[P (x)], (12)where y target and y cal (x) are the sets of physical quantities given as targets and those calculated from the effective model characterized byx, respectively. In addition, P (x) is the priorwhere Si denotes the vector of the spin operator at i-th site. In addition, a periodic
boundary condition is imposed as follows: Si =Si+12 .
In the model parameter estimation,
firstly, the target magnetization curve{mtarget (hj )}j=1,...,Nh is given. Here, hj is
the magnetic field and Nh is the number ofmagnetizations with different hj .
Insteadof the value of posterior distribution itself,
we used the difference between the target
and calculated magnetization curves as y in
Bayesian optimization, which is given as
y=−

Nh

j=1

[mtarget (hj ) − m(hj ; J1 , J2 , J3 )]2 ,(14)where {m(hj ; J1 , J2 , J3 )}j=1,...,Nh is the calculated magnetization curve when the interaction values (J1 , J2 , J3 ) are given. By searchingfor (J1 , J2 , J3 ) such that y is maximized, thedifference between the target and calculated
magnetization curves is minimized, and we canestimate the model parameters that describe
the target magnetization curve.

37

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

We prepared the target magnetization curveusing the Hamiltonian with (J1 , J2 , J3 ) =(1.0, 0.5, 0.3); that is, these values are the solution to the model estimation problem. We
used HΦ package [30] to calculate the magnetization curve, which is a quantum lattice solverthat uses the exact diagonalization method. In
Bayesian optimization, the search space is set
as a grid in which each magnetic interaction is
discretized between 0 and 2 in increments of
0.1 for J1 , J2 , and J3 . Thus, the total numberof input candidates is 213 = 9261. The best
difference as a function of the number of cycles
in Bayesian optimization is shown in Fig. 5.
Using Bayesian optimization, we demonstrated
that better parameters for an effective model
can be found.

Figure 5: Best difference (= −y) during the
optimization as a function of the number of cycles. The results are compared with the resultsof random sampling. The inset is an enlarged
view. Panels reproduced with permission from
Ref. [20].

is defined as the optimal solution obtainedby varying the balance of the objective functions. A metric for determining whether better Pareto solutions are found is the dominated region, which is the area dominatedby Pareto solutions in the objective function
space. The target problem is materials screening, where we search for materials with alarge bandgap and a large electronic dielectric constant. In general, these properties exhibit a trade-off tendency, in other words, as
the bandgap increases, the electronic dielectric
constant decreases. In order to address thisproblem, we used the semiconductor databasefrom Ref. [31], and found the number of materials is 1277. First principles simulation results
are presented in this database. We use thecompositional descriptors generated by Magpie [32] as x.
The number of Pareto solutions obtained by
performing Bayesian optimization with multiple objectives as a function of the number ofcycles is plotted in Fig. 6 (a). For Bayesian optimization, three types of scores were used for
multi-objective optimization, called TS, EHVI,
and HVPI. The results show that Bayesian optimization was able to find many more Pareto
solutions than random sampling. The area ofthe dominated region was calculated for the
results after 200 cycles. A large value of thisarea indicates that better Pareto solutions arefound. Figure 6 (b) shows a violin plot for thisarea using 10 independent runs. Bayesian optimization produced a significantly larger dominated area than random sampling.

5
4.4

Materials screening for multiobjective optimization

Finally, the results of multi-objective optimization problems using Bayesian optimization are
introduced. The purpose of multi-objective
optimization is to find as many Pareto solutions as possible. Here, the Pareto solution

Summary

We introduced a Bayesian optimization technique and demonstrated its application in materials science. Bayesian optimization is a machine learning method that can effectively select the next experiments or simulations. The
efficiency of Bayesian optimization is recognized in materials science, and thus, many

38

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

with the support of the “Project for advancement of software usability in materials science”
in fiscal year 2020 by the Institute for Solid
State Physics, University of Tokyo.

References[1] A. Seko, A. Togo, H. Hayashi, K. Tsuda,
L. Chaput, and I. Tanaka, Phys. Rev.
Lett. 115 (2015) 205901.
[2] S. Ju, T. Shiga, L. Feng, Z. Hou, K.
Tsuda, and J. Shiomi, Phys. Rev. X 7(2017) 021024.
[3] V. Stanev, C. Oses, A.G. Kusne, E. Rodriguez, J. Paglione, S. Curtarolo, and I.
Takeuchi, npj Comput. Mater. 4 (2018) 1.
[4] K. Terayama, R. Tamura, Y. Nose, H.
Hiramatsu, H. Hosono, Y. Okuno, and
K. Tsuda, Phys. Rev. Mater. 3 (2019)033802.
[5] T. Fukazawa, Y. Harashima, Z. Hou, andT. Miyake, Phys. Rev. Mater. 3 (2019)053807.

Figure 6: (a) Number of Pareto solutions
found as a function of the number of cycles
by PHYSBO for a multi-objective optimization problem. (b) Dominated region depending on the method when the number of cycles is200. Panels reproduced with permission from
Ref. [20].

[6] K. Kitai, J. Guo, S. Ju, S. Tanaka, K.
Tsuda, J. Shiomi, and R. Tamura, Phys.
Rev. Res. 2 (2020) 013319.
[7] R. Katsube, K. Terayama, R. Tamura,and Y. Nose, ACS Mater. Lett. 2 (2020)
571.

problems can be solved using this technique inthe future. In particular, using the PHYSBO
package, massive parallel calculations can be
performed using supercomputers, and we expect that more complicated problems can besolved.

[8] R. Tamura, M. Watanabe, H. Mamiya, K.
Washio, M. Yano, K. Danno, A. Kato,and T. Shoji, Sci. Technol. Adv. Mater.
21 (2020) 540.

Acknowledgements[9] K. Terayama, M. Sumita, R. Tamura, and
K. Tsuda, Acc. Chem. Res. 54 (2021)
1334.

We wish to thank Koji Tsuda, Kei Terayama, Masato Sumita, Tsuyoshi Ueno, Koji
Hukushima, and Naoki Kawashima for theirhelpful discussions. PHYSBO was developed[10] I. Ohkubo, Z. Hou, J. N. Lee, T. Aizawa,
M. Lippmaa, T. Chikyow, K. Tsuda, andT. Mori, Mater. Today Phys. 16 (2021)
100296.

39

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo[11] R. Tamura, Y. Takei, S. Imai, M. Nakahara, S. Shibata, T. Nakanishi, and M.
Demura, Sci. Technol. Adv. Mater. Methods 1 (2021) 152.

[24] M. Sumita, R. Tamura, K. Homma, C.
Kaneta, and K. Tsuda, Bull. Chem. Soc.
Jpn. 92 (2019) 1100.

[12] M. M. Noack, K. G. Yager, M. Fukuto,
and G. S. Doerk, R. Li, and J. A. Sethian,Sci. Rep. 9 (2019) 1.

[25] R. Tamura, T. Osada, K. Minagawa, T.
Kohata, M. Hirosawa, K. Tsuda, and
K. Kawagishi, Mater. Des. 198 (2021)
109290.

[13] R. Vargas-Hernández, Y. Guan, D.
Zhang, and R. Krems, New J. Phys. 21(2019) 022001.

[26] C. Lehnert, B. Sitzmann, F. Pfahls, H.
Franz, and M. Hohmann, The Special
Steel 65 (2016) 10.

[14] T. Yamashita, N. Sato, H. Kino, T.
Miyake, K. Tsuda, and T. Oguchi, Phys.
Rev. Mater. 2 (2018) 013803.

[27] R. Tamura and K. Hukushima, Phys. Rev.
B 95 (2017) 064407.

[15] F. Häse, L. M. Roch, C. Kreisbeck, and A.
Aspuru-Guzik, ACS Cent. Sci. 4 (2018)1134.
[16] K. Terayama, K. Tsuda, and R. Tamura,
Jpn. J. Appl. Phys. 58 (2019) 098001.
[17] H. J. Kushner, J. Basic Eng. 86 (1964)
97.

[28] R. Tamura, K. Hukushima, A. Matsuo, K.
Kindo, and M. Hase, Phys. Rev. B 101(2020) 224435.
[29] R. Tamura and K. Hukushima, PLOS
ONE 13 (2018) e0193785.
[30] M. Kawamura, K. Yoshimi, T. Misawa,
Y. Yamaji, S. Todo, and N. Kawashima,
Comput. Phys. Commun. 217 (2017) 180.

[18] J. Mockus, V. Tiesis, and A. Zilinskas, Towards Global Optimization 2 (1978) 2.

[31] A. Takahashi, Y. Kumagai, J. Miyamoto,Y. Mochizuki, and F. Oba, Phys. Rev.
Materials 4 (2020) 103801.

[19] S. Q. Yahyaa and B. Manderick, The 23rd
European Symposium on Artiﬁcial Neural Networks, Computational Intelligenceand Machine Learning (2015).

[32] L. Ward, A. Agrawal, A. Choudhary,and C. Wolverton, npj Comput. Mater.
2 (2016) 16028.

[20] Y. Motoyama, R. Tamura, K. Yoshimi, K.
Terayama, T. Ueno, and K. Tsuda, arXiv:
2110.07900 (2021).
[21] https://www.pasums.issp.utokyo.ac.jp/physbo[22] T. Ueno, T. D. Rhone, Z. Hou, T. Mizoguchi, and K. Tsuda, Mater. Discov. 4(2016) 18.
[23] K. Homma, Y. Liu, M. Sumita, R.
Tamura, N. Fushimi, J. Iwata, K. Tsuda,
and C. Kaneta, J. Phys. Chem. C 124(2020) 12865.

40

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

3.2

First-Principles Calculationof Material Properties

41

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Clarification of Microscopic Mechanisms of Semiconductor Epitaxial
Growth and Device-Interface Formation by Large-Scale Quantum-TheoryBased Computations
Atsushi Oshiyama
Institute of Materials and Systems for Sustainability, Nagoya University
Furo-cho, Chikusa-ku, Nagoya 464-8601
In the fiscal year of 2021, on the basis of theGaN, a premier material in optoelectronics is

total-energy electronic-structure calculations andnow emerging in power electronics due to its

molecular

superior

dynamics

simulations

within thephysicalproperties.

However,todensity-functional theory (DFT), we have studied

guarantee the expected high performance of thethe epitaxial growth of wide-gap power semi-

devices, it is necessary to forge high-quality

conductors, atomic and electronic structures of

epitaxial

semiconductor-insulator interfaces. The main

experimental efforts in this decade, the current

computational tools are our RSDFT (Real Space

quality of GaN crystalline films is unsatisfactoryDFT) code and RS-CPMD (Car-Parrinello Mole-

for replacing Si power devices in the market. To

cular Dynamics) code as well as VASP code.

unveilSpecifically, we have studied 1) the atom-scale

identification of the surfaces on which atomic

mechanism of GaN epitaxial growth [1], 2) thereactions take place is an essential prerequisite.

films

the

of

growthGaN.

Despitephenomena,

many

atom-scale

mechanism of the adatom diffusion on SiC
stepped surface [2], 3) the formation of danglingbond free interface of GaN and a gate insulator[3], and 4) the structural identification of thenano-meter-scale GaN growth surface using
Bayesian

optimization

[4].

We

have

also

developed 5) an order-N orbital-free DFT (OFDFT)

schemebyinventingFig.1: Top view of the stable 6x6 surface

kinetic-energy

structurefunctional using the neural-network [5]. The

discovered

by

the

present

Bayesian optimization (structure name#130 in Fig. 2). The black dashed line

below is the explanation of the issues 4) and 5)

indicates a 6x6 area. Brown, blue andabove.

white atoms correspond to Ga, N and H,
respectively.

Structural identification of GaN (0001) byBayesian optimization

42

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

We have identified the stable structure ofand more complex adsorbate-arrangements, andnanometer-scale GaN (0001) surfaces with Ga-then determination of surface phase diagrams for

and H-adsorbates, which are the fundamental

design of further preferred growth conditions.

basis for crystal growth modeling, by large-scale

Order-N OFDFT scheme with machine

density-functional calculations combined withlearning

machinelearning

Bayesian

optimization

A scheme in DFT in which the kinetic energy

technique. We have been able to reach a single

functional is expressed by the sum of single-

stable structure (Fig. 1) with satisfactorily low

particle orbitals squared is introduced by Kohn

mixing enthalpy by 130 trials based on Bayesianand Sham (KSDFT) and has been applied to a

optimization among

numerous

23C15=490,314

candidatenumberofapplications

withunprecedented success.

structures (Fig. 2). We have found that the

However, solving the Kohn-Sham equations for

obtained structure lacks any postulated highby humanall the occupied orbitals in the system is a

intuition, satisfies electron counting rule locally,

computational burden scaling with the system sizeand shows a complex adsorbate-rearrangement,

N as O(N3). The scheme with lower-order scalingleading to lower mixing enthalpy. The present

is highly demanded in materials science and also

scheme of Bayesian optimization combined within advancing DFT. One of the solutions in a

first-principle calculations paves a way toward

legitimate

identifying surface structures with a larger scale

functional theory (OFDFT) in which the kinetic

symmetry previously introduced

way is the orbital-free density-

energy functional is expressed as a functional of
the electron density ρ (r ) itself and an single
Euler equation rather than Kohn-Sham equations
is solved, being expected to be O(N) scheme.
We express the kinetic energy functional asT [ ρ ] = ∫ τ TF (r ) F ( s 2 , q; W )dr ,where τ TF is the Thomas-Fermi kinetic energy
density, the enhancement factor F is expressed as
Fig. 2: History of the exploration of thea gradient expansion with s = ∇ρ [2(3π 2 )1/3 ρ 4/3 ]surface structure by Bayesian optimization.
The objective is to minimize the mixing

and q = ∇ 2 ρ [4(3π 2 )2/3 ρ 5/3 ] . The enhancement

enthalpy.

factor is determined by the deep learning

The

black

dashedline

corresponds to the minimum value of theusing the neural network where the set ofbaseline models, and the red marker
corresponds to the most stable structure

weight parameters W is determined so as#130 in the present exploration.

to minimize the cost function L expressed43Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyoin terms of the kinetic energy functional

systems which include semiconductors,

derivative δ T δρ :metals, ionic insulators and some of their2=Lpolytypes: diamond, graphene, ds-Si, face-
1 Nt 1  δ T
δ T KS()(rn )  ,−r∑n
Nt n=1 2  δρδρcentered-cubic(fcc)-Si,

beta-tin

Si,

zinc-

functional

blende (3C)-SiC, body-centered-cubic(bcc)-

derivative is computed at each real-space

Li, fcc-Al, fcc-Cu, bcc-Na, and NaCl. The

mesh

the

structural properties, i.e., lattice constants

corresponding values by the Kohn-Shamand bulk moduli of all those materials

scheme. As a training data, we use theobtained by the present functional shows

functional

better agreement with the corresponding

where

the

pointskinetic-energy

andcomparedderivative

in

with

diamond-values by the Kohn Sham scheme.

structured (ds) carbon at some mesh points.

The order N behavior of the computation
time in the present OFDFT scheme isclearly shown in Fig. 3.

The group id codes for the achievements
above are k0042 and m0037.

Fig. 3: Computational time of KSDFT and

Related publications

OFDFT. Comparison of (a) t1 (subspace[1] K. M. Bui, K. Shiraishi and A. Oshiyama,diagonalization), t2 (conjugate gradientAppl. Surf. Sci. 557, 149542 (2021).

minimization and gram-schmidt diagonalization), and t3 (SCF mixing), and (b) total[2] K. Seino and A. Oshiyama, Appl. Surf. Sci.

time for the SCF iteration. The test

561, 149927 (2021).

system is 4H-SiC supercell with thenumber of atoms of 576 -4704. In both (a)[3] K. Chokawa, K. Shiraishi and A. Oshiyama,and (b), data points obtained by KSDFT

Appl. Phys. Lett. 119, 011602 (2021).

and OFDFT are plotted in red and blue

[4] A. Kusaba, Y. Kangawa, T. Kuboyama and A.

colors, respectively.

Oshiyama, Appl. Phys. Lett. 120, 021602 (2022).

The transferability of the kinetic-energy[5] F. Imoto, M. Imada adn A. Oshiyama, Phys.

functional obtained by the deep learning

Rev. Research 3, 033198 (2021).

with the training data of only diamond has
been examined by the application to 23 test

44

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles prediction of stability and functionality ofcomplex materials
Osamu SUGINO
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
In recent years, considerable progress has

systems will also be effective not only forbeen made in predicting material properties

electronic systems but also the hybrid solvation

using the density functional theory (DFT)models that we have long been studying.

simulations

and

the

DFT-basedmodel

In view of ability of meta-GGA in describing

simulations. In our group, we have developed a

the Mott insulators, this functional was used for

scheme to construct the exchange-correlation

our study on exotic materials such as the solid(xc) functional of the Kohn-Sham DFT byoxygens in the high-pressure phases and the Hg-machine-learning the many-body wave function

cuprate (HgBa2Can−1CunO2n+2+x) [4]. We foundof small molecules [1,2]. In our prior study [1],that the lattice parameters and the bandgaps

small molecular systems were simply used as the

become consistent with experiments with thislearning set, but the success was limited tofunctional, indicating that we are now at the startmolecular systems only; problems remain inline of quantitative research.

crystalline systems. To overcome this problem,

One of the open problems of DFT-based

physical conditions applicable to general

simulation is to incorporate the nuclear quantum

materials were introduced into the learning

effect. Although the path integral molecular

process, and the resulting xc functional within

dynamics (PIMD) simulation is an establishedthe meta-GGA format was found to significantly

first-principles scheme, it becomes difficult toimprove the applicability [2]. The improved xc

reducefunctional was implemented to an electronic

temperature is reduced and thus different

structure calculation package VASP and is readyscheme is needed. To overcome this problem forto distribute to supercomputer users. For further

the hydrogen diffusion on metal surfaces, we

progress, we focused on techniques for the DFT

have reformulated the quantum transition state

for classical systems (classical DFT) and, in thistheory that is based on a semi-classicalcase, low-density approximation of the n-

approximation using an apparently full-quantum

particle density was found to be effective [3]. We

formulation. The fluctuation effect was found to

consider that applying this method to electronic

be significantly reduced with the new method

45

the

statisticalfluctuation

as

the

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo[5].

reduction reaction occurring thereon andWe have also investigated the effect ofconsidered the effect of liquid water as well.

nuclear quantum motion on the bandgap ofThese results were shared with experimentalists

insulators. This was done using the Allen-Heine-and helped them in planning the electrode

Cardona (AHC) theory and its extensions [6].

development.

Herein the Debye-Waller terms of AHC wasreformulated using the momentum operator, by

References

which some of the electron-phonon coupling[1] R. Nagai et al.: Phys. Rev. Res. 4 (2022)

terms can be added to infinite order.

013106.

The description of electrochemical interfaces[2] R. Nagai et al.: npj Compt. Mater. 6 (2020)is a challenging problem of first-principles

1.

simulations, on which our group has long been

[3] T. Yokota et al.: Phys. Rev. E 104 (2021)

studying. The difficulty of the simulation is due

014124.

to existence the electric dipole layer (EDL) that[4] A. Tatan et al.: arXiv cond-mat 2204.05719

can extend macroscopically. The thickness of(2022).

EDL, however, is reduced to several nm when[5] Y. Kataoka et al: unpublished.

the ions are densely distributed as in strong[6] K. Ishii et al.: Phys. Rev. B 104 (2021)

acidic/alkaline solutions, but methods for the245144.

simulation has been developed only for the[7]

solution side. Therefore, EDL existing in thecenter-dev/abICS

solid side of the interface remains to be achallenge; this is the case when semiconducting
electrode is used. To simulate the ZrOxN2-xelectrode, which is a candidate for Pt-freeelectrode of the next-generation fuel-cells, wehave applied the first-principles Monte Carlosimulation with abICS [7] and then sped it up
with the help of a machine-learned model
potential.

By

the

simulation,

we

could

successfully obtain the distribution of oxygen
vacancies and the nitrogen impurity atoms, andthe result was used to describe the EDL. We
further investigated efficiency of the oxygen

46

S.

Kasamatsu:

https://github.com/issp-

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analyses related to atomic structures and atom
dynamics at complex structures such as surfaces,interfaces and defects
Satoshi WATANABE
Department of Materials Engineering, the University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656

1

Introduction

Keeping in mind the importance and diﬃculty of atomistic simulations on structuresand dynamics at surfaces, interfaces and defects toward development of novel informationand energy devices, we have been investigating
atomic structures and atom dynamics in various systems by first-principles calculations, insome cases combining them with multi-scale ormachine-learning approaches. In the following,
two of our recent results are described.

2

Band alignment of LiTi2 O4and SrTiO3Recently, it was found in thin-film solid-state
Li batteries using LiTi2 O4 thin films as positive electrodes, the spontaneous Li-ion migration between the solid electrolyte (Li3 PO4 ) andLiTi2 O4 occurs in the case of the conducting
substrate, Nb-doped SrTiO3 (001) [1]. Thatis, the LiTi2 O4 turned to the Li2 Ti2 O4 phasespontaneously.
To understand the above, we have investigated the band alignment of the
LiTi2 O4 /SrTiO3 superlattice model using
the density functional theory (DFT) calculations. Here, we adopted the SrTiO3 without
Nd doping to examine the band alignment
before the charge transfer. The calculated
projected density of states (pDOS) reveals
that the bottom of the conduction band islocated above the Fermi level EF in the central
region of the SrTiO3 layer. Since EF of the
Nb-doped SrTiO3 is considered to be locatednear the bottom of the conduction band,
this result suggests the electron transfer fromthe Nb-doped SrTiO3 to LiTi2 O4 . From thisresult and the absence of a potential gradientin the metallic LiTi2 O4 layer, we can saythat the transferred electrons charge on thesurface of LiTi2 O4 , which leads to a decreasein the electrochemical potential of Li ionsat the LiTi2 O4 surface. Consequently, thespontaneous migration of the Li ions occurs.
The present result suggests the possibility tocontrol the spontaneous Li-ion migration between the solid electrolyte and LiTi2 O4 by tuning the electrochemical potential diﬀerence via
the substrate selection.

3

Neural network potential
for multiple charge states ofdefects

In semiconductors and insulators, defects
and impurities sometimes take various charge
states depending on EF . To examine the point
defect behavior in such multiple charge states,
we have proposed a new scheme of neural network potential (NNP) [2]. In our scheme,
only minimal modifications to the conventional
scheme [3] is needed: One system charge (Qsys )node is added in the input layer. Here, Qsys

47

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyois defined as a constant value times a charge
state of the considered supercell divided by its
volume.
We have applied this scheme to wurzite-GaN
with a nitrogen vacancy [2]. For the charge
states of the vacancy, 0, 1+, 2+, and 3+
have been considered. By performing molecular dynamics simulations using the StillingerWeber potential, we have generated 4,550 pristine GaN structures and 4,550 structures witha N vacancy in total. Then the DFTdata havebeen obtained for these sturctures. Total number of the DFT data is 22,750, because calculations have been performed for 0, 1+, 2+ and3+ charge states in the cases of the structureswith a N vacancy.
The NNP constructed using our scheme andthe aforementioned data predict the total energies and atomic forces accurately for all the
charge states: The root-mean-square-errors of
the total energies and atomic forces were, respectively, 1.45 meV/atom and 63.8 meV/Å
for the training dataset and 1.44 meV/atomand 64.6 meV/Å for the test dataset. Moreover, it has reproduced the phonon band structures and themodynamic properties of the defective systems fairly well.

References[1] K. Nishio, S. Ichinokura, A. Nakanishi,
K. Shimizu, Y. Kobayashi, N. Nakamura,
D. Imazeki, R. Shimizu, T. Hirahara, S.
Watanabe, and T. Hitosugi: Nano Lett.
21 (2021) 10086.
[2] K. Shimizu, Y. Dou, E. F. Arguelles, T.
Moriya, E. Minamitani, and S. Watanabe:
arXiv:2203.16789.
[3] J. Behler and M. Parrinello: Phys. Rev.
Lett. 98 (2007) 146401.

48

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Quantum Simulations on Dynamical Heterogeneous
Catalysts
Y. J. WONG, J. I. ENRIQUEZ, H. H. HALIM, S. E. M. PUTRA, T. N. PHAM,
Y. HAMAMOTO, K. INAGAKI, I. HAMADA, and Y. MORIKAWA
Department of Precision Engineering, Graduate School of Engineering,Osaka University, 2-1 Yamadaoka Suita, Osaka 565-0871

In 2021-2022, we carried out theoretical investigation of chemical processes at surfaces
and interfaces, adsorption and reaction of polymeric formic acid on Cu(111), NO adsorption
and dissociation on Cu(100), oxygen vacancy
migration in SrFeO3−δ and Sr3 Fe2 O7−δ , dry reforming of methane on Co catalysts, and adsorption of CO2 on terrace, stepped and defectsites on Pt surfaces.
In this report, we report the dry reformingof methane on Co catalysts,[1]. The emissionsof greenhouse gases (CH4 and CO2 ) are rising
exponentially due to human activities and increased energy demand, contributing to global
warming and climate changes. To make useof CH4 and CO2 into renewable energy, catalytic dry reforming of methane (DRM) is aneﬃcient pathway to convert them into syngas(CO and H2 ). Currently, active transition metals known to be capable of catalyzing DRM aremainly group VIII elements such as Ru, Rh,
Ni, Co and Pt. Among them, supported Ni
could be the most studied catalyst due to its
relatively high activity and low cost. However,
the eﬃciency of Ni is widely known to be easily
suppressed by carbon deposition.
On the other hand, Co is particularly interesting due to its excellent catalytic activity
and considerably low carbon deposition. Experimentally, Co is more carbon resistant thanNi. Co could enhance the adsorption of CO2 ,which helps to inhibit the deposition of carbon
and enhance carbon removal.

To gain insight into the occurrence of carbon
deposition vs removal during DRM, we calculated the CO* formation reaction throughthe surface reaction of C* and O*, and theCC* formation reaction through the C-C coupling. The present direct quantitative comparison between the activation energies of the involved reactions would clarify the competition
between carbon deposition vs removal over different Co surfaces. In addition, we further
compared our results with those of Ni to reveal the cause of the lower carbon deposition
on Co than on Ni. The quantitative comparison of CO2 activation, C-C coupling, and CO*formation over Co and Ni could reveal the theoretical underlying mechanism of lower carbon
deposition on Co than Ni.
The overall energy diagram illustrating theminimum energy pathway for reactions between CO2 and C* on all the investigated Co
surfaces, which includes CO2 activation (green
region), O* and C* diﬀusion (blue region), andthe competition between CO* formation and
C-C coupling (red region), is summarized in
Figure 1. We consider the reaction of CO2
with two predeposited C*. As observed in Figure 1, the rate-determining step for the reaction between CO2 and C* on all the investigated Co surfaces is located in the red region, indicated by the energy needed for CO*
or CC* dimer formation. Two conclusions canbe drawn from evaluating the competition between CO* and CC* dimer formation on each49

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

surface. First, carbon graphitization is dominant on (111) and possibly on (110) because
the CC* dimer ﬁnal state is of lower or equal
energy r elative to its respective initial state,indicating that the CC* dimer is stable anddoes not dissociate into atomic C*. In addition, CC* dimer formation on these surfaces
has a lower activation energy than CO* formation. Even though the CO* ﬁnal state ismore stable than the CC* dimer, the stabilityof the CC* dimer compared to its initial statemight give rise to nonreversible carbon graphitization, which could eventually cover the active surfaces. Thus, on (111) and (110), CC*
dimer formation has a higher degree of preference than CO* formation. By combining thisresult with the fact that (111) is the most exposed surface of a Co nanoparticle, as indicated by the Wulﬀ constructions, we hereby
deduce that the origin of carbon deposition
that leads to catalyst poisoning during DRM
is caused by the high degree of preference for
C-C coupling than CO* formation, especiallyon (111). Second, on (100), (211), and (221),
CC* dimer formation is not favorable because
the CC* dimer ﬁnal state has a higher energy
level than its respective initial state, indicatingthat the CC* dimer is easily dissociated into
two atomic C*s. In addition, the CO* ﬁnal
state is more stable than the CC* dimer. The
combination of the above mentioned points implies a higher degree of preference for CO* formation on (100), (211) and (221), even though
the energy needed for CC* formation might
be lower than that of CO* formation. On theother hand, other surface reactions, such as
CO2 activation and surface diﬀusion of O* andC* have lower activation energies than those of
CO* and CC* dimer formation on each respective surface (Figure 1). The low energy needed
for CO2 activation implies that surface O*s are
suﬃciently supplied for CO* formation. In addition, the kinetic rate constants for CO* formation, CC* formation, and CC* dissociation
over all the investigated surfaces were calcu-

lated and discussed in Section 12, S.I.. The result corresponds well with the ﬁndings where
C-C coupling has the highest degree of preference on (111), followed by (110), however, is
not favorable on (100), (211), and (221).

Figure 1: Energy diagram showing the minimum energy pathways of reactions between
CO2 and two C* on FCC Co (111), (110),(100), (211), and (221).
The present study provides a comprehensive
clariﬁcation on the mechanism of DRM, specifically on the surface reaction of CO2 and C*
on the major ﬂat and step FCC Co surfaces,
namely, (111), (110), (100), (211), and (221).
and/or promoted Co nanoparticles for DRM
to restrict C-C coupling.

References[1] Y.-J. Wong, H. H. Halim; N. F.
Khairudin, T. N. Pham, S. E. M. Putra,
Y. Hamamoto, K. Inagaki, I. Hamada, A.
R. Mohamed, and Y. Morikawa: J. Phys.
Chem. C 125, 21902-21913 (2021).

50

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Understanding superionic conductivity in disordered systems
using machine learning potential molecular dynamics andMonte Carlo sampling
Shusuke KASAMATSU
Academic Assembly (Faculty of Science),
Yamagata University, Kojirakawa, Yamagata-shi, Yamagata 990-8560
The competition between order and disorderenvironments, Sc-VO-Sc, Sc-VO-Zr, or Zr-VO-

in materials leads to a wide variety of materials

Zr, are responsible for the hydration behavior.

functionalities such as electronic, ionic, andUsing abICS, we have clarified that the former

thermal conductivity/insulation and catalytic

two are active sites for hydration, while the Zr-

activity. However, because of the huge number

VO-Zrof degrees of freedom in disordered systems,

thermodynamic conditions and contributes little

successes in theory-driven design of suchto the hydration reaction [3].

site

seldomexistsunder

normalfunctionalities have been rather limited. In thisIn the case of amorphous systems, we

research project, we tackled this problem

considered the use of the neural network

through a combination of first-principles

potential (NNP) approach originally proposed

calculation and machine learning.

by Behler and Parinello [4]. Although the

For disordered crystalline systems, weneural network potential methodology seems toemployed our abICS (ab Initio Configuration

be a well-established approach at this point, we

Sampling) framework for deriving an on-lattice

have found that it is quite a challenge to apply

neural network model from first-principles

to many-component glass systems. This iscalculations [1] and used that to perform

because the NNP requires that the training set

replica-exchange Monte Carlo sampling. One

sufficiently

system that we have been examining is heavily

relevant configuration space, which will be

Sc-doped BaZrO3, which is known as ahuge for many-component glasses. We observe

promising perovskite proton conductor for solid

regularly that NNP molecular dynamics (MD)oxide fuel cells [2]. The oxygen vacancy is

calculations ‘fall apart’ and exhibit completely

known to be the active site for the hydration

unphysical structures after it wonders into

reaction, which is the key reaction to introduce

regions of previously unlearned configuration

protons into the system. However, it is yet

space. To tackle this issue, we have been trying

unclear which of the three types of vacancy

an active learning cycle approach where we51

coversthethermodynamicallyActivity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

take structures from the NNP-MD trajectory,
perform DFT calculations on those structures,
add them to the training set, and run the NNPMD again with the new NNP. As shown in
Fig. 1 for the AgI-As2Se3 superionic mixed
glass system, increasing the number of cycles
leads to improvement in the NNP predictions,although we have not been able to fully

Fig. 1: Improvement of NNP accuracy withconverge the low energy structures yet.

active learning iterations for AgI-As2Se3

We have also been examining the feasibilityof training on DFT data using high-costfunctionals such as the HSE06 hybrid. Since it
is not feasible to obtain a long enough MD
trajectory to use as the training set with HSE06,
we first performed first-principles MD usingtherelatively

low-cost

GGA

functional.

Afterwards, we took a subset of the structures

Fig. 2: Total structure factors from NNPs(~1500 structures) and recalculated them using

trained on various functionals and compared to

HSE06, which were then used as the training

experiment.

set in NNP training. This approach was applied
to amorphous GeO2, and we were able to obtain

References

structure factors in excellent agreement with

[1] S. Kasamatsu, ISSP Supercomputer Center

experiment (Fig. 2). This shows that NNP

Activity Report 2020, pp. 16-26.

technology is promising for realizing long-time[2] J. Hyodo et al.: Adv. Energy. Mater. J. Phys.

and large-scale MD simulations with theSoc. Jpn. (2020) 2000213.

accuracy of high precision (and high cost)[3] K. Hoshino, S. Kasamatsu, et al., inelectronic structure methods.

preparation.
[4] J. Behler: Int. J. Quant. Chem. 115 (2015)
1032-1050.

52

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Formation energy calcuation of defects in candidates of thermoelectricmaterials
KAZUHIKO KUROKI
Department of Physics, Osaka University
1-1 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Burke-Ernzerhof (PBE) exchange-correlation functional and the projector augmented wave method.
We ﬁnd that the interstitial-site doping of AE =Ca, Mg or G3 = Sc, Y, and G3 = La, Y substitutional doping for the Ca site is favorable both for
CaZn2 X2 (X = As, P) in terms of energy stability. In particular, the formation energy of the La
substitutional doping is the lowest among the considered cases both for CaZn2 X2 (X = As, P) andis negative, so that La is expected to be substituted for the Ca site and provide electron carriers
spontaneously (Fig.1). We also ﬁnd that the formation energy for CaZn2 As2 is smaller than thatfor CaZn2 P2 , so that n-type doping is considered tobe relatively easier in CaZn2 As2 than in CaZn2 P2 .

CAAL2 SI2 -TYPE ZINTL PHASECOMPOUNDS CAZN2 X2 (X = AS,P)

Thermoelectric performance of many kinds of
CaAl2 Si2 -type Zintl phase compounds has beentheoretically estimated by ﬁrst-principles bandcalculations[1]. This work suggests that CaZn2 X2(X = Sb, As, P) exhibits large ZT values in theelectron-doped regime due to its high valley degeneracy of the electronic band structure. Indeed,this kind of 122 Zintl phase compounds have beensynthesized and their electronic structure have also
been investigated theoretically. However, these 122
Zintl phase compounds become p-type semiconductors because the cationsite vacancies are easily
formed under usual synthesis conditions.
Given the above background, in 2021 ﬁscal year,
we have explored the possibility of n-type (electron
carrier) doping of CaZn2 X2 (X = As, P) using ﬁrst
principles calcuation[2]. We have considered thepossibility of n-type doping into CaZn2 X2 for thefollowing two situations: interstitial-site doping of
the alkaline earth metals AE (= Mg, Ca, Sr, Ba)and group 3 elements G3 (= Sc, Y, La), and G3
substitutional doping for the Ca site. The former
is analogous to Mg3 (Sb,Bi,Te)2 , in which excess Mg
is introduced to the interstitial site of Mg3Sb2 so as
to realize n-type doping[3]. On the other hand, thelatter is another possible way to introduce electron
carriers utilizing the diﬀerence in the valence number of the ion (Ca 2+ and G3 3+) , and the relevant
compounds with full rare earth substitution including La, CaAl2 Si2 -type arsenides RE2/3 Zn2 As2 (RE= La, Ce, Pr, Nd, Sm), do exist in reality.

LAOXS2 (X = SB, BI)

In LnOX Ch2 , electron carriers are usually introduced by ﬂuorine substitutional doping for oxygen, or the valence ﬂuctuation of cerium ions for
Ln = Ce compounds. Since atoms in insulating
layers work as a charge reservoir in both ways, thecharge carrier can be introduced without a largechange in the electronic state of the conducting layers, which is also advantageous for studying theirtransport properties. In fact, our previous theoretical study showed that the thermoelectric propertiesof LnOX Ch2 can become very good, provided thatelectron doping by introducing defects makes thesystem metallic without largely changing the elec-

In order to describe dopants and defects in a
crystal under periodic boundary conditions, the supercell approach was adopted in our calculations.
The atomic positions in the supercell were relaxedin the structural optimization after the lattice constants and atomic positions of the primitive cellare optimized. To consider the possibility of chemical doping, its defect formation energy of charged
states was calculated using the supercells. To numerically evaluate the defect formation energy ofchemical doping in CaZn2 X2 (X = As, P), we have
performed ﬁrst-principles calculations within thegeneralized gradient approximation using VASP.
We perform DFT calculations with the Perdew-

FIG. 1. The formation energy of the G3 substitution for
the Ca site against the Fermi energy ∆EF = EF − EV
for CaZn2 As2 . The group 3 elements G3 (= Sc, Y, La)
are chosen as dopant D. The dotted line denotes the
position of the conduction band minimum[2].

53Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo2
placement of O by S) and OS are not stable while
VO (O vacancy) and VS can take place, where theformation energy of VO is higher in X = Sb thanin X = Bi (Fig.2). A characteristic feature is that
VSeq (Seq is the in-plane S) becomes much morestable in X = Sb than in X = Bi, due to the formation of an Sb2 dimer and the occupation of the
impurity energy levels. The formation energies ofcation defects, XS , and SX are found to be positive. We have also found that Fluorine likely replaces oxygen for both X = Sb and Bi. The defect formation energy of FO is negative for bothcompounds, while that for X = Sb is much higher
than X = Bi. Our study has clariﬁed the stability of several point defects and suggested that thein-plane structural instability is enhanced in X =Sb. We expect that, although further study is necessary, the knowledge obtained in the study shouldbe helpful for understanding/controlling the transport properties of LaOXS2 and related compounds
by impurity doping.

FIG. 2. Defect formation energies of anion point defectsfor (a) LaOSbS2 (X = Sb) and (b) LaOBiS2 (X = Bi).
The horizontal line (the Fermi level) is restricted to theenergy range between the band edges. The values of thecharge q of the defects are shown beside the line[6].

tronic structure[4]. However, it has recently beenfound that it is experimentally diﬃcult to enhancethe electrical conductivity in X = Sb compounds
against their robust insulating nature[5].
In 2021 ﬁscal year, in order to shed light on
the puzzling transport properties of the doped layered pnictogen dichalcogenides, we have systematically investigated the defect formation energy ofseveral point defects in LaOXS2 (X = Sb, Bi) using ﬁrst-principles calculation[6]. We used the PBE
parametrization of the generalized gradient approximation and the projector augmented wave method
as implemented in VASP.

[1] H. Usui and K. Kuroki, J. Phys. Soc. Jpn. 89 (2020)
124707.
[2] K. Nishiguchi, M. Ochi, C.H.Lee, and K. Kuroki, toappear in J. Phys. Soc. Jpn.
[3] H. Tamaki, H.K. Sato, and T. Kanno, Advanced
Materials 28 (2016) 10182.
[4] M. Ochi, H. Usui, and K. Kuroki, Phys. Rev. Appl.
8 (064020) (2017).
[5] Y. Goto et al., J. Phys. Soj. Jpn. 289 (2019) 38.
[6] M. Ochi and K. Kuroki, Phys. Rev. B 105 (2022)
094110.

We have found that anion replacements SO (re-54

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Studies on superconductivity in nickelates from a multiorbital viewpoint
KAZUHIKO KUROKI
Department of Physics, Osaka University
1-1 Machikaneyama, Toyonaka, Osaka, 560-0043, Japanplan to publish the results as soon as possible.

DESIGNING NICKELATESUPERCONDUCTORS WITH d8+δELECTRON CONFIGUATIONEFFECT OF RESIDUAL HYDROGEN IN
THE INFINITE LAYER NICKELATESUPERCONDUCTORSIn 2020 ﬁscal year (the last ﬁscal year), we theoretically designed unconventional nickelate superconductors with d8 electron conﬁguration[1]. We
considered d8 nickelates with K2 NiF4 structure,
where the apical oxygens are replaced by halogens or hydrogens. One of the best candidates waselectron-doped Ca2 NiO2 Cl2 . The key point wasthat the large crystal ﬁeld splitting of the orbitalenergy levels, induced by replacing the apical oxygens by halogens or hydrogens, is approximately
equivalent to large interlayer hopping in a bilayer
system. Applying the ﬂuctuation exchange approximation to the ﬁve orbital model of these materials, we showed that the maximum superconducting transition temperature of some of them may beeven higher than that of the high-Tc cuprates.
A major drawback of our proposal was that
Ca2 NiO2 Cl2 has never been synthesized previously,
and it may indeed be diﬃcult to synthesize. On
the other hand, a similar material Sr2 NiO2 Cl2 hasbeen synthesized experimentally[2], but its lattice
constant is too large compared to Ca2 NiO2 Cl2 , resulting in a smaller crystal ﬁeld splitting, and hence
the predicted superconducting Tc , if any, is low. In
fact, a high spin state is suggested in Sr2 NiO2 Cl2 ,which is unfavorable for our mechanism to work,
Given this background, in 2021 ﬁscal year, we studied the hydrostatic pressure eﬀect on Sr2 NiO2 Cl2 in
an attempt to mimic the situation of Ca2 NiO2 Cl2 .
The structural parameters under pressure has been
determined using VASP. We have obtained ﬁve orbital models through Wannierization, and studied
the model using the ﬂuctuation exchange approximation. This is still an ongoing research, and we

Our theory on desigining d8+δ nickelate superconductors may also be related to another newly
discovered superconductor (Nd,Sr)NiO2 [3]. In thissuperconductor, the nickel electron conﬁguration
is expected to be close to d9 , but this might beaﬀected, e.g., by the reduction process during thesynthesis of the material. Since the band structureof (Nd,Sr)NiO2 itself, due to the absence of apical oxygens, resembles that of the proposed mixed
anion-nickelates, (unintentional) reduction of theelectron number in (Nd,Sr)NiO2 may also result ina similar s±-wave superconductivity.
In 2021 ﬁscal year, we have studied the eﬀect ofresidual hydrogen using the adopting the supercell
approach, which contains multiple Ni atoms in aunit cell due to the presence of eccess hyrdogens
added at the apical site periodically. The structural parameters were determined using VASP. We
have so far constructed 10 and 20 orbital modelsof these systems through Wannierization. We plan
to analyze the possibility of superconductivity inthese multiorbital models.

[1] N. Kitamine, M. Ochi and K. Kuroki, Phys. Rev.
Res. 2, 042032(R).
[2] Y. Tsujimoto, C.I. Sathish, Y. Matsushita, K. Yamaura, and T. Uchikoshi, Chem. Commun. 50, 5915
(2014).
[3] D. Li et al., Nature (London) 572, 624 (2019).

55

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First principles studies of impurity-dislocation complexes in
GaNKenji SHIRAISHI
Institute of Materials and Systems for Sustainability,
Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601
Line defects and points defects haveresults indicate that Mg-H complexes do notintensively studied so far [1, 2]. However,form near the screw dislocation, although screw

complexes composed of line defects and point

dislocations attract both Mg and H atoms.

defects have not been considered yet. In thisFigure 2 shows the atomistic structures of the

project, we have studied dislocation-impuritycomplexes in GaN by the first principles
calculations.

b=[0001]

Fig.2: Atomistic structures of a complex
composed of a GaN screw dislocationand Mg and H impurities.
complex composed of a GaN screw dislocationand Mg and H impurities. As shown in thisfigure, the local Mg-N-H structure which is

Fig.1: Atomistic Structures of acalculation model of the complex
composed of GaN screw dislocationand Mg and H impurities.

observed in bulk GaN is broken by the effect of
the screw dislocation. This indicate thatproperties of point defects are totally changed

Calculations were performed by VASP
package.

by the effect of line defects in the dislocation-

We prepared 800 atom unit cells

impurity complexes.

which contain a screw dislocation and Mg andReferences

H impurities as shown in Fig.1.

[1] S. Berber et al. : Phys. Rev. B 77, (2008)

It is well-known in bulk GaN that Mg and H

165405.

impurities tend to form complexes of the Mg-[2]

N-H local structure. However, calculated

645.

56

K. Matsunaga: Acta Mater. , 195, (2020)

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First Pricnciples Study of N Vacancies in Si3N4 for Flash
Memory Application
Kenji SHIRAISHI
Institute of Materials and Systems for Sustainability,
Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601
Defects in Si3N4 are now used for theapplication of 3D NAND flash memories.
Among Defects in Si3N4, N vacancies are
considered as the physical origins of charge
traps used in memory functions [1, 2].
Recently, the charge transfer between charge
traps in Si3N4 has become serious problem inthe miniaturized 3D NAND flash memories.

Fig. 2: Formation energies of various
charged state of the N vacancy as afunction of system Fermi energy. -2, 0
and +2 charged states are stable.

However, the physical mechanisms of thischarge transfer is not clarified. In this study, weinvestigated the charge transfer mechanism byenergy.

the first principles calculations.

energies of a VN-H complex as shown in Fig. 2.

First, we calculated the formation energies

As shown in Fig. 2, stable charged states are -2,of a N vacancy (VN). The results are shown in
Fig. 1.

Next, we calculated the formation

0, and 2 in the Si3N4 Fermi energy. ThisAs shown in Fig. 1, stable charged

indicate that H diffusion from one VN tostates are -1, 0 and +1 in the Si3N4 Fermi

another VN causes charge transfer when VN
traps electrons.

References[1] K. Yamaguchi, A. Otake, K. Kobayashi, andK. Shiraishi, Tech. Digest of IEEE Int. Electron
DevicesMeeting (IEDM), Baltimore, MD, USA,2009, pp. 1–4.
Fig.1: Formation energies of various
charged state of the N vacancy as afunction of system Fermi energy. -1,
0 and +1 charged states are stable.

[2] K. Yamaguchi, A. Otake, K. Kamiya, Y.
Shigeta, and K. Shiraishi,Jpn. J. Appl. Phys.,50,(2011) 04DD05.

57

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of quantum algorithm for imaginary-time
evolution
Yu-ichiro MATSUSHITATokyo Tech Academy for Convergence of Materials and Informatics (TAC-MI),Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8550
hybrid classical-quantum algorithm.

Recently, the development of materials

We have developed a so-called “nonlocal”

computation methods using quantum computers
has attracted a great deal of attention. In

approximationasamethodparticular, we have paid attention to theapproximate

unitary

operators,

imaginary-time evolution method, which hasdeveloped the method to realize quantum

been known for a long time in materials

imaginary-time evolution with a quantum

computation,

thecircuit shallower than the conventional methods

development of algorithms for its execution onof imaginary-time evolution. We constructed ana quantum computer. As a result, we haveactual quantum circuit and applied it to thesucceeded in developing an algorithm for

MAXCUT problem. For the calculations, wequantum imaginary-time evolution methods [1].

verified the effectiveness of the algorithm withOn a quantum computer, only unitary

a quantum circuit simulator. The results showedtransformations and observations must be usedthat the quantum imaginary-time algorithm

to achieve the desired computation. The

does work, and at least 94% of accuracy isimaginary-time evolution operator is a non-achieved for unweighted 3-regular MAXCUT

unitary transformation, and its realization on a

problems with ten vertices. At the same time,quantum computer is non-trivial. One approach

we have found that there is an accuracy limit

developed in this study is to realize thedue to the introduction of an approximate

approximatedunitary operator, and the algorithm does not

and

have

workedimaginary-timeonevolutionforandfinding
have

completely match the exact solution.

operator on a quantum computer by finding aunitary operator that best approximates thequantum state after the operation of theReferences

imaginary-time evolution operator. This method[1] H. Nishi: npj Quantum Information 7

uses a classical computer in finding the unitary(2021) 85.

operator, and its unique feature is that it is a58

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-Principles Molecular-Dynamics Study of Structural andElectronic Properties of Covalent Liquids and Glasses under
Pressure
Fuyuki SHIMOJO
Department of Physics, Kumamoto University, Kumamoto 860-8555
It is important for the investigation of theby using a so-called two-phase simulation

dynamic properties of covalent liquids andmethod based on FPMD [1]. Both results are inglasses under pressure to consider the stability

reasonable agreement with each other.

of materials states under various conditions

We

have

also

obtainedthemeltingfrom the viewpoint of free energy. For thistemperature of binary alkali NaxRb1-x mixture

purpose, the thermodynamic integration (TI)

[2] as a function of concentration x, and foundmethod based on the first-principles molecularthat the melting temperature minimum occurs

dynamics (FPMD) simulations is useful andat x = 0.2, being in agreement with theeffective. However, the system size andexperimental observation. These two findings

simulation time are limited due to the highfor diamond and alkali mixture demonstrate thecalculation cost of FPMD. To solve this cost

validity and usefulness of the current method.

problem, we have used machine-learninginteratomic potential based on artificial neuralnetworks (ANN) trained from the results of
FPMD simulations.
In this study, we have calculated the melting
temperature of diamond, one of the typicalcovalently bonded materials, using the TI
method with the ANN potential as a function ofpressure.

Figure

1

shows

the

Fig. 1: Pressure dependence of melting
temperature of diamond.

pressuredependence of calculated melting temperature.
The results of this study are indicated by the

References

red diamond symbols. The triangle up and[1] A. A. Correa et al., PNAS 103, 1204 (2006).

down symbols indicate the results of the[2] A. Irie et al., J. Phys. Soc. Jpn. 91, 045002

previous theoretical study, which carried out(2022).

the direct simulation of solid/liquid coexistence59Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of first-principles electronic-structure
and transport calculation code RSPACE andsimulations for device
Tomoya ONO
Graduate School of Engineering, Kobe University
Rokkodai-cho, Nada, Kobe 657-8501

at the interface.

Silicon carbide (SiC) attracts attention because it is one of the most promising widebandgap semiconductors for developing nextgeneration switching devices operating in highpower and high-frequency applications. However, the potential of 4H-SiC has not been
fully utilized owing to the low carrier mobilityof 4H-SiC-based metal-oxide-semiconductor
field-eﬀect transistors, which is caused by defects at the 4H-SiC/SiO2 interface. To reducethe density of interface defects and increase
the channel mobilities, post-oxidation annealing using N2 O, NO, or N2 gas has been proposed. In this study, we propose the interface
atomic structures in which N atoms are incorporated by replacing C atoms, and we investigate the total energies and electronic structures of the nitride layers by density functional
theory (DFT) calculation. Universal atomicscale models describing 4H-SiC with a high-Natom-density layer in arbitrary crystal planes
are proposed. To explore the most preferable
crystal plane of 4H-SiC for N-atom incorporation, we study the stability and electronic
states of the nitride layers on a 4H-SiC surface.
We find that the nitride layers grow along thea face, which is consistent with the conclusion
obtained using the bulk model[1]. Any defectstates in the bandgap of 4H-SiC are not generated in our structure. The formation energyof the nitride layers at the topmost layer ofthe interface is smaller than that at the second
layer, indicating that the N atoms accumulate

In our model, the surface of the 4H-SiC substrate is terminated with OH groups to imitate
the SiO2 layer and the other side of the substrate is terminated with H atoms. The rectangular supercells of 10.1 Å × 10.7 Å × 26.3
Å for the a-face model, 10.1 Å × 12.3 Å × 27.3
Å for the m-face model, and 12.3 Å × 10.7
Å × 26.8 Å for the Si(C)-face model were employed. The z-axis is taken to be the direction
perpendicular to the surface. The numbers of
atoms for the a-face, m-face, and Si(C)-facemodels are 176, 208, and 208. We considered
the modification incorporating four Si vacancies (VSi s) and 16 N atoms at C sites (NC s).
The cases in which VSi s are arranged parallel to the surface were investigated to evaluate
the anisotropy of the formation energy of thenitride layer. In our model, the areal N-atomdensity is on the order of 1014 cm−1 , which isconsistent with the experimental results. Although there are two inequivalent lattice sitesof 4H-SiC, i.e., h (hexagonal) and k (quasicubic) sites, our previous studies have shownthat nitride layers tend to grow at the k site.
Thus, we consider the cases in which VSi s arearranged at the k site. The interfaces with
the nitride layer at the second layer are also
investigated for all the faces. For the firstprinciples calculation, we used the RSPACE
code[2, 3], which is based on the real-space
finite-diﬀerence approach within the frameworks of DFT and is developed in this project.

60

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

We employed the local density approximationof the DFT to describe the exchange and correlation eﬀects. Electron–ion interactions are approximated by the projector-augmented wave
method. We adopt 6 × 6 × 1 Monkhorst-packk-point meshes including a Γ-point in the Brillouin zone. The real-space grid spacing is chosen to be ∼ 0.21 Å. The structural optimization is performed until the residual forces are
smaller than 0.001 Hartree/Bohr radius.
We assumed the interaction of the SiC substrate and the arriving NO molecule at the interface as

Table 1: Formation energy of nitride layers defined by Eq. (1).
face
a
a
m
m
Si
Si
C
C

SiC(w/o mod) + 24NO

layer
top
2nd
top
2nd
top
2nd
top
2nd

Eform (eV)
−7.43
−7.10
−7.13
−7.07
−7.07
−7.01
−7.14
−7.01

annealing generates the nitride layers immedi→ SiC+ 4SiO2 + 16CO + 4N2 ,ately below the SiO2 layers without any transition layers. The diﬀerence in the formation
with SiC(w/o mod) (SiC(w/ mod) ) being the interenergy between the nitride layers at the topface without (with) the modification incorpomost and second layers is the largest for the
rating four VSi s and 16 NC s. The formationa face. This result agrees well with the obserenergy of the above interaction for generating
vation that the formation energy of the nitride
one VSi is obtained aslayer along the a face is the smallest. The local(w/ mod)densities of states of the interfaces reveal that
Eform = Etotal/4 + E(SiO2 )(w/o mod)+4µCO + 2µN − Etotal/4 − 6µNO , (1) there are no gap state at the interface. These
results imply that NO annealing after the oxwhere E(SiO2 ) is the total energy of a SiO2 idation can contribute to the reduction in the(w/o mod)unit in a bulk of quartz SiO2 . Etotal
and density of interface defects by forming the ni(w/ mod)Etotalrepresent the total energies of the tride layer immediately below the SiO2 layerinterface without and with N-atom incorpo- of the interface.
ration, respectively. In addition, µNO , µCO ,and µN are the chemical potentials of a NO
References
molecule, a CO molecule, and N atoms in a N2
molecule, respectively. We set the temperature[1] M. Uemoto, N. Komatsu, Y. Egami, andat 1000 K and the partial pressure of NO gas
T. Ono, J. Phys. Soc. Jpn. 90, 124713(pNO ) at 1 atm. The partial pressures of CO(2021).
−5(pCO ) and N2 (pN2 ) gases are set at 10 atm[2] T. Ono and K. Hirose, Phys. Rev. Lett.
and 0.25 × 10−5 atm.
82, 5016 (1999).
The formation energies of the nitride layers
are shown in Table 1. We find that all the re[3] K. Hirose, T. Ono, Y. Fujimoto, andactions are exothermic and the nitride layers
S. Tsukamoto, First Principles Calculagrowing along the a face are the most stabletions in Real-Space Formalism, Electronic
among those along the a, m, C, and Si faces.
Configurations and Transport Properties
The formation energy of the nitride layer at theof Nanostructures (Imperial College, Lontopmost layer is smaller than that at the secdon, 2005).
ond layer, resulting in the localization of the
N atoms at the interface. Note that the NO(w/ mod)61

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analysis of Surface Reactions in Atomic Layer Etching
Processes
Satoshi HAMAGUCHI
Center for Atomic and Molecular Technologies,
Osaka University, 2-1 Yamadaoka, Suita, Osaka 567-0871
Thermal atomic layer etching (ALE)First, we examined the interaction of

can be used for precise and damageless−diketones with a metallic Ni surface,etching. For example, it can be used tousing STATE [6,7]. STATE is a simulation

fabricate magnetic tunnel junction (MTJ)

code based on density functional theory

stacks of magnetoresistive random-access(DFT) with pseudo-potentials and a plane

memory (MRAM) devices [1]. The aim ofwave basis set. It has been found that the

this

the

cleavage of a C-F or C-H bond of amechanisms of thermal ALE of metal in−diketone is more likely to take place

general, whose cycle consists of anthan the deprotonation on a metal surface.

oxidation step and an exposure step to

The surface roughness can also help to−diketones,

form

study

is

to

understand

such

as;

hexafluoroacetylacetone

C-Nibonds,

which

were

also

(hfacH),observed in experiments. The reaction

trifluoroacetylacetone(tfacH),andmechanisms that we observed in theseacetylacetone

molecules.

Forsimulations(acacH)have

revealed

the

self-

instance, thermal ALE of Ni with hfacH

limiting nature of thermal ALE for metals

starts with the deprotonation of hfacH

with −diketone gases in general, which ismolecules after the oxidation of the Ni

consistentsurface.

observations [5,8].

By

increasing

thesurfacewithearlierexperimental

temperature in the range of 300 ~ 400 °C,

Second, we examined the interaction ofvolatile nickel complex Ni(hfac)2 and−diketones with oxidized metal surfaces,

water H2O molecules are formed on theusing TURBOMOLE program [9]. It has

surface and remove the NiO layer. In thisbeen found that, as −diketones approachprocess, once a new metallic Ni surface

anappears, no further etching occurs, which

deprotonate. In this way, volatile metal

ensures the self-liming nature of thecomplexes and H2O molecules can bethermal ALE process [2-5].

formed62oxidized

when

metal

surface,−diketone

theymolecules

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

interact with an oxidized metal surface.

measurement. The results indicate that

The reaction energies of such interactions

carbon contained in the incident CF3+ ionshave been evaluated from the simulations

remove oxygen of Y2O3 more efficiently.

and we found that etch oxidized metal has

Furthermore, high-energy incident CF3+

its own desorption energy or temperatureions promoted the formation of Y-F bonds

to volatilize its metal complex. Therefore,

near the surface region of Y2O3 films more

the applied temperature can be used as aefficiently than low-energy incident CF3+

self-limitingtargetions. Our simulation results are found tocontains different materials. In addition,

be consistent with these experimental

hfacH is found to get more stably bonded

observations.

conditionifthethan acacH or tfacH with an oxidized
metal surface because the negatively

REFERENCES

charged F atoms in CF3 are repelled by O

[1] G. S. Oehrlein and S. Hamaguchi,

atoms of the surface, which forces a

Plasma Sources Sci. Technol. 27, 023001

deprotonated hfac to adsorb on the(2018).

surface nearly vertically. This does not[2] A. H. Basher et al., JJAP 59, 090905

happen to acacH, whose CH3 groups tend

(2020).

to interact directly with the metal oxide.

[3] A. H. Basher et al., JVST A 38, 052602

As a result, hfacH is considered more(2020).

suited for ALD processes than other β-[4] A. H. Basher et al., JVST A 38, 022610

diketones.

(2020).

In addition, we also examined the[5] T. Ito, et al., AVS 65th (2018).

interaction of Y2O3 with incident F+ and[6] I. Hamada, Physical Review B 89 (12),CF3+ ions, using ion beam experiments

121103, (2014).

with XPS and DFT simulations. It has[7] Y. Morikawa et al., Phys. Rev. B, 69,

been found that the penetration depth of

041403 (2004).

F atoms in Y2O3 exposed to F+ or CF3+ ion[8] H. L. Nigg and R. I. Masel, JVST A 17,

injection depends essentially on the3477, (1999).

incident energy and hardly depends on[9]

the ion dose once a sufficient amount ofhttps://www.turbomole.org.

fluorine is provided to the surface andsaturate. We also obtained the atomic
concentration depth profiles by XPS

63

TURBOMOLE

V7.5

2020,

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study on atomic and electronic
structures of graphene/SiC interfaces
Yoshiyuki EGAMI
Division of Applied Physics, Faculty of Engineering, Hokkaido University
Kita 13, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-8628

Graphene is in the limelight as a post-siliconmaterial in next-generation devices due to its
unique electronic and mechanical properties
and conductivity. In recent years, the epitaxial growth in the silicon carbide (SiC) pyrolysis method has attracted attention as one ofuseful methods for producing large-scale andhigh-quality graphene. However, in the pyrolysis method, the bottom graphene layer iscovalently bonded to the Si atom of the SiC
substrate. To separate the bottom layer fromthe substrate, atomic intercalation technique
is employed. As the result, the bottom layer
becomes an ideal single-layer graphene, andthe Dirac cone appears in the electronic band
structure. On the other hand, atomic vacancies are formed in the graphene during the epitaxial growth process. Since the intercalants
can be bonded to the dangling bonds, which
are aﬀected on the energy band structure andthe position of the Dirac point of graphene.
In this study, ﬂuorine atoms are adopted asintercalants, and the eﬀect of the bond between a ﬂuorine atom and a dangling bondon the electronic state of graphene is investigated using the ﬁrst-principles calculation
code: RSPACE[1, 2]. We investigate the difference in the eﬀects of the number of ﬂuorine
atoms adsorbed on the single vacancy in thegraphene on the electronic state. It is foundthat, in the model where two ﬂuorine atoms
are bonded to the defect, the dangling-bondstate is hybridized with the conduction band
bottom of SiC substrate. Moreover, the conju-

gated π state of graphene is extended over theenergy range in which the bandgap of SiC substrate is located (Fig. 1). On the other hand,in the system produced by hydrogen intercalation, the dangling bond state is in the middleof the band gap of the SiC substrate and extends to the inside of the substrate, which cancause a large leakage current.
This work has been performed on System Bof the Supercomputer Center, the Institute for
Solid State Physics, the University of Tokyo.

Figure 1: Local density of states of graphenewith single vacancy on ﬂuorine-intercalated
SiC substrate. Two of dangling bonds are terminated by ﬂuorine atoms.

References[1] K. Hirose et al.: First-principles calculations in real-space formalism (Imperial
College Press, 2005).
[2] Y. Egami, S. Tsukamoto and T. Ono:
Phys. Rev. Res. 3, 013038 (2021).

64Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

High-Throughput Polymer Electret Material Screening Based on
Solid-State Quantum Chemical Calculation and Deep Learning
Yucheng ZHANG, Zetian MAO, and Yuji SUZUKI
Department of Mechanical Engineering
The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656
Electret is a dielectric material withionization potentials (IPs) by the density

quasi-permanent charges and can trap

functional theory (DFT) with polarizable

charges stably for decades. Vibrational

continuum model (PCM) correction agree

electret energy harvester (VEEH) canwell with the trends of the surface charge

generate electricity efficiently from kinetic

density and charge stability measured byenergy via the electrostatic induction. The

the wet experiments.

VEEH with bipolar (both positively andMost recently, by employing the de novo

negatively charged) electret leads to fourmolecule generation and the functionaltimes output power theoretically, thusgroup enrichment analysis, we successfully

specifying the importance of designing

proposed the electret CTX-A/APDEA withhigh-performance bipolar polymer electrets.

high bipolar charging performance via

CYTOP (Cyclic Transparent Optical

combining CTX-A with N-(3-aminopropyl)

Polymer, AGC Chemicals) is one of thediethanolamine [2]. This result encouraged

best polymer electret materials, with three

us to move further to search new amines incommercialized types displayed in Fig. 1.

the open-source database PubChem, aimed

Recently, we utilized quantum chemical

at designing better bipolar polymer electret

analysis for evaluating the charge trap of

based on CYTOP CTX-A after the

CYTOP electrets [1]. It is found thatdehydration reaction.

although the repeat-unit-number of CTX-A
is above 1000, the trapped charge islocalized at the amide bond, which isformed by dehydration reaction between
the carboxyl end group and the amine
introduced. It is also shown that thecomputed electron affinities (EAs) and

Fig. 1. Chemical structure of CYTOP series.

65Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Fig. 2 illustrated the prediction results on
the established dataset with one kind ofdeep learning models named MEGNet [3].
The mean absolute error (MAE) of IP is as
small as 0.326 eV, with computational costdecreased significantly. Therefore, thepresent approach will be employed forscreening bigger database for new highperformance bipolar polymer electrets.
The geometry of the molecule is relaxed
Fig. 2. Prediction of PCM-DFT IPs forunder the open-shell condition and then the

training and test sets using MEGNet.

energy of both open-shell and closed-shell
system are calculated and compared. All

Although solid-state quantum chemical

the quantum chemical calculations arecalculation based on PCM-DFT can give

made with the software GAUSSIAN [4] at

quantitative EA and IP values, the average

the DFT level with the CAM-B3LYP

computation time is 41.4 CPU hours perfunctional and 6-31+G(d,p) basis set, whilemonomer molecule and even as high as

PCM is combined for solid-state analysis

2500 CPU hours per hexamer molecule. To

due to the solvation effect correction.

reduce such heavy computational cost, we
employdeeplearning

modelsThis work was partially supported byto

JST CREST Grant Number JPMJCR15Q3

approximate the EAs and IPs efficiently.

and JPMJCR19Q1. The calculations are

To prepare the labeled data, 5522 amines

performed with SGI ICE XA ISSP systemwere initially sampled from the PubChem.

B and every calculation is done with 1 node

Thereafter, the virtual dehydration reaction(24 CPUs).

was conducted and PCM-DFT computation

References

was automatically made. Subsequently, a[1] Kim S., et al., J. Phys. Chem. B, Vol.

dataset mapping the PCM-DFT IPs and124, No. 46, pp. 10507-10513 (2020).

molecular structures was establised and[2] Zhang, Y., et al., Appl. Phy. Lett., 118,

splited into training-validation-test sets

223904 (2021).

with the ration of 80%, 10%, and 10%,[3] Mao, Z., et al., IEEE Conf. Electr. Insul.

where the training set was used to teach theDielectr. Phenom., pp. 667-670 (2021).

deep learning models and the performance[4] M. Frisch et al., “Gaussian 09, Rev. A.

of the models were tested on the test set.

1,” Gaussian, Inc. Wellingford, CT, (2009).

66

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles calculations on muon in solids
Mineo SAITO
Institute of Science and Technology, Kanazawa University
Kakuma, Kanazawa, 920-1192 Japan

Hydrogen plays an importantdensity functional theory is 1.36 eV, whichrole in semiconductor materials;

is close to the experimental value. On the

Well known examples are hydrogen

other hand, the value calculated based on

passivation and carrier injection. The

the GGA is small (0.71 eV). The Simuon spin resonance is an effective tool tomonovacancy is found to form a triangle

determine the dynamics of hydrogen inof the C2v symmetry and to induce a mid-

semiconductors since muonium consisting

gap level having large amplitudes at theof a positive muon and an electron bears

equivalent two atomic sites.

similarities

tohydrogen.

hyperfinestructures

Observed

provideWe findusefulthat the monohydrogen-vacancy pair induces the gap level.

information on the atomic site ofOnmuonium, and thus that of hydrogen. In a

dihydrogen passivates the defect level. It

previous study, we clarified that negative

is suggested from out calculation thatFermi contact terms are caused by thetrihydrogen-vacancy pair leads to n-type

electron correlation and observing thedoping. We conclude that hydrogenation

negative value suggests the formation ofplays various roles in barium silicide,resonance bond of hydrogen [1].

which depends on the concentration of

the

other

hand,

we

find

that

One of the scientifically importanthydrogen. The muon spin resonancenew targets is hydrogen impurity inmeasurement is expected to confirm thebarium silicide (BaSi2), which is a

atomic geometry of the monohydrogen-candidate for solar cell materials. It isvacancy pair.

known that hydrogen passivates the defectlevel of Si vacancy. This crystal includes[1] M. N. Manal, S. Minami, F. Ishii and

Si tetrahedrons and electrons transfer from

M. Saito, Jpn. J. Appl. Phys., 58 (2019)barium to silicon. We first confirm that

081008.

this crystal has an indirect gap and the gap
value calculated based on the hybrid

67

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

GW + BSE calculation of RIXS spectraby the all-electron mixed basis program, TOMBO
Kaoru OHNO
Graduate School of Engineering, Yokohama National University79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501
The initial state of X-ray emission spectroscopy (XES) and resonant inelastic X-ray emission spectroscopy (RIXS) is a highly excited
eigenstate with a deep core hole after the X-ray
photoelectron spectroscopy (XPS) and X-ray
photoabsorption spectroscopy (XAS) processes,
so that the XES and RIXS calculation offers agood example of extended quasiparticle theory(EQPT) [1] associated with many-body pertur-

Fig. 1: Calculated (above) and experimental [3]bation theory. Moreover, to overcome the basis(below) RIXS spectra of a CH3OH molecule.

set incompleteness problem, we adopt the all-theory [4], we gave a justification and comment

electron mixed basis program, TOMBO, whichof applying the method relying on time-depen-

uses both plane waves and numerical atomic

dent density functional theory as well as theorbitals as basis functions. We have success-one-shot GW + BSE approach to this problem.

fully applied this approach in our previous XES[2] study. Here we applied the standard one-

References

shot GW + Bethe--Salpeter equation (BSE)[1] K. Ohno, S. Ono, and H. Isobe: J. Chem.

approach in MBPT to this problem on the basis

Phys. 146 (2017) 084108.

of EQPT and analyze XES and RIXS energies[2] T. Aoki and K. Ohno: Phys. Rev. B 100

for CH4, NH3, H2O, and CH3OH molecules.

(2019) 075149.

Figure 1 shows the RIXS spectra of a[3] A. Benkert, F. Meyer, D. Hauschild, M.

CH3OH molecule calculated by our method

Blum, W. Yang, R. G. Wilks, M. Bär, F. Reinert,

together with the experimental data [3]. Both

C. Heske and L. Weinhardt,: J. Phys. Chem. A

results coincides very well without introducing

120 (2016) 2260.

any empirical fitting parameter.

[4] T. Nakashima, H. Raebiger, and K. Ohno:
Phys. Rev. B 104 (2021) L201116.

Moreover, according to extended Kohn- Sham

68

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical study of electric double-layer structure of MXene
electrode dependent on surface functional groups
Atsuo YAMADA
Department of Chemical System Engineering,
The University of Tokyo, Bunkyo-ku, Hongo, Tokyo 113-8656
Aqueous electric double-layer capacitor

while electrolytes were described using the(EDLC) is promising candidate for large-scale

RISM method. All the ESM-RISM calculations

stationary storage due to non-flammability, lowwere conducted with Quantum Espresso code.

materials cost, and non-toxicity of aqueous

The calculated EDL capacitance increased

electrolyte. Transition metal carbides/nitrides

with the increase in the atomic number of(MXenes) are appealing electrode materials for

halogen atoms (F < Cl < Br < I) (Fig.1a). The

aqueous EDLCs owing to their high specificincreased EDL capacitance is due to the biased

capacitance (> 300 F/g) in conventional

distribution of excess electrons in the electrodeaqueous electrolyte. Herein, we investigated thetoward the electrolyte, thus reducing the EDL

dependence of EDL capacitances on the surface

thickness (Fig. 1b). The induction of electrodefunctional groups of the MXene electrodes [1].

electrons into the EDL region is facilitated by

The ESM-RISM method was adopted tothe smaller negative charges of surface halogen

evaluate the capacitance of the MXene

atoms with lower electronegativity. Therefore,

electrodes. The simulation cells are composed

lowering the valence numbers of the MXeneof MXene Ti3C2T2 with different surface

surface atoms should enhance the capacitance.

functional groups (T = F, Cl, Br, and I) and theReferences

1 M KOTf/H2O electrolyte. Here, MXene[1] T. Shimada N. Takenaka, Y. Ando, M. Otani, M.

electrodes were treated quantum-mechanicallyOkubo, A. Yamada, Chem. Mater., 34, 2069 (2022).

using the density functional theory method,

Figure 1 (a) Calculated capacitances per unit surface area of MXene. (b) Spacial distributions of excess electronsof the electrode (red) and counter positive charges of the electrolyte (blue) at the electrode/electrolyte interface.

69

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Elucidation of mechanism and theoretical prediction ofsuper-functional materials using high-density hydrogen
Shinji TSUNEYUKI
Department of Physics, School of Science,
The University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo 113-0033
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
Hydrogen, a ubiquitous element, is present as an

exhibit without experiments. In this project, we

impurity in various materials and is known toapplied the methods to elucidate the mechanism

significantly change materials' electrical andof the photo-induced metallization of Yttrium

mechanical properties by assuming different

oxyhydride recently discovered by a Tokyo Techchargegroup experimentally [1].

statesdependingontheatoms'

environment. In recent years, record-breaking

Insuperconductors and superionic conductors havesignificantly reduced the electrical resistance ofbeen discovered in which protons and hydrides

an insulator YOxHy epitaxial thin film, and theare major components. One of the most common

metallic state was maintained on a scale ofproblems in studying these materials is theseveraldifficulty in experimentally quantifying and

YOxHy on glass substrates exhibits a one-digit

observing the position of hydrogen, which has

decrease in electrical resistance upon solar

no inner-shell electrons.

irradiation, while the epitaxial thin film has

Electronic structure calculations based onachieved a resistance reduction of more thandensity-functional theory and first-principles

three orders of magnitude. Furthermore, UV

molecular

allow

laser irradiation of the epitaxial thin film

quantitatively predicting materials' structure andreduced the electrical resistance by more thanphysicalseven orders of magnitude.

dynamics

properties

methods

without

empirical

theirexperiment,

days.

light

Conventional

irradiation

polycrystalline

parameters. By these methods, the energy of the

To explain these results, we constructed asystem and the forces acting on the atoms can be

structural model based on high-resolution

calculated using atomic configurations as input

measurements of the local structure anddata. In principle, it is possible to predict how

chemical composition, and calculated themuch and where hydrogen atoms are stable in aelectronic structure based on this model. As acrystal and what physical properties they will

result, we found that the hydrogen atoms change

70

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

their position and the charge state, leading to thefound that the ion conductivity of the high-T

long-life metallization [1,2].

phase is enhanced one order of magnitude by the

Another topic in this project is the study ofconcerted motion of Li ions and another one

ionic superconductor LiCB9H10. We first appliedorder of magnitude by the rotation of thethe data assimilation method for structure

CB9H10- complex [4].

prediction [3] to find no significant difference
between the high-T and low-T structures. From

References

a first-principles molecular dynamics simulation,[1] Y. Komatsu et al.,, Chem. Mater. 34, 3616

we found that the motion of Li ions strongly(2022).

correlates with the rotation of the CB9H10-[2] R. Sato et al., to be submitted.

complex. Finally, by constructing neural-[3] N. Tsujimoto, D. Adachi, R. Akashi, S.

network interatomic potentials, we calculated

Todo and S. Tsuneyuki, Phys. Rev. Materials 2,

the ion conductivity by a large-scale molecular

053801 (2018).

dynamics simulation in good agreement with

[4] R. Sato et al., submitted.

experiments. Through these simulations, we

71

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Reduction of Rare Metals in Fuel Cell Catalysts
and Hydrogen Permeable Membrane
Norihito Sakaguchi
Center for Advanced Research of Energy and Materials, Faculty of Engineering,
Hokkaido University, Sapporo, Hokkaido 060-8628

We investigated the catalyst adsorption

diffusion and coarsening. In addition, we also

and diffusion properties on light-element

revealed that the Cl- ion adsorption enhances

doped graphene supported on the magnetic

the anisotropic catalyst nanorod growth.[1]substrates and hydrogen dissolution and

We

also

investigatedthehydrogendiffusion properties in the amorphous ceramic

dissolution and diffusion properties in thematerials, with the aid of the first-principles

amorphous ceramic materials. We considered

calculation based on the density functional

the Al2O3 as the hydrogen permeation

theory (DFT) and machine learning potentials.

membrane.

Since

DFT

calculationsofAt first, we investigated the stabilities ofamorphous materials require quite large

Pt atoms on light-element doped graphenecomputing costs, we constructed the machine

supported on the magnetic substrates. We

learning

considered Fe and Ni as the magnetic

interatomic potentials obtained with DFT

substrates. We performed the total energy andcalculations. We performed melt-quenching

electronic structure calculations using The

technique to obtain the amorphous structure.

Vienna Ab initio simulation package (VASP).

We performed 2000 DFT calculations with

We revealed that the adsorption of Pt atoms

various hydrogen positions in amorphouson light-element doped graphene with flat

Al2O3 to construct the database for machine

structures

becomes

supportingon

potential

toreproducethestrongerthroughlearning. The obtained machine learningmagnetic

substrates.

potentials reproduce the stable adsorption

However, in most cases of steric light-

structures, however, cannot reproduce theelement

diffusion

doped

the

graphene,themagnetic

barriers

obtained

with

DFT

substrates weaken the Pt adsorption on thecalculations

light-element doped graphene. We also found

Referencesthat the magnetic substrates reduce the[1] M. J. Saw, M. T. Nguyen, Y. Kunisada, T.

diffusion barriers of Pt atoms. Therefore, theTokunaga, T. Yonezawa, ACS Omega 7

magnetic substrates enhance the catalyst(2022) 7414.

72

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Reduction of Rare Metals in Formic Acid Decomposition
Catalysts and Oxygen Storage Materials
Yuji KUNISADA
Center for Advanced Research of Energy and Materials, Faculty of Engineering,
Hokkaido University, Sapporo, Hokkaido 060-8628

We investigated the catalyst adsorption

graphene. This is because the active dangling

and diffusion properties on light-elementbond forms strong chemical bonds with

doped graphene supported on the magnetic

magnetic surfaces, hence, Cu atoms cannot

substrates with the aid of the first-principles

form stable chemical bonds with the light-

calculation based on the density functional

element doped graphene. We also investigatedtheory (DFT). Besides, we performed electron

the diffusion properties of Cu atoms on light-

energy loss spectroscopy (EELS) simulations

element doped graphene supported on theof heteroatom-substituted brownmillerite-typemagnetic substrates. We found that theoxides to characterize the EELS spectra

magnetic substrates reduce the diffusion

obtainedbarriers of Cu atoms. In addition, we also

withtransmission

electronrevealed the effect of Cl- ions on the catalyst

microscopy.
At first, we investigated the stabilities ofnanorod growth.[1]Cu atoms on light-element doped graphene

We performed EELS spectra of the

supported on the magnetic substrates. We

partially

considered Fe and Ni as the magnetic

considered Sr dopants, which show promising

substrates. We performed the total energy andoxygenelectronic structure calculations using The

obtained EELS spectra show good agreement

Vienna Ab initio simulation package (VASP).

with the experimental results.

We installed a parallelized VASP with Intel®

References

MPI Library and Intel® Math Kernel Library.

[1] M. J. Saw, M. T. Nguyen, Y. Kunisada, T.

We revealed that the adsorption of Cu atoms

Tokunaga, T. Yonezawa, ACSOmega 7

on light-element doped graphene becomes(2022) 7414.

stronger

with

the

magnetic

substituted

absorption

Ca2AlMnO5.

properties.[2]

We

The

substrates.

[2] K. Tanahashi, Y. Omura, H. Naya, K.

However, in cases of some light-element

Miyazaki, G. Saito, Y. Kunisada, N.

dopants, the magnetic substrates weaken the

Sakaguchi, T. Nomura, ACS Sustain.

Cu adsorption on the light-element doped

Chem. Eng. 9 (2021) 9317.

73

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles calculation of energy materials
Fumiyuki ISHII, Naoya YAMAGUCHI, Rifky SYARIATI,
Hikaru SAWAHATA, Hana Pratiwi KADARISMAN, Kaiki SHIBATA,
Sefty YUNITASARI, Yaotang ZHANG, Vierta SARASWATI,
Takahiro TOMINAGA, Yedija Yusua Sibuea TEWENG, Juhri HENDRAWAN
Nanomaterials Research Institute, Kanazawa University
Kanazawa, 920-1192, Japan

1. Topological thermoelectric materials
Thermoelectric conversion based on theanomalous Nernst eﬀect has received a lot of
attention as ANE achieves more eﬃcient heatrecovery and heat recovery from more heatsources than those based on the Seebeck effect. For the anomalous Nernst eﬀect, thetopological nature of the wave functions, andthe Berry curvature, a ﬁctitious magnetic ﬁeld,
is essential. We have studied the anomalous
Nernst eﬀect of iron-based ferromagnetic materials such as Fe3 X(X=Al, Ga)[1] and FeCl2 [2]by ﬁrst-principles density functional calculations. To evaluate the anomalous Nernst coefﬁcient, a detailed Fermi energy dependence of
the anomalous Hall conductivity is required.
We have implemented a ﬁnite diﬀerence algorithm in OpenMX[3] to calculate the Berrycurvature of metallic system given by the averaged local Berry phase of the momentum
space[4]. This implementations open up the
possibility of eﬃcient thermoelectric material
design based on high-throughput screening.
2. Photovoltaics
Material property data was extracted fromabout 1500 papers on organic thin ﬁlm
non-fullerene solar cell materials, and highperformance material conditions were derived
based on data statistical methods[5]. One of
the conditions obtained was the empiricallyknown ”open-circuit voltage (Voc) of 0.8-0.9 V
is appropriate”, and the database we createdrediscovered this rule of thumb. In addition, it
was suggested that the sulfur atom content is
an important factor for high performance photovoltaics materials.
We have performed ﬁrst-principles calculations of the topological phase transition instrained inorganic halide perovskite CsPbI3 .
For the experimental lattice constant, thebandgap decreases from 0.15 eV to 0 eV
when a strain of c/a > 1 is applied. Increasing the strain will gradually open the
bandgap. We calculated the topological Z2 invariants that characterize the topological insulating phase. From the results, the bulk crystal CsPbI3 showed a strain-induced topologicalphase transition, changing from a trivial insulator to a topological insulator phase. This
topological phase transition of the strained inorganic halide perovskite has the potential tobe applied to new energy devices.
3. Graphene and diamond
Applying the supercell scheme to the study ofalloys and various perturbed system including
impurities and vacancies raises band folding
problems. The unfolding method is expected
to obtain the meaningful energy-momentum
relationships by avoiding it. The method proposed by Chi-Cheng Lee et al proved[6] very
useful for calculating the electronic structureof a vacancies system with OpenMX code. We
have calculated and observe the graphene ﬂake
size dependence of Dirac cone in the unfolding74

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

band structures.
Negatively charged diamond nitrogenvacancy centers are promising for many
applications, such as high-resolution sensors
for electric ﬁelds and quantum computer
Qubits . Density functional calculations areoften performed in supercell systems. However, as the number of supercells increases,
the ﬁrst Brillouin zone (FBZ) shrinks and theband becomes more complex. An unfolding
band method calculation was performed to
study the electronic properties of the nitrogenvacancy center diamond using the OpenMX
code. Our results show that the unfoldedband of the bulk diamond supercell and thenitrogen vacancy center of the diamond havefewer lines than those of the traditional folded
band. The shape of the unfolded energy band
matches the primitive cell band. The dedailed
electronic band structure of diamond withnitrogen vacancy center are analyzed.

that has been observed in experiments and 3
brand new structures, and then performed detailed ﬁrst-principles analysis of the elctronic
structures to predict their physical properties.
We calculated the Z2 topological invariant andspin-textures of the new structures. Amongthe 3 new structures, we found that two structures with centro symmetry were strong topological insulators, and one structure without
centrosymmetry had wide band gap and strong
Rashba splitting.

References[1] A. Sakai, S. Minami, T. Koretsune, T.
Chen, T. Higo, Y. Wang, T. Nomoto, M.
Hirayama, S. Miwa, D. Nishio-Hamane,
F. Ishii, R. Arita and S. Nakatsuji, Nature 581, 53(2020).
[2] S. Rifky, S. Minami, H. Sawahata, and F.
Ishii, APL Materials 8, 041105 (2020).

The Al2 O3 /diamond(111) interface containing three types of impurities was calculated.
We predicted three diﬀerent
Al2 O3 /diamond(111) interface structures andinvestigated their band edge changes. Bandedges are evaluated by calculating the local
electron density. Compared to diamond bulk,
the band of Al2 O3 bulk is generally shifted
downward. The band oﬀsets for dangling
bonds, C-H bonds, the ideal O-terminal interface are estimated. Our research helps toassess the impact of interface structure on device performance and provide a reference for
improving experimental methods.

[3] T. Ozaki et al., http://www.openmxsquare.org/[4] H. Sawahata, N. Yamaguchi, S. Minami,
and F. Ishii, arXiv:2204.05949.
[5] N. Yamaguchi, H. Sano, H. Sawahata, M.
Nakano, T. Taima, F. Ishii, M. Karakawa,
Jpn. J. Appl. Phys. 61 030905 (2022), selected for Spotlights 2022.
[6] C-C. Lee, Y. Yamada-Takamura, and T.
Ozaki, J. Phys.: Condens. Matter 25345501 (2013).

4. Crystal structure prediction for spintronics materials
Bismuth tellurium iodide (BiTeI) has attracted
great interest as a potential material for spintronics device. We have performed crystal
structure prediction for BiTeI crystals by genetic algorithms and density functional calculations. We found 4 BiTeI crystal structureswith high stability , including one structure75

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of crystal structure prediction methods using
machine learning
Tomoki YAMASHITATop Runner Incubation Center for Academia-Industry Fusion,
Nagaoka University of Technology
1603-1 Kamitomioka-machi, Nagaoka, Niigata, 940-2188
We

We search for solid electrolyte materials that

have

also

studiedonalgorithm

can be synthesized in the systems of Li-Mg-

development for CSP. Look Ahead based on

SiO4 using crystal structure prediction (CSP) by

Quadratic Approximation (LAQA), which is

CrySPY [1]. We investigate whether it is

one of the selection-type algorithms wepossible to synthesize structures with high ionicpreviously developed [3], can control the

conductivity by changing the ratio of Li to Mg

optimization priority of the candidates. We

from

CSP

have proposed an improved score of LAQA,

simulations with random search. In the CSP

where the stress term is added to overcome thesimulations, first-principles calculations were

drawbacks

carried out using the VASP code [2], and asimulations by this improved algorithm are

generalized

performed

Li2MgSiO4.

We

gradient

performed

approximation

was

of

to

the

previous

investigate

score.

theCSP

searchingemployed for exchange-correlation functional.

efficiency for typical materials such as Si (16The compositions calculated in this study were

atoms), Al2O3 (10 atoms), NaCl (16 atoms), andLi2MgSiO4,

andSrCO3 (20 atoms). We used the CrySPY code

Li2.5Mg0.75SiO4. The number of searching trials

for the CSP simulations. For the system offor each composition was 200, which were

SrCO3, we employed the VASP code to

conducted using the ISSP supercomputer. Ourevaluate the energy and to carry out the local

calculated formation energies showed thatstructure

Li2MgSiO4 can be synthesized, however,supercomputer. For the other systems, theLi1.5Mg1.25SiO4are

QUANTUM ESPRESSO was also used. The

unlikely to be synthesized, leading to phasetotal-energy calculations were performed using

separation. These results are consistent with ourthe density functional theory with the projector-

experiments. Therefore, it is difficult toaugmented wave method. The generalized

synthesize solid electrolytes in the system ofgradient approximation was used for exchange-

Li-Mg-SiO4 except for Li2MgSiO4.

correlation functional. Figure 1 illustrates theLi1.5Mg1.25SiO4,

and

Li2.5Mg0.75SiO476

optimization

using

the

ISSP

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

number of total optimization steps required toReferences

find the most stable structure, obtained by the[1] T. Yamashita, S. Kanehira, N. Sato, H. Kino,

CSP simulations using random search (RS),H. Sawahata, T. Sato, F. Utsuno, K. Tsuda, T.

Greedy, and LAQA. The searching efficiencies

Miyake, and T. Oguchi: Sci. Technol. Adv.

of LAQA with the weight parameter of stress

Mater. Meth. 1 (2021) 87.

wS of 10 (red bars in Fig. 1) are not always the[2] G. Kresse and J. Furthmüller: Phys. Rev. B

best, however, it demonstrates high searching

54 (1996) 11169.

efficiency on various data sets. In other words,[3] K. Terayama, T. Yamashita, T. Oguchi, andthe introduction of the stress term makes

K. Tsuda, npj Comut. Mater.: 4 (2018) 32.

LAQA more robust and versatile [4].

[4] T. Yamashita and H. Sekine: Sci. Technol.
Adv. Mater. Meth. 2 (2022) 84.

Fig. 1: Number of total optimization steps required to find the most stable structure.

77

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of Exciton Maps for Identifying Active/Inactive
Thermally Activated Delayed Fluorescence Molecules
Yoshifumi NOGUCHI
Department of Applied Chemistry and Biochemical Engineering, Graduate School ofEngineering, Shizuoka University, Johoku 3-5-1, Hamamatsu, Shizuoka 432-8561, Japan
electroluminescencethat our method successfully reproduced thequantum efficiency in the third-generation

spectra. By sandwiching an arbitrary operator

organic light-emitting diodes is based on thewith the exciton wave functions, we estimatedmechanism of thermally activated delayed

the expected values such as the exciton size,

fluorescence (TADF), in which triplet spinelectron-hole separation distance, electron (orexcitons are converted to singlet spin excitonshole) delocalization, and exciton binding

via reverse intersystem crossing (RISC). Theenergy based on two-particle picture andexisting energy barrier between a singlet spin

proposed an exciton map [2]. We revealed that

exciton and a triplet spin exciton, commonly

the TADF active/inactive molecules could be

named as singlet-triplet splitting (Δ!" ), shouldclassified well in the exciton map by choosing

be almost zero for TADF to occur. In recent

the exciton binding energy as the vertical axis

experimental

certainand the ratio of electron and hole delocalization

carbazole benzonitrile (CzBN) derivatives, inas the horizontal axis. Indeed, we concluded

which the carbazole moiety acts as an electronthat there are two kinds of TADF active

donor and the benzonitrile moiety acts as anmolecules existed based on the following: first,

electron acceptor, can be TADF active andthe ratio of electron and hole delocalization wasinactive: nevertheless, their Δ!" are typically

proportional to the exciton binding energy, andabout 0.2 eV. However, we must reconsider thesecond, the hole state spatially localized moremechanism of TADF to completely understandthan the electron.

A

high

internalstudies,

however,it. We have studied the mechanism of TADF
using the first-principles GW+Bethe-Salpeter

References

method and exciton analysis method with

[1] T. Hosokai, H. Noda, H. Nakanotani, T.

exciton wave functions [2]. Before discussing

Nawata, Y. Nakayama, H. Matsuzaki, and C.

the optical properties of CzBN, we compared

Adachi, J. Photonics Energy, 8, (2018) 032102.

the simulated photoabsorption spectra with the[2] Yoshifumi Noguchi, J. Chem. Phys., 155,

available experimental spectra and confirmed(2021) 204302.

78

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Maximization of interface magnetoelectric couplingwith Bayesian optimization
Yoshihiro GOHDA
Department of Materials Science and Engineering, Tokyo Institute of Technology
J1-3, Nagatsuta-cho 4259, Midori-ku, Yokohama 226-8502, JapanTo reduce energy consumption in magnetic
devices, the control of magnetism by the electric current through the magnetic ﬁeld should
be replaced with that by the electric ﬁeld. Interface multiferroicity is promising, because
the magnetoelectric (ME) coupling is muchlarger than that of single phase multiferroics [1]. In addition to choosing optimal materials for ferromagnetic and ferroelectric phases,
the interface modiﬁcation is also a choice to enhance the ME coupling.

density of states close to the Fermi level [2]. In
contrast, the following three cases exhibit tiny
ME coupling. Insuﬃcient occupancy causes
stronger ionicity reducing interaction with Ti.
Excess occupancy makes the hybridized states
too deep. In addition, 4d electrons are too itinerant to have suﬃcient hybridization with Ti.
In addition, the enhancement of the ME
coupling due to the change in the magnetic
anisotropy has also been studied. Changes in
the magnetic anisotropy of a whole ferromagnet by the exchange coupling [5] are further enhanced by the strain eﬀect at the interface [3].

In this project, we performed large-scaleﬁrst-principles calculations of multiferroic interfaces [2, 3, 4].
We explored better
insertion of transition-metal atomic layers
into Fe3 Si/BaTiO3 (001) interfaces using theBayesian optimization.
As is shown in
Fig. 1(a), the Bayesian optimization improved
the interface ME coupling by 55% that is obviously much better than the random search.

(a)

(b)

Figure 1:(a) The Bayesian optimization of
Fe3 Si/BaTiO3 interfaces with inserted atomic layers. (b) The change in the interface magnetic moments.

As a by-product of the Bayesian optimization, we successfully provided an explanation of the mechanism for the multiferroicity enhancement [2]. Figure 1(b) shows thedependence of the change in the interface
magnetic moment on the exchange-correlation
functional and the electron localization controlled by the Hubbard U parameter. The
large ME coupling due to the change in themagnetic moment in V comes from the nearly
half occupied 3d bands causing peaks in the[1] T. Taniyama, J. Phys.: Condens. Matter 27,
504001 (2015).
[2] R. Costa–Amaral and Y. Gohda, Phys. Rev.
Appl. 15, 064014 (2021).
[3] S. Fujii, Y. Gohda, et al., NPG Asia Mater., inpress.
[4] S. Tsuna, R. Costa–Amaral, and Y. Gohda,
submitted.
[5] K. Fujita and Y. Gohda, Phys. Rev. Appl. 11,024006 (2019).

79

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-Principles Design of
Spin-Polarized Bandstructure at MoTe2/Bi2Se3 Interface
Kunihiko Yamauchi
Institute of Scientific and Industrial Research (ISIR-SANKEN), Osaka University, 8-1
Mihogaoka, Ibaraki, Osaka 567-0047

andmay merge. We show that MoTe2 and Bi2Se3

topological properties in various materials bylattices match well and in-plane strain provides

means of the first-principles density functionala handle to manipulate the spin-polarized band

theory (DFT) calculations aiming at thealignment near the Fermi energy. This interface

spintronics application.

shows the various spin degree of freedom, and it

We

are

studying

magnetism

Since last year, we have investigated the

may be useful as an advanced spin generator [2].

magnetic stability in 2D magnetic material VI3

In this year, we also studied the cathodemaking a comparison with CrI3 using the VASP

properties of sodium transition-metal oxides

code at the ISSP ohtaka supercomputer. In VI3,

(such as Na2NiTiO4) by means of DFT

it turned out that under the trigonal crystal fieldcalculations and the machine-learning approachwith D3d point group, the t2g orbital state is split

to reduce reliance on Li-ion batteries and aim at

into a1g and eg’ states. The a1g orbital state plays

the sustainable development goals. We found aan important role in inter-layer magnetic

strong relation between the cation ionic radii andexchange interaction in a bilayer structure. By

the structural stability. This finding may lead tousing Wannier90 code that is interfaced with thethe future industrial application to the sodium-

VASP code, we estimated the hopping integral

ion rechargeable battery [3].

and discussed the inter-layer magnetic exchangeinteraction

based

on

the

References

virtual-hopping

mechanism. This finding may pave a way to the[1] T. P. T. Nguyen, K. Yamauchi*, T. Oguchi,

spintronics application with 2D materials [1].

D. Amoroso, and S. Picozzi, Phys. Rev. B 104,

Next, we explored a heterostructure that

014414 (2021).

consists of transition-metal dichalcogenide and[2] K. Yamauchi, R. Shimazu, and T. Oguchi, J.

3D topological-insulator to investigate thePhys. Soc. Jpn. 91, 044705 (2022).

hybrid spin state in which the out-of-layer spin[3] K. Yamauchi, H. Momida, and T. Oguchi, J.

polarization and the helical spin polarization

Phys. Soc. Jpn. 91, 034704 (2022) .

80

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles lattice-dynamics calculations
for negative-thermal-expansion materials
Yasuhide Mochizuki,1 Soungmin Bae,2 and Hannes Raebiger2
1

Department of Materials Science and Engineering,Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo
2

Department of Physics,

Yokohama National University, Yokohama 240-8501
Negative-thermal-expansion(NTE)materials have attracted considerable attention
because they contribute to sustaining largely
expanding materials and also because of theirfascinating

andcounter-intuitive

thermalproperties. The well-known and representative
NTE materials are Si [1], ReO3 [2], ScF3 [3]ZrW2O8 [4] and KZr2P3O12 [5]. Since the reportsof negative thermal expansion in various
materials in the past few decades, it has been
widely known that the mechanism for NTE is thetransverse acoustic phonon modes, which havenegative Grüneisen parameters. However, thedetailed mechanisms for the NTE properties are
uncovered ever since now. Here, we report ourprogress for elucidating the microscopic origin

Fig 1. Calculated phonon bands for (a) Si, (b)of NTE in Si, ReO3, and KZr2P3O12.
Our

first-principles

calculations

ReO3, and (c) KZr2P3O12 and Grüneisen

wereparameters for (d) Si, (e) ReO3, and (f)performed by using the projector augmented-

KZr2P3O12. The red and blue respectively

wave method [6] as implemented in VASP

indicate the degrees of positive and negative[7]. The phonon band structures were derived

values of Grüneisen parameters.

from the calculated force constants using
calculation results of phonon band with

PHONOPY [8].

Grüneisen parameters for Si, ReO3, andAs shown in Fig. 1, we present the81Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoKZr2P3O12. From Figs. 1(a, b, d, e), one can seethat the zone-boundary phonon modes in Si and
ReO3 generate negative Grüneisen parameters,
triggering the NTE. In Si, the most importantphonons for realizing NTE are the atomic
vibration eigenvectors which transform as
irreducible representations X4 and L3–. On theother hand, in ReO3, the most important phonons
for the NTE are the eigenvectors transforming as+

Fig 2. Theoretical and experimental thermal–

irreducible representations M2 and R5 . The+

expansion coefficients for KZr2P3O12. The blue–

phonon modes of M2 and R5 correspond to theand red colors respectively indicate the results

ReO6 octahedral rotations. Note that these zone-

from calculations and experiments. The redboundary phonon modes of Si and ReO3 are low-

broken line is derived by least-square method.

energy transverse acoustic phonon modes. It is

References

also noteworthy that transverse acoustic phonon[1] S. Biernacki and M. Scheffler, Phys. Rev. Lett.

modes do have crystal momentums, which

63, 290 (1989).

clearly indicate that they must be Brillouin-[2] T. Chatterji et al., Phys. Rev. B 78, 134105

zone-boundary phonon modes. Very intriguingly,(2008).

however, as shown in Figs. 1(c, f), a Brillouinzone-boundarymode

transforming[3] B. K. Greve et al., J. Am. Chem. Soc. 132,as

15496 (2010).

irreducible representation Γ2+ in KZr2P3O12[4] C. Martinek and F. Hummel, J. Am. Ceram.

contributes to NTE the most. These results

Soc. 51, 227 (1968); T. A. Mary et al., Sciencesuggest that not all negative Grüneisen

272, 90 (1996).

parameters are from transverse acoustic phonons.

[5] W. Miller et al., J. Mater. Sci. 44, 5441

Further, to confirm the validity of our(2009).

calculation results for KZr2P3O12, we also

[6] P. E. Blöchl, Phys. Rev. B 50, 17953 (1994).

prepared the polycrystal of KZr2P3O12 and[7] G. Kresse and J. Furthmüller, Phys. Rev. B

examined the thermal expansion coefficient byconducting

X-ray

diffractionin54, 11169 (1996); G. Kresse and D. Joubert, ibid

relevant

59, 1758 (1999).

temperatures. As shown in Fig. 2, our[8] A. Togo and I. Tanaka, Scr. Mater. 108, 1

calculations are qualitatively consistent with the(2015).

experimental results.

82

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analyses on electronic structure and magnetoelectric effect inhigh-performance spintronics and magnetic materials
Tatsuki ODA1,2, Ko HYODO2, Daiki YOSHIKAWA2, Daichi TAKAGI2, Masao OBATA1,2
1

Institute of Science and Engineering, Kanazawa University, Kanazawa, Ishikawa 920-1192
2

Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa,
Ishikawa, 920-1192
We have studied several systems in high-was evaluated using the total energy (TE) andperformance spintronics and magnetic materials

grand-canonical force theorem (GCFT) [1,2].

on electronic structure and magnetoelectric

Our self-consistent calculations revealed that theeffect. In these investigations, we took someintra-c-plane AFM configuration was stabilized

attempts for improving physical accuracy oras the ground state for both of the materials. The

finding new candidates in the materials of

MCAE is obtained to be negative, indicating a

spintronics application. Here, we report thefavor of in-plane anisotropy. The absolute value

developments of (A) investigation on magneticof MCAE tends to decrease as the ratio of latticeanisotropy energy (MAE) in antiferromagnet

constants c/a increases. The SMAE is always(AFM) L10-MnX (X=Ir, Pt), (B) optimization inpositive, reflecting the AFM configuration. In

a computational code for quasi-particle self-

MnPt, we obtained an anisotropy transition inconsistent GW (QSGW) method, and (C)the investigated range of strain, namely, theinvestigation on electronic structure in magnetic

whole MAE became positive (perpendicular toshape memory alloy (MSMA) Ni2MnGa.

c-plane) at larger c/a, from the in-plane(A) MAE in AFM MnX (X=Ir, Pt)

anisotropy. Through this investigation, theWe investigated the control of magnetic

approach GCFT was confirmed to be an efficient

properties by structural strain using the first-

approach to analysis of MAE.

principles calculations based on spin-density(B) QSGW method

functional theory (SDFT) in L10-type Mn alloy;

It is well known that the DFT suffers from

MnIr and MnPt. Contributions to the MAE weremany deficiencies such as small band gap,

calculated from both the magnetocrystalline

electron over binding property, etc.. To improveanisotropy energy (MCAE) arising from thethese deficiencies, extension methods of DFT

spin-orbit coupling and the shape magnetic

such as DFT+U have been developed. However,anisotropy energy (SMAE) arising from thethey often have a semiempirical character, andmagnetic dipole interaction energy. The MCAE

are not universal and parameter-free. In the other83

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

decrease in parallelization efficiency was foundto be due to the communication time among PEs.
(C) Electronic structure in Ni2MnGa
Recent results on Ni2MnGa show that themodulatedmartensite

phase

is

more

energetically stable than the non-modulated(NM) phase, supporting an importance ofelectron-correlation effect [4]. The GGA+U

Fig. 1: Speedup factor in the new code.

reveals that the stability of the austenite andhand, QSGW is a universal approach to themartensite phases is dependent on U. We

reliable prediction of electronic structure [3].

investigated the electronic structure of MSMA

The idea of QSGW is an optimization of the one-Ni2MnGa using QSGW [4,5]. The Ni eg orbitals

body Hamiltonian by performing a self-

in the cubic (austenite) phase, which lead toconsistent

many-bodymartensite phase transition by band Jahn-Teller

approach with GW approximation, where theeffect, were found to locate on the Fermi level.

self-consistency is constructed to minimize the

The NM and 4O structures of Ni2MnGa were

perturbation. QSGW has already had success incalculated with QSGW. The peak of density ofthe estimation of band gaps and other properties

states near the Fermi level for the minority-spin

for a wide range of materials. The requirement

channel was located above the Fermi level into be paid is computational cost. QSGW needs

NM and below the Fermi level in 4O. Thisroughly 100-1000 times more expensive in

difference might be related to the presence ofcomputational time than DFT. We parallelized

nanotwin double layer in modulated martensite

the part of calculation for the polarization

phases.

function (PF) in GW approach, which is one ofReferences

the most expensive (time-consuming) parts in[1] I. Pardede et al., J. Magn. Magn. Mater., 500,

QSGW. As a result, the computational time of

166357 (2020).

PF was reduced from 11 hours to 1 hour in the[2] I. Pardede et al., Crystals 10, 1118 (2020).

application to 4O structure (16 atoms in the unit

[3] T. Kotani, J. Phys. Soc. Jpn. 83, 094711

cell) of Ni2MnGa. The parallelization efficiency,(2014); ecalj: https://github.com/tkotani/ecalj/.

as shown in Fig. 1, was almost ideal when the[4] M. Zelený et al., Materials&Design, 209,

number of processor elements (PEs) was small,

109917 (2021).

but decreased as the number of PEs increases;[5] M. Obata et al., submitted, (2022).

calculation

in

the

with an efficiency of 60% at 30 PEs. This

84

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Prediction of new crystal structures based on the densest ternary sphere packings

Ryotaro Koshoji and Taisuke Ozaki
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
Densest unary sphere packing was proven to

P6/mmm symmetry, and if a line of small spherebe the FCC structure in the 2000s, but thein the (4-3-1) structure is replaced of one small

densest binary and ternary sphere packings havesphere, we can get the crystal of 𝑆𝑚𝐶𝑜5. Note

not yet been identified analytically. To discoverthat we name a PDTSP consisting of 𝑙 small, 𝑚

the unknown putative densest packings, we havemedium, and 𝑛 large spheres per unit cell as (𝑙-created an algorithm to explore them, and we𝑚-𝑛) structure, and the small, medium, and large

successfully found the 12 putative densest

spheres in figures are represented by pink,binarywithyellow, and purple balls, respectively. The (9-7-confirming the known PDBSPs with a small3), (10-6-3), and (13-3-1) structures can becorrection of the phase diagram [1].

derived from the Perovskite structure, and they

spherepackings(PDBSPs)

On top of the success of the discovery, we

have the 𝑃𝑚3̅𝑚 symmetry. Remarkably, an

planned to explore the putative densest ternaryedge of unit cell of the (9-7-3) structure issphere packings (PDTSPs). If we only search theconstituted by a line of four medium spheres.

periodic packings of 𝑛 different sizes of spheres,

The (13-2-1) has the 𝐹𝑚3̅𝑚 symmetry. Largethe packing fraction at a given composition ratio

spheres constitute the FCC structure without

is maximized by filling the space with not morecontact, and a tetrahedral site is occupied by one

than 𝑛 kinds of packing structures. Since no

medium sphere. The medium and large spheres

seminal study seems to construct the phaseare surrounded small spheres constituting semi-

diagram, we made the ternary phase diagrams toidentify the PDTSPs that are denser than any
other combination of packing structures. The
example of the ternary phase diagram is shownin Fig. 1.
As a result, we have discovered the 59 kindsof PDTSPs [2,3]. The newly found PDTSPs
have unique structural properties, and some of

Fig.1: An example of ternary phase diagram

them have high symmetry. The (4-3-1) has the85Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

regular polyhedrons. This structure is predicted

hydrides that have the isotypic crystal structures

to become the PDTSP at the several radius ratios

to the (13-2-1) and (13-3-1) structures, but thesuch as 0:44 : 0:64 : 1:00, at which small andcalculations have not yet been finished.

medium spheres would be too large to be placed

The computational cost of the structuralin the tetrahedral and octahedral sites if large

optimizations is low, so all the process can be

spheres comprising the FCC structure withfinished in one processor, so the exploration ofcontacts. Finally, large spheres in the (16-2-2)

the structures was effectively parallelized.

structure are surrounded by the network

References

structures of small and medium spheres.
The six exemplified PDTSPs might be used

[1] R. Koshoji, M. Kawamura, M. Fukuda and T.

as the structural prototypes for crystals under

Ozaki: Phys. Rev. E 103 (2021) 023307.

pressure. For example, the (13-2-1) and (13-3-1)[2] R. Koshoji and T. Ozaki: Phys. Rev. E 104

structures might be realized by metal hydrides(2021) 024101.

with replacing small spheres of hydrogen atoms.

[3] R. Koshoji and T. Ozaki: arXiv:2110.15505

We have been exploring the quartic metal

Fig. 2: (4-3-1)

Fig.3: (9-7-3)

Fig.4: (10-6-3)

structure

structure

structure

Fig.5: (13-2-1)

Fig.6: (13-3-1)

Fig.7: (16-2-2)

structure

structure

structure86

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Low Thermal Conductance Generated by van Der Waals
Interaction
Masato OHNISHI
Department of Mechanical Engineering,
The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

Clathrate compounds are promisingphonon (SCP) theory [1] and unified

candidates

theory [2]. The SCP theory is used toforthermoelectricmaterials in terms of the “electron-

considercrystalanharmonic potential and to obtainphonon-glass”

concept.

effectsofforth-order

Clathrate compounds are composed

temperature-dependentof guest atoms encapsulated ininteratomic force constants (IFCs).

cagelike structures. It is expected

Using the unified theory, one canthat electrons can transport in theconsider the coherent contribution,framework

lessthat of interbranch tunneling, toforheat transport as well as thephonons because of guest atoms

population contribution, which isleading

phononconsidered also in the context of

scattering. Particularly, in type-I

Peierls Boltzmann transport theory.

clathrate compounds, guest atoms

We

vibrate in a strong anharmonic

package [1] to perform the above

potential because they are composed

approaches and VASP to calculate

of a Weaire-Phelan structure, which

forces on atoms.

scattering

with
rate

to

much
than

that

significant

divides a space with the maximum
volume

with

the

same

have

employedharmonic

ALAMODE

While phonon dispersion haveimaginarycross-(negative)

frequencies

sectional area (Fig. 1(a)). In thiswhen guest atoms have negative

study,

harmonic

wehavestudies

type-I

potential

atlow

Ba8Ga16X30 (BGX, X = Si, Ge, Sn) totemperatures, negative frequencies

gain insights of the effect of phonon

becameanharmonicity on heat transport.

temperatures, as shown in Fig. 1(b).

Phononproperties

positiveatfinitewere

For type-I BGSn, harmonic potential

calculated with the self-consistentwas positive above 100 K, and87

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Fig. 1 Phonon properties of type-I clathrate compounds. (a) Crystal structures of typeI clathrate. (b) Phonon dispersion of Ba8Ga16Sn30 (BGSn) without considering
renormalization (grey), at 300 K (blue), and at 600 K (red). (c) Temperature-dependent
thermal conductivities of BGSn. Population (blue), coherent (orange), and electron(green and red) contributions were considered.

thermalconductivities

could

be

temperature-dependence of type-I

calculated at this temperature range.

clathrate at low temperatures (≈ 10

The

thermalK) have been widely studies, we haveall

revealed

calculated

conductivities

includingtheintriguing

phononcontributions (population, coherent,

properties at high temperatures inand electron contributions) were in

type-I clathrate [3].

good agreement with experimental
data, as shown in Fig. 1(c). To gain

References

insights into the effect of phonon[1] T. Tadano and S. Tsuneyuki, J. Phys. Soc. Jpn.

anharmonicity,

87, 041015 (2018).

we

have

also

analyzed mode dependent phonon[2] M. Simoncelli et al., Nat. Phys. 395, 1 (2019).

properties at high temperatures in[3] M. Ohnishi et al., arXiv:2103.00413.

details (> 100 K). While a unique

88Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

A Unified Understanding of Thermodynamic
Properties in Icy Planets and Icy Moons
Yu KOMATSU†‡ , Terumasa TADANO ¶ , Yasunori HORI†‡†
Astrobiology Center, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan.
‡
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan.
¶
Research Center for Magnetic and Spintronic Materials,
National Institute for Materials Science, Tsukuba 305-0047, Japan.
The high-pressure properties of hydrogensulfide have drawn considerable attention interms of its superconductivity and metalization [1]. Astronomical observations have detected H2 S from the atmosphere of icy planets(ice giants) like Neptune and Uranus [2, 3], andalso in plumes coming from the interior oceanof Enceladus, a Jupiter icy moon [4]. Thesefindings provide insight for estimating the interior of icy bodies and their physical and chemical origins. Although H2 S would be one of thetypical minor components of ice mantle in icy
planets and satellites inside and outside oursolar system [5], the phase diagrams and properties of H2 S and its mixture have not yet been
revealed, especially at high P -T conditions.
Our project aims to elucidate possible mixing states and thermodynamic conditions in
the icy bodies by ab initio calculations. We
focus on the properties of H2 S as the first onset from the interest above and perform density functional molecular dynamics (DFT-MD)
simulations for H2 S in the temperature rangeof 500 ∼ 10,000 K and the density range of 1
∼ 5 g/cm3 using the Quantum ESPRESSO
package. More than 10 ps for MD simulations
are allowed after thermal relaxation with a 2 ×
2 × 2 supercell containing 32 H2 S molecules,
and the ion temperature is controlled in the
N V T ensemble with an energy cutoff of 80 Ry.
Pressures in our calculations were up to ∼250 GPa, corresponding to the values at the

Figure 1: Radial distribution function gHS for
Pmc21 structure.

deep mantle of ice giants [6]. Figure 1 presents
the radial distribution function between H andS atoms for Pmc21 phase of H2 S. The fluid
phase emerged at higher temperatures (e.g.,∼3,000 K with 3 ∼ 5 g/cm3 ), and at lower
densities like 1 g/cm3 , the phase appeared atmore higher temperatures. Moreover, diffusion coefficients in Figure 2 implicate the transition from the solid phase to the superionicand then to the fluid, like H2 O and NH3 [6].
The difference in diffusion between hydrogenand sulfide becomes more prominent at higher

89

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo[6] Cavazzoni, C.; Chiarotti, G. L.; Scandolo,S.; Tosatti, E.; Bernasconi, M.; Parrinello,
M. Science 1999, 283, 44–46.

Figure 2: Diffusion coefficient of H and S for
Pmc21 structure.
temperatures (all the conditions are not plotted in Figure 2). Thermodynamic quantities,e.g., free energy, are being evaluated, and an
equation of state (EOS) including H2 S is being constructed, which are significant for understanding conditions realized in icy bodies.
The computation was partly carried out using the computer resource offered under the
category of General Projects by the ResearchInstitute for Information Technology, Kyushu
University.

References[1] Li, Y.; Hao, J.; Liu, H.; Li, Y.; Ma, Y. The
Journal of Chemical Physics 2014, 140,
174712.
[2] Irwin, P. G. J.; Toledo, D.; Garland, R.;
Teanby, N. A.; Fletcher, L. N.; Orton,
G. A.; Bézard, B. Nature Astronomy 2018,
2, 420–427.
[3] Irwin, P. G. J.; Toledo, D.; Garland,R.; Teanby, N. A.; Fletcher, L. N.; Orton, G. S.; Bézard, B. Icarus 2019, 321,
550–563.
[4] Waite, J. H., Jr; et al. Nature 2009, 460,
487–490.
[5] Johnson, T. V.; Mousis, O.; Lunine, J. I.;
Madhusudhan, N. The Astrophysical Journal 2012, 757, 192.

90

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles transport calculations for single-molecularjunctionsTatsuhiko OHTO
Graduate School of Engineering Science,
Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531
Single-molecule devices attract attentions

the MD trajectory. We observed that the peak top

because of possible bottom-up construction,

value largely depends on the molecular junction

potential

structures.

fordeviceminiaturization,andutilization of unique electrical responses oforganic materials. Since it is not possible todirectly observe the bridging structure of themolecule between electrodes, the presence of themolecule should be confirmed through theconductancehistogram.

The

conductancehistogram is normally broad, ranging orders of
conductance values, while conventional firstprinciples transport calculations are performed

Fig. 1: Snapshots of the molecular dynamics

only for the most stable structure, which is

trajectory.

assumed to be the peak top value of the
conductance histogram. A combined molecular
dynamics and transport calculation is required toreproduce the broad conductance histogram anddiscuss the structure-property relationship.
In this work, a reactive force field to simulate
the break junction procedure has been developed.

Fig. 2: Calculated conductance histograms for

Three junction structures (on top, bridge, and

Au-BDT-Au molecular junctions.

hollow) were prepared and 200 break junctions
for each structure were simulated using theReferences

molecular dynamics (MD) method. We further[1] A. R Rocha et al. Phys. Rev. B 73, 085414

performed first-principles transport calculations(2008).

using the SMEAGOL codes for the snapshots for91

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study ofquantum transport in nanostructuresNOBUHIKO KOBAYASHI
Department of Applied Physics, University of Tsukuba
1-1-1 Tennodai Tsukuba Ibaraki 305-8573

An atomic-scale understanding of quantum
transport properties in materials is an important issue in materials science and nanotechnology. The aim of this project is to reveal
and predict quantum transport properties inmaterials from first-principles. We have developed the nonequilibrium Green’s function(NEGF) method, and the O(N) time dependent wave-packet diﬀusion (TD-WPD) methodon the basis of the density functional theory(DFT). By using these methods, we have investigated charge, head and spin transport properties of materials. [1]We have developed a Simulation code for
Atomistic Kohn-sham Equation (SAKE) for
the ab-initio electron transport calculation
based on the DFT and NEGF formalism. [2]We have applied the method to analyses ofthermoelectricity of Heusler compounds. The
electronic structures and thermoelectric properties are analyzed, and high performance systems are designed.

Figure 1: Schematic pictures of the C8 DNBDT monolayer organic field-eﬀect transistor.
attention, since the ionic liquids induce an intense electric field at a semiconductor interface, resulting in a high concentration of charge
carriers. We elucidated that strong electricfields and highly doped charges induce significant modulation eﬀects on the electronic band
structure and the mobility.

We developed the O(N) TD-WPD method
for the quantum transport calculation of hugesystems of up to 100 million atoms a decadeago. It is possible to calculate the conductivity and the mobility of the system withmicron-order lengths at room temperature at
the atomistic levels. We have recently expand
the method to analyze thermoelectric properties, and demonstrated Seebeck coeﬃcient andpower factor calculations for a huge system of
100 million atoms.

References[1] N. Kobayashi, H. Ishii, K. Hirose, in 3D Local Structure and Functionality Design of Materials eds H. Daimon, Y. C. Sasaki (World
Scientific, 2018) p133.

Furthermore, we have analyzed the gate induced modulation eﬀects of electronic statesin monolayer organic field-eﬀect transistor as
shown in Fig. 1. [3] Organic field-eﬀect transistors with ionic liquids have attracted much[2] H.Takaki, N.Kobayashi, K.Hirose,
J. Phys.: Condens. Matter. 32 325901(2020)[3] H. Ishii, N. Kasuya, N. Kobayashi, K. Hirose,
S. Kumagai, S. Watanabe, and J. Takeya,
Appl. Phys. Lett. 119 223301 (2021).
92

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study on charging-induced structure phasetransitions of thin film oxides
Takashi NAKAYAMA
Department of Physics, Chiba University
1-33 Yayoi, Inage, Chiba 263-8522
HfO2 has various crystal structures dependingon the growth conditions. Although the orthorhombic (Ortho) HfO2 is thermodynamicallyunstable, it can be grown on metal electrodesubstrates such as TiN and Pt and has giant
ferroelectricity, thus being expected as a promisingmaterial for future memory devices. However, it
has not been clarified why such unstable Orthophase is realized in experiments. In this work, we
study the stabilization mechanism of Ortho HfO2
phase using the first- principles calculations.
Since the ferroelectric phase of representative
BaTiO3 is normally realized by the substrateinduced strain, we first consider the effect of strain.
Fig.1 shows formation energies of stablemonoclinic (Mono) and unstable Ortho phases inbulk and thin-film forms as a function of thecross-section area, i.e., biaxial strain. The energy
increase in thin films occurs due to the surface
energy loss. As seen in both figures, by applying
tensile or compressive strain, the Mono phaseincreases the energy compared to the Ortho phase.
This is because the Mono phase is stabilized bylowing its crystal symmetry and the deformationfrom such stable structure promotes large energy
loss. However, the Ortho phase always has larger
energy than the Mono one. Thus, the strain is not asingle origin of the Ortho-phase formation.
Next, we consider the effect of oxygen vacancy(Vo), which is a representative defect and is often
generated in oxides. Vo produces an electronoccupied state below the conduction bands, thus
stabilized by the positive ionization. Fig.2 showsthe energy difference between Ortho and Monophases as a function of Vo ionization charge. From
this figure, we know that the Ortho phase becomesFig.1. Calculated formation energies of Mono andOrtho HfO2 in bulk (left) and thin-film (right)
forms under (111) biaxial strain, relative to themost stable Monoclinic bulk phase, as a functionof an area of formula unit.

Fig.2. Calculated difference in energy between
Ortho and Mono phases in bulk forms, as afunction of the ionization charge of oxygen
vacancy (Vo). The zero energy corresponds to the
Mono phase.

the most stable when the 4-5% Vo’s exist and they
are +2 charged. However, considering that theformation energy of Vo, is relatively large around
4-5eV, the assumed composition 4-5% is still large.
Thus, the ionization of Vo is also not a single originof the Ortho-phase formation.

93

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Fig.4. Calculated local-potential profile around
Ortho HfO2 (001) thin film. To correct theperiodic boundary condition of the repeatedslab geometry, the artificial electrodes areinserted in vacuum region so as to keep thehorizontal potential.

calculation method using the thin film geometry
should be developed. Thus, we try to calculate thepolarization charge using the conventional
repeated-slab unit cell.
Due to the cancellation of electric fields causedby the front and back surfaces of the film, thepotential should be flat outside the ferroelectric film.
To realize such situation, we arrange the artificial
electrodes (dipole) in the vacuum region in the unit
cell, as shown in Fig.4. Then, we calculate thepolarization charge using the Ortho HfO2 (001) thinfilm. The calculated polarization charge is about
53μC/cm2, which agrees with the values by the
Berry phase method around 40-50μC/cm2 and theobserved values around 40μC/cm2. In the future,
we will use this method and study how thepolarization changes with varying the substrate.
All these calculations were performed using thexTAPP, VASP, and our original pspwf codes. In
order to realize the calculations for the present
thin-film systems, because the system is made of alarge number of atoms (1000-2000 atoms), theadvanced computing facility having multi-task andhigher-speed CPU (more than 1280 cores × 2.0GHz), larger-size memory (around 256GB), andlarger-size strange (more than 2 TB) is indispensable. These conditions are realized only by thepresent ISSP supercomputing systems.

Fig.3. Calculated difference in energy between
Ortho and Mono phases in thin-film forms,
with/without 1-4% strain and 3% charged
oxygen vacancy (Vo). The cases of (a) (111)tensile strain and (b) (001) compressive strain
are shown.

Then, we consider the case when both the strain
and the Vo ionization coexist in HfO2. Fig.3 showsthe energy difference between Ortho and Monophases for the cases with/without strain and Vo
charging. Figures 3(a) and 3(b) respectively
correspond to the cases of (111) tensile strain and(001) compressive strain. It can be seen that boththe strain and the Vo charging work cooperatively
to stabilize the Ortho phase. In these ways, we canconclude that not only the substrate-induced strain
but also the ionization of Vo are important factors
to grow and stabilize the ferroelectric Ortho phase.
Finally, we consider the ferroelectricity of Ortho
HfO2. It is well known that the polarization chargeof ferroelectric material can be calculated by the
Berry phase method using the bulk unit cell. The
result by this method corresponds to the freestanding ferroelectric film located isolate in thevacuum. However, in experiments, such material isgrown on some substrates. In order to study theeffect of the substrate on the ferroelectricity, the94Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Elucidation of surface structure and reactive property of (100)exposed CeO2 nanocubes through first-principles calculation
Akira Yoko
Advanced Institute for Material Research,
Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai, Miyagi 980-8577
CeO2 nanocubes with (100) facet exposed

Cr2O3 and CeO2 [3]. The Monkhorst-Pack k-have been synthesized by supercritical method,point mesh of 4×4×4 was used for the unit celland it was found to have high oxygen storageofcapacity. In this study, the stabilization of the

conducted with supercell of 2 × 2 × 2 extension(100) facet by organic modification was studied(96 atoms).The slab model exposing (100) facet

by using first-principles calculations.

includes 60 atoms, and that for (111) facet

Another approach to improve oxygen

CeO2.

The

defectsimulations

were

includes 108 atoms. The Monkhorst -Pack k-

storage capacity of CeO2 is metal doping into

point mesh for the slab model was 4×4×.

the structure. In this study, Cr-doping into CeO2

Figure 1a and 1b show CeO2 (100) and (111)

was also studied. The structural effects bysurface structure. The (111) facet of CeO2 isdoping were investigated.

nonpolar, contrary to the polar surface of (100).

In this study, first principles simulations

For the (100) facet model, half of the oxygen

based on density functional theory (DFT) was

was moved to the other side to exclude polarity

conducted. Plane wave basis DFT simulations

keeping the CeO2 composition. The surface

were conducted using VASP code. Structures ofenergy obtained from these calculations were

CeO2 at surface and bulk were calculated with

1.46 J/m2 for (100) and 0.78 eV/m2 for (111).

generalized gradient approximation proposed

The CeO2 (111) is more stable than CeO2 (100).

by Perdew, Burke, and Ernzerhof (PBE) [1].

The instability of (100) is the origin of high

The

the

activity as catalysts. When CeO2 is synthesized

pseudopotentials were 5s25p64f15d16s2 for Ce,

with organic surfactant, it is known that (100)3s23p63d54s1 for Cr, and 2s22p6 for O. The

facet exposes. In Figure 1c, structure of

DFT+U method introduced by Dudarev et al.

carboxylic acid attachment on CeO2 (100) is[2]was used to treat electron localization. The

shown. When calculating carboxylic attachment,

parameter U-J was set to 3.5 eV for Cr3d, 5.0

dipolar correction implemented in VASP waseV for Ce4f, and 5.5 eV for O2p states,used. After the deprotonation of the carboxylic

respectively, based on previous studies ofacid one oxygen of COO locates between twovalenceconfigurationsof95

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ce atoms and the other oxygen locates on one

exists as 4+. Figure 2c shows the structure that

Ce atom. The adsorption energy was found to

one of the oxygen coordinating Cr (O-1 inbe -26.6 kJ/mol. The apparent surface energy

Figure 2b) was removed. As a result of the

includingvacancy introduction, local structure around Cr

theadsorptionenergyofthechanged to six-coordination, and Cr became 3+

surfactant is lower in (100) than (111).

state, and the oxygen vacancy formation energy
was 0.99 eV. The significant decrease inoxygenvacancyformationenergywasobserved. Also in this case, Ce3+ exits in thenext nearest neighbor of oxygen vacancy.
Further oxygen removal (O-2 in Figure 2c)occurred with lower oxygen vacancy formationenergy as 0.65 eV. The local structure and thevalence of Cr did not change, and two more
Ce3+ are formed at the next nearest neighbor of

Fig. 1 Surface structures of CeO2. a) CeO2
(100),b) CeO2 (111),

the oxygen vacancy. At the vicinity of Crc) Carboxylic aciddopant oxygen vacancy can be formed easily.

adsorption on CeO2(100).

Moreover, an oxygen atom, which is not at theThe bulk calculation was conducted tonext of Cr surrounded by four Ce4+ (O-3 inobtain the oxygen vacancy formation energy in

Figure 2d) was removed. As a result, thethe Cr-doped system. The supercell consisting

structure shown in Figure 2e was obtained. For

96 atoms were used. Figure 2 shows the local

the three oxygen vacancies, one Cr3+ and 5

structureThe

Ce3; was formed. Five Ce3+ locates not at the

information about the structures is summarizednearest neighbor (NN) of oxygen vacancy but

in Table 1. Figure 2a shows the pure CeO2,

at the next nearest neighbor of the oxygen

which includes an oxygen vacancy. Two Ce3+

vacancies. The oxygen vacancy in this case wasions exist in the next nearest neighbor (NNN)1.20 eV, and significantly lower than pureof the oxygen vacancy. The oxygen vacancy

CeO2 although the local structure was similar.

formation energy was 2.00 eV. Figure 2b shows

This is not the oxygen vacancies around dopant.

the structure of Cr doped CeO2, which one of

Doping affects whole the structure occurring

the Ce are substituted with Cr. The doping

distortion, which results in the lower oxygen

concentration is corresponding to 3 at%. In thisvacancy formation energy at far position fromcase four oxygen atoms coordinates Cr, and Cr

the dopant.

aroundoxygenvacancies.

96Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 2
substituted

Structure of Cr 3% doped CeO2 a)Non-doped CeO2 with an oxygen vacancy, b) Cr4+
CeO2,c) ～ e)

Cr

doped

97

CeO2

with

1-3

oxygenvacancies

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 1 Structural information about Cr 3% doped CeO2Bader charge, |e|
Structure

Ce3+

Ce4+

Cr3+

Non-doped CeO2
with 1 VO+2.11 +2.44 n/a(Figure 6A)
Cr4+ doped CeO2
n/a
(Figure 6B)+2.45 n/a

Cr4+

O

VO
positionsE(distancefrom Vo
[eV]
Cr)

-1.28
to
n/a
-1.20
-1.24
+2.00 to
No VO
-1.16

Cr3+ doped CeO2
with 1 VO+2.15 +2.44 +1.86 n/a(Figure 6C)
Cr3+ doped CeO2
with 2 VO+2.15 +2.43 +1.85 n/a(Figure 6D)
Cr3+ doped CeO2
with 3 VO+2.13 +2.42 +1.85 n/a(Figure 6E)

Ce3+ positions
relative to VO

2.00

NNN (2Ce3+)

n/a

n/a

-1.26
O-1 in Figure 6B
0.99
to
(2 Å)
-1.17
O-1 in Figure 6B
-1.27
(2 Å)
to
O-2 in Figure 6C
-1.20
0.65
(2 Å)
O-1 in Figure 6B
(2 Å)
-1.37
O-2 in Figure 6C
to
(2 Å)
-1.20
O-3 in Figure 6D
1.20
(6 Å)

NNN (1Ce3+)

NNN (3Ce3+)

NNN (5Ce3+)

発表（投稿）論文等
1．Hao, X., Yoko, A., Inoue, K., Xu, Y., Saito, M., Chen, C., Seong, G., Tomai, T., Takami, S.,
Shluger, A.L., Xu, B., Adschiri, T., Ikuhara, Y.
“Atomistic Origin of High-Concentration Ce3+ in {100}-Faceted Cr-Doped CeO2 Nanocrystals”
Acta Materialia, 203, 116473 (2021)
DOI: 10.1016/j.actamat.2020.11.015
References[1] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys.
Rev. Lett., 77 (1996), p. 38650.
[2] S. Dudarev, G. Botton, S. Savrasov, C. Humphreys, A. Sutton, Electron-energy-loss spectra andthe structural stability of nickel oxide: An LSDA+ U study, Phys. Rev. B, 57 (1998), p. 1505
[3] P.R. Keating, D.O. Scanlon, B.J. Morgan, N.M. Galea, G.W. Watson, Analysis of intrinsic
defects in CeO2 using a Koopmans-like GGA+ U approach, J. Phys. Chem. C, 116 (2012), pp.
2443-2452

98

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Magnetocaloric Eﬀect of Transition-Metal Alloys
Hung Ba TRAN1 and Tamio OGUCHI1,2
1
SANKEN, Osaka University, Mihogaoka, Ibaraki, Osaka 567-0047, Japan
2
CSRN, Osaka University, Machikaneyama, Toyonaka, Osaka 560-8531, Japan

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We study the magnetocaloric eﬀect oftransition-metal alloys by combining ﬁrstprinciples calculations and Monte-Carlo simulations. Several types of the magnetocaloric
eﬀect such as conventional (direct) magnetocaloric eﬀect, giant magnetocaloric eﬀect,
anisotropic magnetocaloric eﬀect, and inverse
magnetocaloric eﬀect can be considered by using our in-house program [1–6]. The peakin magnetization when applying an intermediate magnetic ﬁeld along the hard axis of
CrI3 , a well-known 2D material for the spintronic application, is successfully reproduced
by using our program as shown in Fig. 1.
The origin comes from the competition between magnetic anisotropy and external magnetic ﬁelds, where the temperature dependence of magnetic anisotropy energy plays
the role. The ﬁnite magnetic anisotropy atslightly higher than Curie temperature is reproduced, where the magnetization anisotropy
and anisotropic magnetic susceptibility is the
crucial factor. The high accuracy in the estimation of anisotropic magnetic entropy change
in CrI3 paves the way to predict the magnetocaloric properties of new materials. In thenext step, we have some ideas to enhance theaccuracy and predict some novel propertiesof magnetic materials within the theoreticalframework.

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[6].
[2] H. B. Tran, T. Fukushima, Y. Makino,
and T. Oguchi, Solid State Commun. 323,
114077 (2021).
[3] H. B. Tran, T. Fukushima, H. Momida, K.
Sato, Y. Makino, and T. Oguchi, Comput.
Mater. Sci. 188, 110227 (2021).
[4] H. B. Tran, T. Fukushima, H. Momida,
K. Sato, Y. Makino, and T. Oguchi, Direct and Inverse Magnetocaloric Eﬀects
in FeRh Alloy: A Theoretical Study,
http://dx.doi.org/10.2139/ssrn.3799705.
[5] H. B. Tran, H. Momida, Y. Matsushita,
K. Sato, Y. Makino, K. Shirai, and T.
Oguchi, Phys. Rev. B 105, 134402 (2022).
[6] H. B. Tran, H. Momida, Y. Matsushita,
K. Shirai, and T. Oguchi, Acta Mater.
231, 117851 (2022).

References[1] H. B. Tran, T. Fukushima, K. Sato, Y.
Makino, and T. Oguchi, J. Alloys Compd.
854, 157063 (2021).

99

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo!"#$%&'$(#)*$+",&#+$%*'-,+-+"./*/,0/*-1,2#-/*%.,30-$%*'-+",$+"$0"+%*'-,4,*)5"*$*%,/'"6+%*'-,)'2#" 7!"#$%&'()&*&!"#$%$&$'()*+(,*-%.(,$/$'(012#%3#4
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F$2'D#a$"0D#a#&%% GU[@`H#P`[BD

100

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study of Efficient Training Data Generation Method
for Constructing Artificial Neural Network Force Field III
Kohei Shimamura
Department of Physics,
Kumamoto University, 2-39-1 Kurokami, Chuo-ku, Kumamoto 860-8555
Machine Learning Interatomic Potential

potentials is closely related to pressure. Thus, it(MLIP) not only achieves high accuracy byhas been found that without pressure training,learning

obviousfromfirst-principles

molecular

dynamics (MD) data, but also has low

errors

can

occur

in

thermalconductivity [2].

computational cost. Active Learning is the

Since the current MLIPs are trained not only

driving force behind the recent development ofwith potential energy but also with atomic force

MLIPs. This approach primarily uses theand pressures, the cost function is composed of

uncertainty in the output of MLIPs to discovertheand generate unlearned data for efficiently

training, adjustable coefficients are therefore

constructing robust potentials. In this study, we

introduced into these terms having different

continued to work on improving Active

units and data size. Although previous studies

Learning. The MLIP using artificial neuraldidnetwork (called ANN potential) was used. In

demonstrated that the coefficient adjustment

the previous studies, the use of standard

was a significant effect on the accuracy of ANN

deviation of atomic force is consideredpotentials [3].

effective for finding unlearned data. We havecorrespondingnotemphasize

terms.

theFor

efficiently

importance,weNo matter how efficiently untrained data canalso found that the method worked well.

be obtained, it becomes meaningless if theOn the other hand, we found that the MLIPs

training is inadequate. As the application oftraining method needs to be improved. The

MLIPs expands, the training of pressure and thecurrent standard training method does notcoefficient adjustment would become essential.

guarantee the accuracy of pressure required for

References

MD. We have demonstrated that the training of[1] A. Irie, et al.: J. Phys. Soc. Japan 90,

pressure is essential for ANN potentials to

094603 (2021).

reproduce the solid-liquid phase transition [1].

[2] K. Shimamura, et al.: Chem. Phys. Lett. 778,

Pressure training is also essential for thermal

138748 (2021).

conductivity calculations using MLIPs. The[3] A. Irie, et al.: J. Phys. Soc. Japan 91,

heat flux in the Green-Kubo formula for ANN

045003 (2022).

101

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Structure stability and electronic structures ofpoint defects in wide-gap oxide materials
Hiroyoshi MOMIDA
Institute of Scientific and Industrial Research (SANKEN), Osaka University
8-1 Mihogaoka, Ibaraki, Osaka 567-0047

The wide-gap oxide materials such as Al2 O3
and Ga2 O3 have been attracted great interests
in applications for power electronics devices.
In this work, we have studied the structuraland electronic properties of oxygen defects (vacancies or interstitials) in several amorphousoxides by the first-principles calculations.
The amorphous model structures of a-Al2 O3
and a-Ga2 O3 are generated by the firstprinciples molecular dynamics simulations andthe melt-and-quench techniques. Figure 1
shows an example of the generated model
structures using the 120-atom supercells. The
mass densities are set to be 3.3 g/cm3 for aAl2 O3 and 4.5 g/cm3 for a-Ga2 O3 , which arein their respective experimental ranges and arelower than those of the α crystal phases (4.0
and 6.4 g/cm3 for Al2 O3 and Ga2 O3 , respectively). The O coordination numbers around
Al are four (60.4%), five (29.2%), and six(10.4%) in a-Al2 O3 , and those around Ga are
four (66.7%) and five (33.3%) in a-Ga2 O3 .

(a) a-Al2O3O(b) a-Ga2O3

Al

Ga

0
O Al Oi

Figure 2: Density of states (DOS) of a-Al2 O3
with the excess O (O0i ). Total (black line withleft scale) and O0i (red line with right scale)DOSs are shown. The inset shows the local
structure near O0i , forming the peroxy linkage.
The O defects are introduced by adding andremoving O (interstitials Oqi and vacancies VOq )in the pristine oxide models, considering thecharged states q of defects. In the charge neutral state (q = 0), it is found that O0i tends
to form the O–O peroxy linkage, giving theπ ∗ - and σ ∗ -type O2 -like states near the valenceband top and the conduction band bottom regions, respectively (Fig. 2). It is also foundthat such the O2 -like states show interesting
behavior by changing q, and similar properties
of Oqi are confirmed in a-Ga2 O3 and in several
oxide crystals. We also study electric properties due to VOq in oxides to discuss ReRAM [1].

O

References
Figure 1: Amorphous structures of (a) a-Al2 O3and (b) a-Ga2 O3 120-atom supercell models.

[1] H. Momida and T. Ohno: Appl. Phys. Lett.
117 (2020) 103504.

102

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical study for magnetic-nano-particles formationfrom first-principles calculations
Yasutomi TATETSU
Meio University, Biimata, Nago, Okinawa 905-8585
There is a growing interest in searching novel materials that are not only thermodynamicallystable, but also thermodynamically unstable for applications. Chemical synthesize techniques, which
control nano particles precisely, are being developed in order to find new functional materials fortechnologies. Recently, Teranishi’s group at Kyoto University found a new behavior of crystal
structure transformation for an ionic nanocrystal [1], and a new Z3-type Fe(Pd,In)3 crystal structure,
which was synthesized by introducing a third element of In into L12-FePd3 [2].
In this report, we performed first-principles non-collinear calculations in order to explain thehigher coercivity value in the Z3-Fe(Pd,In)3 structure. We used the ab-initio code, OpenMX [3], forcalculating the magnetic anisotropy energies of L12-(Fe,In)Pd3 and Z3-Fe(Pd,In)3 structures andcompared these energies to find easy axes. In each calculation, the spin directions of each atom inthese systems were set from [001] to [100] when 𝜑 = 0 and from [100] to [110] when 𝜃 = 0. We
found that the magnetic anisotropy energies show −1.38 μeV/atom for the L12-(Fe,In)Pd3 structureand −0.213 meV/atom for the Z3-Fe(Pd,In)3 structure. The easy axis for Z3-Fe8(Pd20,In4) is the c axis,
as shown in the figure. The tendency which the Z3-Fe(Pd,In)3 structure has higher coercivity values
than the L12-(Fe,In)Pd3 structure is consistent with the experimental measurement. We assume that
added In atoms might be one of the reasons toincrease the magnetic anisotropy of the Z3Fe(Pd,In)3 structure. Further theoretical studies areneeded to explain the mechanism of the coercivity
increase in the Z3-Fe(Pd,In)3 structure.

References[1] Z. Li, M. Saruyama, T. Asaka, Y. Tatetsu, and T.
Teranishi, Science, 373, 332 (2021).
[2] K. Matsumoto et al., Nat. Commun., 13, 1047

Figure: Total energy analysis for the Z3Fe(Pd,In)3 structure depending on the spin

(2022).

directions.

[3] http://www.openmx-square.org

103

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Evolutionary algorithm for simulation of fastchemical reaction process
Koichi KUSAKABE
Graduate School of Science, University of Hyogo
Kouto, Kamigori, Hyogo 5-8581

1

Introduction

One methodology in the quantum materials informatics, based on density functional theory
to evaluate many-body correlation eﬀects, hasrecently been used to determine the electronic
phase diagram of oxides [1], to design hightemperature superconductors [2], and spinelectronic devices based on atomic layer material [3]. Materials design of measurementbased quantum computing devices [4, 5], andthe elucidation of unknown photo-induced
phase transitions based on measured data [6]were performed. We have also designed an
activation method of catalytic properties andevolutionary operations for detonation processes.

2

nanographene catalyst, in which multiple active sites are involved in the reaction, conﬁrm that propylene generation from propane
on our catalytic structure has the eﬀect of signiﬁcantly lowering the endothermic reaction
heat.
At the same time, in-situ AI analysis of timedependent small-scale data during the synthesis of catalytic materials was requested toelucidate the experimental procedures. Theoretical analysis of emission spectra during
the material conditioning (activation processby high-energy particle irradiation) was performed. As a result, it became possible to develop a measurement method to support insitu observation of molecular desorption by
adopting machine-learned classiﬁcation using
ResNet.

Alkane dehydrogenation on
3
nanographene catalyst

To support designed activated nanographene
catalysts for dehydrogenation of alkane, several dehydrogenation reaction pathways were
determined based on density functional theory
calculations. The catalytic eﬀect of vacancy
created graphene surfaces is simulated using
the alkane decomposition reaction as an example.
The eﬀect of the atomic defects was investigated, and the eﬀect of lowering the reaction energy barrier due to substitution by nitrogen and other group V elements was conﬁrmed. Furthermore, the characteristics of the

Algorithms for elucidationof detonation reaction paths

We are also promoting the elucidation of thedetonation reaction mechanism by combining
evolutionary algorithms, which reveals oxidation and reduction reactions in the TNT-RDX
composite that produces the detonation diamond. An evolutionary algorithm systematically generates intermediate states of chemical
reaction processes.
Stable crystals initiate rapid chemical reactions triggered by mass transport. We introduced mass transport into the evolutionary algorithm. The basis for the continuation of the104

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

reaction was found by structural optimization
calculations, ﬁrst-principles molecular dynamics calculations, and the migration paths ofradicals within the crystal.
Consider that radical species are supplied toadjacent material phases in the processes ofredox reactions. To determine the initiation
process of this chain reaction, we applied theaccelerated chemical reaction simulation using
the generational operation of the evolutionary
process. We applied this method to oxidationof RDX and reduction of TNT, and conﬁrmedthat our acceleration method works
The initiation point of the detonation process is considered to be the formation of OH
radicals by electron transfer excitation. The
OH radicals pull out hydrogen atoms andrapidly destabilize RDX. RDX then decomposes to form NO2 . (Figure 1 (a), (b))
Hydrogen radicals are supplied to TNT fromthe destabilized RDX. When a certain amountof hydrogen radicals are added, the nitro
groups of TNT are decomposed to generatewater, resulting in nitroso groups. This nitrosogroup functions to join adjacent carbon skeletons. (Figure 1 (c)) From these carbon skeleton linkages, the formation of clusters withlarger carbon skeletons may follow.
By conﬁrming that the supply of hydrogenradicals to TNT and OH radicals to RDX initiate rapid reactions, and by successfully drawing the initial reaction cycle, we conﬁrmed that
our method has potential for providing insight
into real-time evolution problems.

Acknowledgement
The author is grateful to Dr. T. Ishikawa, Mr.
Y. Makino, and Prof. S. Sakamoto for theircollaboration. This work is partly supported
by collaborative joint research in 2021 on “Research of detonation soot as a non-oxidative
dehydrogenation catalyst” and “Study of detonation reaction mechanisms combining molecular dynamics and evolutionary algorithms”

with Daicel engineering science joint researchin Osaka university.

Figure 1: Molecular structures arising from operations of evolutionary algorithms. (a) RDX,
which is destabilized by the addition of hydroxyl radical, generates (b) a water moleculeand simultaneously releases of NO2 . (c) TNT
destabilized by hydrogenation can generate
carbon clusters bridged by NO groups.

References[1] S. Teranishi, K. Nishiguchi, S. Yunoki, K.
Kusakabe, J. Phys. Soc. Jpn., 90, 094707(2021).
[2] S. Teranishi, K. Nishiguchi, K. Kusakabe,
J. Phys. Soc. Jpn., 90, 054705 (2021).
[3] H. Harfah, Y. Wicaksono, G. K. Sunnardianto, M. A. Majidi, K. Kusakabe,
Nanoscale Adv., 4, 117 (2022).
[4] N. Morishita, Y. Oishi, T. Yamaguchi,
K. Kusakabe, Appl. Phys. Express 14,
121005 (2021).
[5] N. Morishita, K. Kusakabe, Phys. Lett. A,
408, 127462 (2021).
[6] M. Nagai, Y. Higashitani, M. Ashida,
K. Kusakabe, H. Niioka, A. Hattori, H.
Tanaka, G. Isoyama, N. Ozaki, Researchsquare, DOI:10.21203/rs.3.rs-130295/v1(Preprint).

105

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study on Hydration Process of Cellobiose by First Principles Calculations
Tomomi Kondo1,2, Daisuke Akazawa1,2, Takehiko Sasaki1，Motoyuki Shiga2
1 Department of Complexity Science and Engineering, Graduate School of Frontier

Sciences, The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8561
2 Center for Computational Science and E-Systems, Japan Atomic Energy Agency

148-4 Kashiwanoha Campus, 178-4 Wakashiba, Kashiwa, Chiba, 277-0871

Cyclizationof

30 water molecules, and acidic molecules suchpolyalcohol in hot water has been proven to be

as HCl added under the same thermodynamic

efficient method for utilization of biomass

conditions as in Experiment [1] (20 MPa, 523 K).

materials [1]. For this purpose we proposed a

CV is defined for each product as shown in Table

new

1. Fig. 2 shows the illustration for 1,4-AHSO3

methoddehydrationofreactionrefinement(improved

metadynamics method: Refined MTD),

andas one example. The dihedral angle φ between

applied it to cyclization dehydration of 2,5-

the hydroxyl group and the main chain, theHexanediol (HDO) [2]. Based on these results

difference d in the O-C distances of leaving and

we studied cyclization dehydration process of d-bonding, and the proton coordination number nsorbitol (SBT) yielding 1,4-Anhydro-d-sorbitolof the hydroxyl group were set according to the(1,4-AHSO),

2,5-Anhydro-d-sorbitol(2,5-

reaction path. Reaction processes in HCl(aq),AHSO)

1,5-Anhydro-d-sorbitol(1,5-

H2CO3 (aq) and pure water were examined.

andAHSO) as shown in Fig. 1.

Fig. 2 Illustration for CV of 1,4-AHSO3Table 1 Definitions of CVs
Fig. 1 Cyclization dehydration process of d-sorbitol.

Calculations were conducted using software
PIMD [3] working with DFTB or VASP. The

According to DFTB based calculations overcalculation system consists of 1 SBT molecule,3 ns dehydration reaction was observed and the106Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

transition state was found on the free energy

barriers for two of the pathways leading to thecontour map at CV with φ =155° , d=0.0 andfive-membered ring products, 1,4-AHSO and

n=2.1. Molecular dynamics calculations were

2,5-AHSO were found to be lower than those

conducted around this transition state so that theleading ot the six membered ring product, 1,5-

real time mechanism is visualized. After proton

AHSO. This is in agreement with experiments

is bonded on the oxygen atom (Fig. 3 ①) thewhere only the five-membered ring products

dehydration (Fig. 3 ②) and the formation of O-

were detected. The reaction pathway to the five-

C bond (Fig. 3 ③) occur almost simultaneously,

membered ring products goes through a

indicating that the five-membered ring is formed

metasbable state of SBT in the confined

via SN2 process.

conformation. These results were published in➀ 0 ps➁ 0.145 ps[4].
n = 2.1

We also calculated ab initio molecular
dynamics (MD) simulations for cellobiose
aqueous solution using PIMD and CP2K

➂ 0.240 ps➃ 0.498 ps

program and the subsequent C-K edge XAS
spectra simulation using CP2K. Experimental
XAS spectra can be interpreted by watermolecules interacting with the cellobiose
molecule [5].

Fig. 3 Reaction process from SBT to 1,4-AHSO

References[1] A. Yamaguchi et al., Green Chem., 13,873 (2011).
[2] T. Kondo et al., J. Comput. Chem., 42, 156(2021).
Fig. 4 Dehydration mechanism for SBT.

[3]http://ccse.jaea.go.jp/ja/download/pimd/in
dex.jp.html.

The mechanism is summarized in Fig. 4. The[4] T. Kondo et al., J. Comput. Chem., 42,

simulation results predict that the reaction is1783(2021).

faster in HCl solution than in carbonic acid[5] D. Akazawa et al., J. Chem. Phys., 156

solution, due to the acid-catalyzed mechanism.

044202 (2022).

In most of the calculated conditions, the reaction

107Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio calculation for structural stability oftransition-metal-oxide superlattice
Kazuma NAKAMURA
Quantum Physics Section, Kyushu Institute of Technology
1-1 Sensui-cho, Tobata, Kitakyushu, Fukuoka, 804-8550

0.20

D H (eV/f.u.)

In this study, we investigate the structural stability of transition-metal-oxide superlattices using first-principles calculations.
We consider superlattices built by polar andnon-polar transition-metal oxides. The polar type is a transition-metal oxide in which
the charge neutrality of the constituent parts
is not maintained, but the entire charge neutrality is maintained. For example, in a perovskite LaAlO3 , it is made as the stacking
structure consisting of a LaO plane charged
with +1 valence and an AlO2 plane charged
with −1 valence. On the other hand, in the
non-polar type, the charge neutrality is maintained including the partial system; for example, in SrTiO3 , it consists of charge-neutral
SrO and TiO2 planes. We consider 10 typesof superlattices consisting of SrTiO3 , SrVO3 ,BaTiO3 , LaAlO3 , CaCuO2 . In the present report, we focus on SrTiO3 /SrVO3 (STO/SVO)
and CaCuO2 /SrTiO3 (CCO/STO) superlattices. Also, we write the superlattice as An /Bn
where A and B specify materials, and n is their
number. We used xTAPP [1](a) STO/SVO

0.5

DH
DHI
DHS

0.15
0.10

(b) CCO/STO
DH
DHI
DHS

0.4
0.3
0.2

0.05

0.1
0.0

0.00
1

2

3

4

5
Number of layers n in [An/Bn]

1

2

3

4

5

Number of layers n in [An/Bn]

Figure 1: Calculated standard formation
enthalpy ∆H(n) (black lines) for the (a)(STO)n /(SVO)n and (b) (CCO)n /(STO)n superlattices. Red and blue lines are an interfacial contribution ∆HI (n) due to the interface
formation, and a strain-storage one ∆HS (n)due to the lattice mismatch.
and

 

∆HS (n)= E(A, akn ) − E(A) + E(B, akn ) − E(B) , (3)respectively. ∆HI (n) is an interface energy
due to the interface formation, and ∆HS (n) is
a strain-storage energy due to the lattice mismatch. Also, ak is an in-plane lattice parameter of the superlattice.
Figure 1 shows our calculated standard forTo discuss the structural stability of the su- mation enthalpy ∆H(n) (black lines), as wellperlattice, we calculate the n dependence of as its decomposition ∆HI (n) (red lines) andthe following standard enthalpy of formation ∆HS (n) (blue lines). Panels (a) and (b) are
the results for STO/SVO and CCO/STO su∆H(n) as
perlattices, respectively. The case ∆HI (n) >∆HS (n) indicates that superlattice does not∆H(n) = ∆HI (n) + ∆HS (n),(1)
develop epitaxially; the STO/SVO superlattice
is stable with the epitaxial growth, while thewhere ∆HI (n) and ∆HS (n) are defined as
CCO/STO superlattice is unstable.
About the optimized structure of the superE[An /Bn ] ∆HI (n)=− E(A, akn )+E(B, akn ) , (2) lattice, the following trends were observed:n108

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo(a) Before relaxation(b) After relaxation

(a)

(b)
−

E
+

E=0
SrO
: Sr, Ba, La: Ti, V, Al

TiO2
Ca
CuO 2

E

:O

E=0

: Ca

: Cu

−
STO
Insulator
+
CCO
Metal
−

E
+

Figure 2: Ferroelectric displacement occurredin the CCO-based superlattice.
1. In the superlattices composed only of theperovskite-type oxides, an in-plane lattice
constant ak shows a tendency to converge
to an averaged value of the two materials
that make up the superlattice.

Figure 3: Left: Calculated effective potential for electrons in the superlattice, along thestacking direction z. Right: A schematic figure
for the resulting electric field.
Table 1: Interfacial charge in the CCO-based
superlattice. Unit of e.

2. The average c length of of each block constituting the superlattice basically reflects
the bulk parameters.

Interfacial charge
n

3

4

5

CCO/STO 0.33 0.30 0.28 0.27
CCO/BTO 0.33 0.33 0.31 0.29
CCO/LAO 0.38 0.31 0.28 0.26
LAO/SVO 0.25 0.20 0.19 0.16

3. In the superlattice of polar and insulating
non-polar transition-metal oxides, a significant ferroelectric displacement occurs
in the non-polar side (Fig. 2).
To understand the tendency of the standard
formation enthalpy (Fig. 1) and the ferroelectric displacement in the CCO-based superlattice (Fig. 2), we calculated an effective potential for electrons in the superlattice along a
stacking direction z. Figure 3 (a) displays results for the CCO/STO superlattice. From thefigure, we see that a potential gradient is occurring in the STO side (blue arrow), leading to
the electric field from TiO2 /Ca to CuO2 /SrO
interfaces. From the behavior of this effective
potential, the CCO/STO superlattice can be
regarded as dielectric inserted into a capacitor [Fig. 3 (b)]. With this view, the interfacial
charge can be estimated from the classical elec-

2

tromagnetism as
s
Q=

ǫ
ǫ0



ǫ0

dv(z)
∆S.
dz

(4)

Table 1 shows our estimated interfacial
charges for the CCO-based superlattice, weshow an n dependence. The resulting charge
is near 0.3 e, which gives the electric field of
0.87 VÅ−1 .

References[1] http://xtapp.cp.is.s.u-tokyo.ac.jp

109Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study on Removal Mechanism of Single-Crystalline Si
Planarized by Catalyst-Referred Etching in Pure Water
Pho Van BUI, Taku HAGIWARA, Kiyoto KAYAO, Daisetsu TOH, Kouji INAGAKI,
Yoshitada MORIKAWA
Graduate School of Engineering,Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871
There is a growing demand for ultra-

Our recent studies indicated that the

precision optical components for scientific andremoval mechanism of SiC and SiO2 etchingindustrial applications, especially in extreme

via CARE is a hydrolysis reaction, in which theultraviolet (EUV) and X-ray regimes. Using

catalyst

short-wavelength light, scientific imaging ofstabilization of the hypervalent state, increasing

cutting-edge materials/biological samples andthe rate of the reaction [3]. Thus, the purpose ofnanoscale lithography has become possible

the proposed research is to clarify the removal

thanksopticalmechanism of Si etching via CARE using first-

components. Si is the material of choice forprinciples calculations. Additionally, in Si

optical components, thanks to its attractive

polishing, the effect of self-oxidation byproperties,

to

the

such

ultra-precisionwater

dissociationandhighercleanliness,

oxygen and water is still not well understoodworkability.

A highly

due to the instability of Si under ambient

ordered surface with a root mean squareconditions. Thus, the oxidation effects ofroughness at the level of several tens ofoxygen and water are also taken into account.

machinability,

and

as

assists

picometer is greatly desired for the highest

The mechanistic removal pathway of CARE

reflectivity and the lowest unwanted scattering

for Si(111) has been clarified and shown in Fig.

[1].

1. In the pathway with the Pt catalyst, at first, a

In this study, we apply catalyst-referredwater molecule is dissociatively adsorbed on Pt.

etching (CARE), an abrasive-free polishing

In the next step, the adsorbed OH is transferred

method, to the planarization of a crystalline Si

to the targeted Si, forming the five-foldsurface, using Pt as the catalyst and pure water

coordinated state in the metastable state (MS).

as the etching solution [2]. An atomicallyAt this state, the Si-Si back-bond is elongatedsmooth surface with sub-Angstrom root-mean-

and weekend. Finally, the Si─Si back-bond issquare roughness is achieved on the Si

broken by a proton transfer at the final state

substrate.

(FS). The activation barrier is reduced from 1.0

110

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoeV (without the Pt) to 0.6 eV (with the Pt).

The obtained results indicated that the

Similar results are observed on a Si(100).

oxidation occurs readily in the air at a step-edgesite but not at a terrace site. The obtained
results are consistent with the previous study[4]. The obtained results also explained why thewettability of the Si surface could last forseveral hours in the ambient conditions in theprevious experimental study [5].

Fig. 1: Mechanistic reaction pathways of the Ptcatalyzed water etching of Si(111).
To investigate the effect of oxidation for an
HF-treated Si(100) surface, Si(100) with an Hterminated surface was used. Si-H and Si-OH
exchange reaction is investigated, as shown in
Fig. 4: Oxidation by an oxygen molecule at aFig. 2. The activation barrier is 0.75 eV.

step-edge and a terrace site.
The study has clarified the mechanistic
removal pathway of CARE for Si in pure water
Fig. 2: Oxidation effect of Si(100) by waterand the oxidation effect of a Si surface by

To investigate the effect of oxidation by

oxygen or water. Oxygen plays a main role inoxygen at the terrace and step-edge sites,

surface oxidation. Moreover, the combinedSi(111) is employed, as illustrated in Fig. 3.

oxidation effects of oxygen and water might be

The corresponding activation barriers are 0.46

an important factor to be considered in futureand 0.15 eV, respectively (Fig. 4).

studies.

References[1] R. J. Noll: Opt. Eng. 19 (1980) 249.
[2] H. Hara et al.: J. Electron Mater. 35 (2006) L11.
[3] P.V. Bui at al.: Jpn. J. Appl. Phys. 57 (2018)055703.
[4] F. A. Soria, E. M. Patrito, and P. Paredes-Olivera:

Fig. 2: Si(111) oxidation effects by oxygen at

J. Phys. Chem. C 116 (2012) 24607.

the terrace and step-edge sites (top-view).

[5] M. Niwano at al.: J. Appl. Phys. 76 (1994) 2157.

111

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio molecular dynamics study on ion-conduction
mechanisms of perovskite-type oxide
Satoshi OHMURA
Department of Environmental and Civil Engineering,
Hiroshima Institute of Technology, Miyake 2-1-1, Saeki-ku, Hiroshima 731-5193
We have investigated the mechanism ofcrosswise position from the potential valleys ofphotoinduced oxygen dynamics in cobalt

the ground state via intersection of the potential

double-perovskite

densityenergy curves in the excited and ground state atfunctional theory (DFT) based quantum-~1 Å. Figure 2 shows the ionic configurations

molecular-dynamics (QMD) simulations.

of the oxide ion (O1) as it moves from thecrystalusing

We adopted the LR-TDDFT for calculating

diagonal to the crosswise position. The oxide ion

light-absorption spectra, which are calculated as

is subjected to the repulsive and attractive forces

folded oscillator strengths

from the other oxide and cobalt ions,
respectively.

Fig. 2. Ionic configurations during
the travel of the oxide ion
Fig. 1. Calculated oscillator strength

Referencesof EuBaCo2O5.39 crystal[1] M. Hada, S. Ohmura et al.: Carbon. 18(2021) 612.

We found that the photoexcitation with an[2] M. Hada, S. Ohmura et al.: Appl. Mater.

energy exceeding 3 eV provides the oxide ion

Today 24 (2022) 101167.

with excess energy, arrowing it to pass throughthe barrier. The oxide ion may travel to the112

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Atomic structure of metal-oxide interfaces and oxide
grain boundaries
Kazutoshi INOUE1 , Mitsuhiro SAITO2 , and Yuichi IKUHARA1,2,∗
1Advanced Institute for Materials Research, Tohoku University, Sendai, Miyagi, 980-8577
2
Institute of Engineering Innovation, The University of Tokyo, Yayoi, Tokyo, 113-8656

The atomic structures of SiO2 /4H-SiC(0001) [Si face] and (0001̄) [C face] interfaces were analyzed by ﬁrst-principles molecular dynamics (MD) calculations combinedwith aberration-corrected scanning transmission electron microscopy (STEM). MD simulations were performed using the Vienna
ab initio Simulation Package (VASP). The
generalized gradient approximation (GGA)in the form of the Perdew–Burke–Ernzerhof(PBE) exchange-correlation functional was implemented. A kinetic energy cutoﬀ of 450 eV
was used for the expansion of the charge density, and all calculations were performed usinga Brillouin zone sampling with 2 × 2 × 1 kmesh. The cell sizes are 1.070 nm (∼ 4 unit
cells of SiC) along the [11̄00] axis and 0.926
nm (∼ 3 unit cells of 4H-SiC) along the [112̄0]axis where 6 Si-C bilayers along the [0001] axis
were involved as the 4H-SiC substrates. SiO2
structures were constructed by randomly distributed 30 Si and 60 O atoms on each faces
as the initial models. The opposite side of the
4H-SiC {0001} slabs was passivated by hydrogen atoms to eliminate the eﬀects of dangling
bonds, and a vacuum slab with a thickness of
1.5 nm along the [0001] axis was embedded
into the outer side of SiO2 amorphous layer toavoid unwanted interactions. The supercell includes 246 atoms in total, including 102 silicon,
72 carbon, 60 oxygen and 12 hydrogen atoms.
The initial model was heated at 3500 K for 15.0
ps, cooled at −355 K/ps, and then relaxed at
300 K for 9.0 ps. Finally, the atomic positions

were fully relaxed until the maximal force oneach atom decreased to below 0.05 eV/Åandthe total energy converged to less than 1.0 ×
10−4 eV/atom.
We observed the interfacial O atoms on theamorphous SiO2 layer on the Si face show clear
atomic ordering with a rigid O-Si bridge structure across the SiO2 /4H-SiC interface, whichindicates a slow oxidation rate. The C faceinterface, on the other hand, was atomicallyrough and formed many dangling bonds withhigh oxidation rate. We concluded that theformation of a stable and ﬂat oxidation front
by O atom ordering and the suppression of interface defects or residual C will be useful for
designing high-performance 4H-SiC MOSFET
devices [1].
Polycrystalline ZnO is widely used andits properties are largely inﬂuenced by grainboundaries (GBs). We systematically investigated [0001]-symmetrical tilt GBs in polycrystalline wurtzite ZnO by ﬁrst-principles
calculations and atomic-resolution aberrationcorrected STEM. The Zn sites form an octahedron capped by Zn tetrahedra, with O atoms
located at the center, forming a Zn octahedron
which can be regarded as a hexagon viewed
along the c = [0001]-axis. The misorientationof ZnO [0001]-symmetrical tilt GBs is deﬁned
by the dihedral angle 2θ between the (112̄0)planes in adjacent grains, where θ is the dihedral angle between the (112̄0) and (p q p + q 0)GB planes.
The stable structures of the Σ7 (1230) at

113

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

21.79◦ , Σ13 (257̄0) at 27.80◦ and Σ13 (1340)
at 32.20◦ CSL GBs were independently simulated. The upper crystal was shifted toward
the lower crystal by 0.01 nm along the x-, y, and z-directions. Static lattice calculations
were carried out with General Utility Lattice
Program (GULP) using the Buckingham-form
two-body interatomic potential for ZnO. The
local minima were then optimized in the ﬁrstprinciples calculations with the plane-wave basis projector-augmented wave method included
in VASP. The GGA was used for the exchangecorrelation potentials in the PBE form and thecutoﬀ energy was 400 eV for all plane-wave basis sets. All ionic positions as well as the supercell volume were relaxed such that all forceswere < 1.0×10−5 eV/Å, and the residual force
on each relaxed atom was < 0.05 eV/Å under the constant pressure of 0 Pa and constanttemperature of 0 K. The Brillouin-zone integrations were performed over a 4 × 2 × 4 kpoint mesh generated by the Monkhorst-Packscheme.
The GB and bulk structural units foundin this study are similar to capped trigonal
prisms (CTPs) and octahedra, corresponding to octagons and hexagons viewed along
the c-axis, respectively.
After relaxation,
the stable atomic structures were obtained
for the Σ7 (123̄0) GB at 21.79◦ concave octagons are aligned periodically and are ﬁlled
in by two hexagons. On the other hand,the stable atomic structure for the Σ13 (134̄0)
GB at 32.20◦ was alternative arrangement ofa hexagon and a concave octagon in a period. The stable atomic structure calculated
for the Σ13 (257̄0) GB is composed of four
hexagons alternately arranged with three octagons, which is reportedly a one-to-one combination of the Σ7 (123̄0) GB at 21.79◦ and theΣ13 (134̄0) GB at 32.20◦ . These hexagons andconcave octagons are fundamental structuralunits to describe [0001]-symmetrical tilt GBs
in wurtzite ZnO, and we found that the arrangement of structural units changes aroundthe critical angle of 32.20◦ , where the (134̄0)
GB at 32.20◦ is considered a singular GB. The
zigzag arrangements are achieved because of
the octagons inclined at ±30◦ to the GB plane
above 32.20◦ , exhibiting the same core structure as the Σ7 (1230) GB at 21.79◦ [2].

References[1] M. Saito, H. Li, K. Inoue, H. Matsuhata,
Y. Ikuhara: Acta Mater. 221, 117360(2021).
[2] K. Inoue, J.Y. Roh, K. Kawahara, M.
Saito, M. Kotani, Y. Ikuhara: Acta
Mater. 212, 116864 (2021).

114

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Structure and Property of Basalt Melt and Glass
Toshiaki IITAKA
RIKEN Center for Computational Science,
2-1 Hirosawa, Wako, Saitama, 351-0198 JAPANKnowledge of the macroscopic physicaltemperatures of 2200 K (0 to 82 GPa) and 3000

properties of silicate melt (magma) under highK (40–70 GPa). A key finding is that, althoughtemperature and high pressure is extremely

the density and coordination numbers around Si

important for understanding the phenomena ofand Al increase with pressure, the Si–O and Al–

terrestrial planets such as the formation of the

O bonds become more ionic and weaker. The

early Earth, the transport of volatile elements,

temporal atomic interactions at high pressureand volcanic eruptions.

are fluxional and fragile, making the atoms

We study the influence of the microscopic

more mobile and reversing the trend in

structures (structural factors, radial distribution

transport properties at pressures near 50 GPa.

function,

network

The reversed melt viscosity under lower mantle

topology, etc.) of basalt melts and basalt glasses,

conditions allows new constraints on thewhich are related to the history of earth

timescales of the early Earth’s magma oceansformation, on their macroscopic physicalandproperties

viscosity,

explanation for the horizontal deflections ofthermal conductivity, etc.), paying particularsuperplumes at ~1000 km below the Earth’s

attention to the medium-range structure, trace

surface [1, 2].

coordination(density,

number,diffusivity,

also

provides

the

first

tantalizing

References

elements, and entropy effect (temperature[1]

effect).

A. Majumdar et al., Nature

Transport properties like diffusivity andCommunications 11, 4815 (2020).

viscosity of melts dictated the evolution of the

http://dx.doi.org/10.1038/s41467-

Earth’s early magma oceans. We reported the020-18660-w

structure,[2]

density,diffusivity,

electrical

S. Q. Feng et al., Phys.

conductivity and viscosity of a model basaltic

Chem. Miner. 48, 41 (2021).

(Ca 11 Mg 7 Al 8 Si 22 O 74 )http://dx.doi.org/10.1007/s00269-

melt

from

first-

021-01165-3

principles molecular dynamics calculations at

115

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First principles calculations of two-dimensional ordering
process at organic/inorganic materials interface
Tomoya Shiota,1 Yuuichi Orimoto,2 Yuriko Aoki2
1

Department of Molecular and Material Sciences, Interdisciplinary Graduate School ofEngineering Sciences, Kyushu University, Fukuoka 816-8580, Japan.
2

Department of Material Sciences, Faculty of Engineering Sciences,
Kyushu University, Fukuoka 816-8580, Japan

We have studied dynamic processes at the

500K. The kinetic Monte Carlo simulation atinterface between the organic and inorganic

500K using the energy barriers obtained by thesemiconductor materials by means of the first-

DFT calculations generally reproduced theprinciples calculations and the kinetic Monteexperimental observation.

Carlo simulations. All the first-principles

Toward a more accurate simulation, we

calculations were conducted within the density

investigated the flip-flop motions of surfacefunctional theory (DFT) via the Vienna ab initio

buckled dimers both for the clean Si andsimulation package (VASP), version 5.4.4 in theGe(001) as elementary processes because their

ISSP's massively parallel supercomputer system.

flip-flop motions are well known for their

In this project, a system of 3,4,9,10 - perylene

dynamic properties on both surfaces. It was(PTCDA)

found that the flip-flop motion is not a simple

molecules adsorbed on a Ge(001) surface wasseesaw motion but a two-step motion. In

employed as a prototype of the organic-

addition, by considering the flip-flop motion, theinorganic semiconductor interface. Previously,

diffusion barriers of a PTCDA molecule on

we found that a solely adsorbed PTCDA

Ge(001) were reduced by about 20%.

tetracarboxylic

dianhydride

molecule is not mobile at 500K but is mobile at
700K. Furthermore, it was found that the
PTCDA molecules diffuse concertedly with the
dynamics of Ge(001) surface, involving the flipflop motion of the Ge buckled dimers. [1]First, we explored the diffusion process ofinteractions. As a result, it was found that theFig. 1. (a) Adsorption of PTCDA on Ge(001)surface. (b) The flip-flop motion of the Si andGe(001) surfaces.

diffusion mechanism of PTCDA molecules

References

under the intermolecular interactions is similar[1] T. Shiota, W. Mizukami, H. Tochihara, K.

to that of the lone adsorbed molecule, and the

Yagyu, T. Suzuki, and Y. Aoki, J. Phys. Chem. C

PTCDA molecules were found to be mobile

124, 24704 (2020)

PTCDA molecules under the intermoleculareven under the intermolecular interactions at

116

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoRSDFT calculation of atomic displacement captured byenergy dissipation channel of noncontact atomic force
microscope
Toyoko ARAI1, Takahiro Kato1, Jun-Ichi Iwata2, Atsushi Oshiyama3
1

Graduate school of Natural Science and Technology, Kanazawa University, Kanazawa,
Ishikawa, 920-1192
2

Institute of Innovative Research, Tokyo Institute of Technology, Tokyo 152-8550
3

IMaSS, Nagoya University, Nagoya, Aichi 464-8601

In the last two decades the conservative andbackbonds of the Si adatom and subsequent

non-conservative (dissipative) force interactions

bond formation in an alternative atomic

between a tip and a sample in proximity haveconfiguration of the Si surface atoms, including

been intensively examined by non-contact

the Si atom at the apex of AFM tip as shown inatomicIn

Fig. 1. In this study, to explicate the mechanism

particular, the channel of nc-AFM to measureof the phenomena, the forces between Si tip andthe energy dissipation through the non-Si(111)-(7×7) surface were calculated using

conservative

been

real-space density functional theory (RSDFT)

regarded to have great potential to explore nano-[2]. RSDFT is a first-principles program

mechanical phenomena; the dissipation channel

developed by Oshiyama and Iwata, which uses agives the change in the amount of mechanicalreal-spaceenergy to maintain the constant oscillation

pseudopotential method.

force

microscopy

force(nc-AFM).

interactions

hasdifference

methodandaamplitude of an AFM cantilever. We had

First, we optimized the structure of a Si(111)-

experimentally found that, when the nc-AFM(7×7) reconstructed surface consisting of 298 Si

image showed the high resolution for theatoms, the back surface of which was terminatedindividual adatoms on a Si(111)-(7×7) surface,with 49 H atoms, and the structure of a [001]-

the simultaneously obtained energy dissipation

oriented Si tip by RSDFT; the tip consisted of 30

signal increased in close proximity over the

Si atoms having a Si dimer at the tip apex, thehollow sites surrounded by a Si adatom and a Si

back side of which was terminated with 18 H

rest atom with a dangling bond per each [1].

atoms, named “dimer tip” [3]. Next, we

Based on the experimental results, the dynamic

calculated the structure changes and the forces

atomic processes responsible for the dissipation

acting between the tip and the Si surface during

had been discussed in regard to breaking of the

tip approaching and retracting over the hollow

117

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Fig. 1 Model of backbond breaking andformation during a tip approach and retraction
cycle with a hysteresis loop in the forcedistance curve, which is estimated fromexperimental results.

distance curves with hysteresis loop weresite at the separations between the tip apex atom

obtained by RSDFT calculations. The greyed

and the Si adatom on the surface from 5.0 to 2.0

area

Å, as shown in Fig. 2. On the approaching at 3.5

corresponding

Å, one of the three backbonds of the adatom wasdissipation energy, was about 1.6 eV. This value

broken, and the adatom was pulled toward thewas larger than the value of about 0.4 eV thattip. At 2.2 Å, the force between the tip and thewas experimentally measured in ref. １. Thissurface turned to repulsive. At 2.05 Å, the tipmeans that the initial structure of the tip should

apex atom bonded with the rest atom under abe reconsidered to clarify the mechanism for thestrong attractive force. Starting from thedissipation energy of the tip–sample system.

Fig. 2 Force–distance (separation) curve withthe optimized structures of the Si tip andSi(111)-(7×7) surface, calculated by RSDFT.

surroundedthetocurves
the

in

Fig.

2,

nonconservative

structure of the tip and the Si surface, we
calculate the optimized structure by retracting

References

the tip by 0.1 Å step, which was the separation[1] T. Arai, R. Inamura, D. Kura, and M.

between the H-terminated Si planes of the tip

Tomitori, Phys. Rev. B 97, 115428 (2018).

and the Si surface. Up to the separation of 2.8 Å,[2] J.-I. Iwata, D. Takahashi, A. Oshiyama, T.

the attractive force became stronger, and at 2.9

Boku, K. Shiraishi, S. Okada, and K. Yabana, J.

Å the structure and the force almost reverted toComput. Phys. 229, 2339 (2010).

those at 2.9 Å on the approaching. When being[3] P. Pou, S. A. Ghasemi, P. Jelinek, T.

further retracted, the structure and the force were

Lenosky, S. Goedecker and R. Perezet,

the same as those on approaching. The force-

Nanotechnology 20, 264015 (2009).

118

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Elucidation of Photocatalytic Reaction Mechanism by Ab
Initio Calculations
Tatsuya JOUTSUKA
Institute of Quantum Beam Science, Graduate School of Science and Engineering, Ibaraki
University, Hitachi, 316-8511 Ibaraki, Japan

Frontier Research Center for Applied Atomic Sciences, Ibaraki University, 162-1
Shirakata, Tokai, Ibaraki 319-1106, Japan.
We have studied the reaction mechanism ofanalysis, [4] and compute the band structure in

photocatalytic oxidation in TiO2 [1] using cp2k
program packagetitania and the other photocatalysts.

(MPI parallelization withmultiple threads). We focused on the energetics
and dynamics during the polaron migration.
This is a collaborative work with the Prof.
Satoshi Yamauchi at Ibaraki University, who
conducted the LPCVD experiment.
This experimental and theoretical study
clarifies

the

facet

dependence

of

the

photocatalytic reaction at the anatase TiO2
surface. The <112>-oriented anatase TiO2 layer
is deposited on the Ru(0001) substrate at 360°C

Fig. 1: Molecular mechanism of hole migration.

by low-pressure chemical vapor deposition.
The deposition rate is three times higher thanReferencesthat of the multi-orientation layer on the Pylex[1] T. Joutsuka, H. Yoshinari, and S. Yamauchi:

glass. The density functional theory (DFT)

Bull. Chem. Soc. Jpn., 94 (2021) 106–111.

calculations using the constrained DFT method(Selected Paper, Inside Cover, Open Access).

[2-3] and the hybrid functionals show that the[2] T. Joutsuka and K. Ando: J. Phys. Chem. B,(112) surface stabilizes the adsorbed water

124 (2020) 8323–8330.

molecule most strongly.

[3] T. Joutsuka and K. Ando: Chem. Lett., 50

We are extending this study to analyze thedynamical

properties

by

the

(2021) 1325–1328.

constrained[4] T. Joutsuka and K. Ando: J. Phys. Chem. A,

DFT[1-3] and the dynamical reaction path

115 (2011) 678–684.

119

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical Analysis of Metal Film Growth Mechanism in
Chemical Vapor Deposition
Tatsuya JOUTSUKA
Institute of Quantum Beam Science, Graduate School of Science and Engineering, Ibaraki
University, Hitachi, 316-8511 Ibaraki, Japan

Frontier Research Center for Applied Atomic Sciences, Ibaraki University, 162-1
Shirakata, Tokai, Ibaraki 319-1106, Japan.
We have studied low-pressure chemical

catalytic performance by chemically modifying

vapor deposition of Cu on Ru substrate using

the catalytic reaction field.

CuI using cp2k and VASP program packages(MPI parallelization with multiple threads). In
this year, we also studied the mechanism of Cu
nanoparticles by reducing spinel type oxides.
This

is

a collaborative work withtheexperimentalists [1-3] (Prof. Satoshi Yamauchi
and Assistant Prof. Shohei Tada at Ibaraki

Fig.

University), who conducted the experiment.

nanoparticles by H2 reduction of inverse spinel

In this study, we elucidated the molecular1:

FormationmechanismofCutype Cu-doped MgAl2O4.

mechanism of Cu deposition using copper(I)iodide (CuI) on Ru substrate by low-pressure

Referenceschemical vapor deposition through density[1] T. Joutsuka, S. Yamauchi: Chem. Phys. Lett.

functional theory (DFT) molecular dynamics

741 (2020) 137108.

(MD) simulations by cp2k. In addition, the[2] T. Nishikawa, K. Horiuchi, T. Joutsuka andcharge and chemical environment around Cu

S. Yamauchi: J. Cryst. Growth, 549 (2020)

atoms in spinel type oxide Cu-doped MgAl2O4.

125849.

Figure 1 shows the proposed formation[3] T. Joutsuka, S. Tada, et al.: submitted.

mechanism of Cu nanoparticles after reducing[4] T. Joutsuka and K. Ando: Chem. Lett., 50

inverse spinel-type Cu-doped MgAl2O4.

(2021) 1325–1328.

Based on this study, we are developing the[5]computational method to compute the surface

T.

Joutsuka:submitted

10.26434/chemrxiv-2022-9t6vf).

acidity on solid oxides, [4-5] and improving the

120

(DOI:

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Prediction of properties of organic ferroelectrics andpiezoelectrics by ﬁrst-principles calculation
Shoji ISHIBASHI
Research Center for Computational Design of Advanced Functional Materials (CD-FMat),
National Institute of Advanced Industrial Science and Technology (AIST)
Tsukuba, Ibaraki 305-8568

Among hydrogen-bonded systems consistingof small organic molecules, some shows ferroelectricity or antiferroelectricity [1]. They
contain neither toxic nor rare elements andare expected as environmentally friendly materials.
Spontaneous polarization, which
is one of the most important properties
for the ferroelectrics, can be predictedby electronic-structure calculations together
with the Berry phase theory.
We calculated polarization values for seven representative hydrogen-bonded ferroelectrics (croconic acid (CRCA), 2-phenylmalondialdehyde(PhMDA), 3-hydroxyphenalenone (HPLN),
cyclobutene-1,2-dicarboxylic acid (CBDC),
2-methylbenzimidazole (MBI), 5,6-dichloro2-methylbenzimidazole (DC-MBI), and 3anilinoacrolein anil (ALAA)) and the obtained
results are in excellent agreement with the experimental results [2]. These calculations were
performed using experimentally obtained crystal structures with only hydrogen positions
computationally optimized. It is well known
that hydrogen positions are diﬃcult to accurately determine by x-ray diﬀraction analysis. Accurate experimental structure data are
not always available. In such cases, computational optimizations for all of the crystal structure parameters are necessary. Nonetheless,the van der Waals interaction, which is often
crucial in organic solids, cannot be accurately
described by the local density approximation(LDA) or the generalized gradient approxima-tion (GGA). In the present study, we apply
van der Waals density-functional theory (vdWDFT) calculations to reproduce crystal structure parameters of the seven compounds mentioned above. For the vdW-DFT method, weused two forms: the van der Waals densityfunctional consistent-exchange (cx) method [3]and the revised Vydrov–van Voorhis (rVV10)
method [4]. Calculations were performed using
the QMAS code.
Figure 1 shows the deviations of the calculated structure parameters (lattice parameters a, b, and c, and hydrogen-bond lengthd, namely, the O· · ·O or N· · ·N distance) (a)from room-temperature experimental resultsand (b) from 0-K extrapolated values, as wellas (c) their averages and bounds [5]. The calculated results obtained by the LDA and thePBE version of the GGA are also shown. The
experimental structures are at room temperature, whereas the calculation results correspond to 0 K. Unfortunately, only a limited
number of low-temperature structures havebeen reported and the 0-K values were extrapolated using them to prepare Fig. 1 (b). The
vdW-DFT results show good agreement withexperimental results, implying that an important step for the computational materials design of organic ferroelectrics has been achieved.
Spontaneous polarization values obtained by
the vdW-DFT calculations are again in good
agreement with the experimental results. The
success in reproducing the structure parame-121

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo
25(c) Overall(b) 0 K Extrapolated(a) Room Temperature

cx

20

rVV10
LDA
PBE

Deviation (%)

15

10

5

0

-5

-10

abcd

abcd

CRCA

abcd

abcd

HPLN
PhMDA

abcd

abcd

MBI
CBDC

abcd

abcd

ALAA

CRCA

DC-MBI

abcd

abcd

abcd

HPLN
PhMDA

abcd

abcd

MBI
CBDC

abcd

RT

0 K

ALAA
DC-MBI

Figure 1: Deviations of calculated structure parameters (a) from room-temperature experimental
results and (b) from 0-K extrapolated values, as well as (c) their averages and bounds (S.
Ishibashi, S. Horiuchi, and R. Kumai, “Hydrogen-bonded single-component organic ferroelectrics
revisited by van der Waals density-functional theory calculations”, Phys. Rev. Mater. 5, 094409(2021), DOI: 10.1103/PhysRevMaterials.5.094409).
ters also enables the simulation of electromechanical responses. Direct and converse piezoelectric coeﬃcients are evaluated for CRCA,
PhMDA and DC-MBI and the resultant values show acceptable agreement with the experimental values if possible objective factors
are considered [5].

Organic antiferroelectrics also are promising. For example, their applications as highpower electrical energy storage materials are
expected utilizing electric-ﬁeld-induced phasechanges. Usually, they consist of two or morepolar subunits. For squaric acid (SQA), we
have demonstrated that the polarization of theelectric-ﬁeld-induced phase can be estimatedby proper summation of the subunit polarization vectors [6]. By applying this procedure,
we have successfully predicted polarization values for the electric-ﬁeld-induce phases of several organic antiferroelectrics and the obtained
results are in excellent agreement with experimental results [7].

References[1] S. Horiuchi and S. Ishibashi, J. Phys. Soc.
Jpn. 89, 051009 (2020).
[2] S. Horiuchi, K. Kobayashi, R. Kumai,
and S. Ishibashi, Nat. Commun. 8, 14426(2017).
[3] K. Berland and P. Hyldgaard, Phys. Rev.
B 89, 035412 (2014).
[4] O. A. Vydrov and T. Van Voorhis, J.
Chem. Phys. 133, 244103 (2010); R.
Sabatini, T. Gorni, and S. de Gironcoli,
Phys. Rev. B 87, 041108(R) (2013).
[5] S. Ishibashi, S. Horiuchi, and R. Kumai,
Phys. Rev. Mater. 5, 094409 (2021).
[6] S. Horiuchi, R. Kumai, and S. Ishibashi,
Chem. Sci. 9, 425 (2018).
[7] S. Horiuchi and S. Ishibashi, Chem. Sci.
12, 14198 (2021).

122

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Global search for the stable structures of two-dimensional
materials based on Gaussian process regression
Yuji HAMAMOTO
Department of Precision Engineering, Graduate School of Engineering,Osaka University, Yamada-oka, Suita, Osaka 565-0871
Silicene, a silicon analog of graphene has

algorithms. As an example, we here apply

drawn a great deal of attention not only as a

GOFEE to the global search for the stablepromising candidate for topological insulatorsstructures of silicene supported on the Ag(111)from a scientific point of view, but also as ansurface. Our results reveal that GOFEE not only

atomically thin semiconductor material from an

reproduces successfully the stable structures

application point of view. On the Ag(111)

identified so far, but also predicts the existence

surface, however, the sp3-like buckling nature ofof a variety of metastable structures which are

its honeycomb lattice leads to the emergence of

too subtle to determine experimentally.

a varieties of phases characterized by different
patterns of buckling structures as compared withthe freestanding structure predicted theoretically[1], hindering the elucidation of the whole
picture of the electronic and structural propertiesof silicene supported on solid surfaces.
First-principles calculation based on thedensity functional theory (DFT) is a powerful
technique to predict stable structures of newmaterials, but its performance depends on the

Figure: Obtained structures corresponding toinitial guesses, and the global search for stablethe 4×4-a and b (top left and right) and thestructures is computationally demanding in most

Ö13´Ö13-a and b (bottom left and right) phases

cases. To tackle the difficulty in the globalof silicene on the Ag(111) surface.

structure search by the DFT calculation, we

References

adopt an efficient machine-learning technique[1] K. Takeda and K. Shiraishi, Phys. Rev. B

named global optimization with first-principles

50, 14916 (1994).

energy expression (GOFEE) [2], which is based[2] M. K. Bisbo and B. Hammer, Phys. Rev.

on Gaussian process regression and evolutionary

Lett. 124, 086102 (2020).

123

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study on the origin of phase stabilityof Mg–Zn–Y alloys with long-period stacking order
Takao TSUMURAYA
POIE, Kumamoto University, Kumamoto 860-8555, Japan
Magnesium Research Center, Kumamoto University, Kumamoto 860-8555, JapanThe design of alloys based on magnesium(Mg) has attracted much attention since Mg
is the lightest substance element for structural metals. A dilute Mg alloy containing
one at.% of Zn and two at.% of Y showed
high-strength properties with a tensile yieldstrength of ∼600 MPa [1]. This strength iscoupled with the appearance of a unique crystal structure called long-period stacking order(LPSO). In the LPSO-based Mg alloy, soluteatoms of Zn and Y are enriched in a few layers of the (0001) plane of the hexagonal closepacked (HCP) Mg matrix [2]. Shockley partial
dislocation (stacking faults) occurs in the solute atoms enriched layer, which orders periodically along the [001] direction of the hexagonallattice. Furthermore, structural analysis using scanning transmission electron microscopy(STEM) revealed that L12 -type clusters of solute elements (Zn and Y) are embedded in the
Mg matrix near the stacking fault [3].
In this study, the electronic origin of thephase stability of Mg–Zn–Y based alloys with
LPSO is studied based on ﬁrst-principles
density-functional theory (DFT) calculations.
In particular, we aim to understand the role of
the Zn atom in 18R–Mg58 Zn7 Y8 alloy, and thepossible realization of Zn vacancy formationis studied using a convex hull energy diagram.
The heat of formation as a function of the number of Zn vacancies is calculated, and we show
how the electronic structure near the Fermi
level aﬀects structural stability. In the present
DFT calculations used a pseudopotential tech-nique with plane-wave basis sets adopting
the projected augmented-wave method implemented in Quantum ESPRESSO. The
exchange-correlation functional is the generalized gradient approximation proposed by
Perdew, Burke, and Ernzerhof.
For calculating the heat of formation, thenumber of Zn atoms in Mg58 Zn7 Y8 is deduced
using the ﬁxed number of Mg and Y atoms
to understand whether the Mg-Zn-Y alloy includes Zn vacancies that can be formed fromthe elemental metals of Mg, Zn, and Y. The
obtained scatter plot of the heat of formation
as a function of the Zn composition ratio indicates that all phases, including Zn vacancies,
are thermodynamically unstable and decomposed into Mg58 Zn7 Y8 (x = 0) and elemental metals of 58Mg+8Y phases. Nevertheless,the hull distance decreases as vacancies (x) decrease. Therefore, we consider the state inwhich Zn7 Y8 clusters with an L12 structure are
already formed and plot the convex hull diagram. Zn vacancies with x = 1 and 3 are on theconvex hull. These states should be observed
below the decomposition temperature. Therefore, we conclude that the Zn atoms in the
LPSO alloy are stable even if they are about
half of the number of Y atoms.
In general, the density of states (DOS) for
HCP metal is characterized by a deep valley
or dip near the Fermi level (EF ), where EF isat the lowest position of the valley. The depthof the valleys in the DOS represents the magnitude of splitting the prominent peaks of the124Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

DOS between those in occupied and unoccupied states. The width of the valley or dip
appears as a diﬀerence in the enthalpy of formation (or cohesive energy) between diﬀerent
metals [4, 5]. By focusing on the partial DOS
of Zn and its neighboring Mg, we ﬁnd that theformation of the bonding state between Zn andthe surrounding Mg atoms has a crucial role instabilizing the LPSO structure.

References[1] Y. Kawamura, K. Hayashi, A. Inoue, andT. Masumoto, Mater. Trans. 42 1172
(2001).
[2] E. Abe, Y. Kawamura, K. Hayashi, and
A. Inoue, Acta Metall. 50 3845 (2002).
[3] D. Egusa and E. Abe: Acta Mater. 60 166(2012).
[4] S. Inoue and J. Yamashita: J. Phys. Soc.
Jpn 35 677 (1973).
[5] T. Tsumuraya, I. Watanabe, and T.
Sawaguchi: Phys. Rev. Research 3 033215(2021).

125

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Metastability of 2D and 3D binary ordered alloys
Shota ONO
Department of Electrical, Electronic and Computer Engineering, Gifu University
Gifu 501-1193

It is well-known that the fcc (hcp) metals
in the hcp (fcc) structure are dynamically stable, while the fcc (bcc) metals in the bcc (fcc)
structure are unstable [1]. To understand themetastability relationship between diﬀerent
crystal structures, we calculated phonon dispersions for 2D and 3D systems using densityfunctional perturbation theory implemented in
Quantum ESPRESSO [2]. The calculations
were done using system B and C.
In our previous work, we showed that if theelementals metals in the 2D hexagonal structure is dynamically stable, then the fcc and hcp
strcutures are also dynamically stable, showing that 2D structures serve as building blocks
for constructing the 3D structures [3]. In thepresent work, we extend this investigation tobinary ordered alloys of CuX with X being 46
metallic elements [4, 5]. We showed that if the
CuX in the AB layer structure is dynamicallystable, then that in the AB and ABC stacking structures is also dynamically stable (seeFig. 1 for the crystal structures). In addition,
we calculated phonon dispersions for the CuX,
AgX, and AuX in the AB layer structure, andfound that 48 out of 135 ordered alloys are dynamically stable, predicting that those alloys
in the AB and ABC stacking structures arealso dynamically stable [5]. The present work
has shed light on the 2D structures as a building block for computational material design.
We also predicted potential substrates thatallow immiscible metals (Pb and Sn) to form
the surface alloys by using density-functional
theory [6]. The prediction of their surface geometry is left for future work.

!"#.&/01#,23'(.04#56*0/'672-!"#$%&'()*+#,"!-!"8#$%&'()*+#,9:"-Figure 1: Schematic illustration of 2D and 3D
strcutures.

References[1] G. Grimvall et al., Rev. Mod. Phys. 84(2012) 945.
[2] P. Giannozzi et al., J. Phys.: Condens.
Matter 29 (2017) 465901.
[3] S. Ono: Phys. Rev. B 102 (2020) 165424.
[4] S. Ono: Sci. Rep. 11 (2021) 14588.
[5] S. Ono: Phys. Rev. Materials 5 (2021)
104004.
[6] S. Ono, J. Yuhara, and J. Onoe: Chem.
Phys. Lett. 776 (2021) 138696.

126

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab Initio Molecular Dynamics Study on Static Structure of
Glass Materials
Akihide KOURA
Technical division,
Kumamoto University, Kurokami, Chuo-ku, Kumamot,o 860-8555

We have studied a condensed matter system

based on the AIMD simulations of liquid andwhich are crystal, liquids, and amorphous. In

amorphous V2O5. Figure 1 shows the root mean

this project, we focused on the static structure

square errors (RMSE) and partial radialof amorphous V2O5 state. The ab initio

distribution functions 𝑔𝑔𝛼𝛼𝛼𝛼 (𝑟𝑟) (𝛼𝛼, 𝛽𝛽 ∈ V, O) of

molecular dynamics (AIMD) simulations wereliquid V2O5. According to our previous study

performed with our original QXMD code [1].

[3], considering not only energy but also atomic

In order to investigate the static structure offorce and virial tensor improves ANN potential

amorphous V2O5, we employed the machine

better. Based on the learning condition, our MD

learning method using artificial neural network

simulation using the ANN potential basically(ANN) to construct the interatomic potential [2].

represent the FPMD simulations except for the

The Aenet package [2] was used for training

unreasonable peak of 𝑔𝑔OO (𝑟𝑟) at approximately

𝑟𝑟 = 0.4 Å. In the future work, we develop thetraining method by other technics, e.g., active

learning from the result of MD simulations
with ANN potential for liquid systems.

References[1] F. Shimojo, S. Fukushima, H. Kumazoe, M.
Misawa, S. Ohmura, P. Rajak, K. Shimamura, L.
Bassman, S. Tiwari, R. K. Kalia, A. Nakano,and P. Vashishta: SoftwareX 10 (2019).
[2] N. Artrith and A. Urban: Comput. Mater.
Sci. 114 (2016) 135.
[3] A. irie, S. Fukushima, A. Koura, K.
Fig. 1: (Left) Root mean square errors and(right) partial radial distribution functions.

Shimamura, and F. Shimojo, J. Phys. Soc. Jpn.
90, 094603 (2021).

127

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Atomistic simulations for excited materials by strong laser
Yasushi Shinohara1,2 , Mizuki Tani3
1

Photon Science Center,

The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656.
2

NTT Basic Research Laboratories,

NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198.
3

Department of Nuclear Engineering and Management

The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656.
We have performed investigations thatelectron occupation shows symptom of multiple

describe nonequilibrium electron-ion dynamics

Rabi-flopping to higher energy bands for bulk Al.

realized by strong laser fields irradiation.

We

have

developedasemiclassicalComplex pathways accompany these dynamics

theoretical framework for electron-ion coupledalong different phases depending on time anddynamics under a strong laser field [3]. Free-

positions.

andelectronic behavior of metal is accurately

nonequilibrium characteristics prohibit direct

reproduced with more than 50-times lightermeasurements for the intermediate processes ofcomputational

the dynamics. Our investigation is aimed tolightweight cost allows us to simulate spatially

understand what processes could happen in thelarger systems, including non-uniform structures,

laser-excited materials, including insulators andsuch as surfaces or impurity, and electron-ion

metals, via theoretical simulations.

coupled dynamics for the laser-excited material

These

multi-physicalWe have accumulated simulated electronic

cost

than

TDDFT.

The

response.

structure data just after ultrashort laser pulse byusing SALMON code [1] based on time-

References

dependent density-functional theory [2]. This

[1] Erich Runge and E. K. U. Gross, Phys. Rev.

data is the key quantity of the laser-excited

Lett. 52 (1984) 997.

dynamics' initial process, which triggers whole[2] M. Noda, et al., Comp. Phys. Comm. 235

subsequent processes. We reported Rabi-type(2018) 356.

absorption oscillation in bulk Al with resonant[3] Mizuki Tani, Tomohito Otobe, Yasushi

excitation by increasing the intensity of the

Shinohara, and Kenichi L. Ishikawa, Phys. Rev.

electric field [3]. By analyzing the occupation

B 104 (2021) 075157.

evolution as a function of the intensity, the128

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study on structural elementary excitations at
semiconductor surfaces and interfaces
Hiroyuki KAGESHIMA
Graduate School of Natural Science and Technology, Shimane University
1060 Nishi-Kawatsucho, Matsue, Shimane 690-8504

In this project, we have been focused on
physical properties of structural elementary
excitations of semiconductor surfaces and interfaces. In this year, we have focused on
the physical properties of defects in SiO2 .
The calculations were performed based on theﬁrst-principles calculation. Program package
PHASE/0 was employed. [1]Defects in SiO2 have been widely studied
because they are the source of device performance degradation for MOS ﬁeld-eﬀect transistors (MOSFETs), which is widely used forthe integrated circuits. The gate insulator of
MOSFET is made of silicon oxide SiO2 . Thosestudies revealed that O vacancies, one of typical defects, can trap charges, assist gate leakcurrent, and also lead to the formation of eternal gate leakage paths. They also revealed
the role of post oxidation annealing. However,recent progress of integrated circuit technology have forced the MOSFET device structurefrom planar to three dimensional. If we consider the vertical body-channel-MOSFET withsilicon oxide gate insulator, the oxide can bestrained because of the device formation process. The interface oxide might be compressed
and the surface oxide be expanded due to thethermal oxidation of silicon for the gate formation process. The compressive and expanded
strain are expected as much as 3% in the worst
case. Such strain should aﬀect on the physicalproperties of defects in silicon oxide gate insulator

and studied strain dependence of its formationenergy and diﬀusion barrier. Based on theseresults, in this year, we have studied stability of various defects including the O vacancy,
the charging eﬀects on them, and their strain
dependences. Some of the vacancies we havestudies are fully terminated by H atom or OH
group, and other are partially terminated. We
modeled the host SiO2 by alpha-quartz crystal with supercell containing 24 Si and 48 O
atoms.
First, we have found a novel O vacancy defect which has only two -OSi bonds. This defect is unique because the widely known O vacancy defect has three -OSi bonds. This new
O vacancy defect is stable because it accompanies a three-Si-member ring within the model,
while ordinary alpha-quartz just contains only
six-Si-member rings. Next, we have found thata dangling bond of Si can surely assist thegate leakage current because they show charging levels in the middle of band gap. Then, we
have found that the compressive strain makes
it easier to release the terminators H or OH,
while it does not signiﬁcally change the charging level positions. From these results, we have
conﬁrmed that strain in the gate insulator silicon oxide surely enhances the device performance degradation. Careful device formation
process must be necessary.

References[1] https://azuma.nims.go.jp

Therefore, we ﬁrst focused on the O vacancy

129

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab-initio molecular-dynamics calculations for moleculemodified nanointerfaces
Kenji TSURUTA, Masaaki MISAWA, Narumi MACHIDA,
Kyosuke SATO, and Satoshi OHMURAa
Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530aDepartment of Civil and Environmental Engineering, Hiroshima Institute of Technology,
Hiroshima 731-5193
Surfaces and/or interfaces of oxide materials
are often modified by other molecules in order
not only to stabilize their structure against
deterioration but also to control surface
morphology. Calcium carbonate (CaCO3),
which is widely used as filler in resins, plastics,
and rubber materials to improve their physical,
mechanical, and thermal properties, is a typicalexample of such phenomena. To control particle
morphology and to improve affinity with basematerials, calcium carbonate is often surfacetreated with organic compounds. This activatedcalcium carbonates (ACCs) not only exhibit
excellent application properties, but also can beapplied as eco-friendly inorganic-organic hybridmaterials. It has been reported [1] that surface
deposits with ~5 nm thickness exist on the (104)surface of calcite covered with stearic acid (SA).
Since this thickness corresponds to about twice
the length of a SA molecule, it is suggested thatSA bilayers may be formed on the calcite (104)surface, but the detailed adsorption state has notbeen clarified to date.
In this study, we performed first-principles
calculations based on density functional theory
using the Vienna Ab initio Simulation Package(VASP). We created a simulation model for three
types of SA-SA and two types of calcite-SAinterfaces as shown schematically in Fig. 1 A-E.
First-principles molecular dynamics (FPMD)
simulations with canonical ensembles at room
temperature were performed for these models,
and the presence or absence of adsorption wasverified by observing changes in the interface
structure in each model. We also verified thestability of the interface structures by analyzing
the energetic properties in the relaxed system.
According to the results of the FPMD
simulations, we considered that the interface
structure in the A, B, and E models are
intrinsically unstable because the interatomic
distance of the bonding part in each modelFig. 1 Schematic illustration of the simulation models
for SA-SA (A-C) and calcite-SA (D, E) interfaces.

gradually increased at room temperature . On theother hand, such behavior has not been observedin the C and D models. Comparing of thepotential energy of the C model with that of two
isolated SA molecule, it was found that theenergy of the C model was 0.4 eV lower. This
result indicates that the C model is energeticallyfavorable and stable interface structure may beformed with an adsorption with C model. Fromthese results, it is considered that despite the firstSA layer is favorable with D model, somemolecules on the first layer may be inverted (or"alternately aligned") in order to adsorb the
second layer with C model in the SA bilayer on
calcite (104) surface[2]. Further computation
with larger system size is necessary to validate
this hypothesis. Development of an effective
interatomic potential based on a Deep-Learning(DL)-based molecular design methods [3] is inprogress for simulations of the bilayer system.
References[1] M. Ricci et al., Langmuir 31, 7563 (2015).
[2] N. Machida, M. Misawa, Y. Kezuka, and K.
Tsuruta (to be published).
[3] K. Sato and K. Tsuruta, Mater. Sci. Forum
1016, 1492 (2021).

130

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles Calculations of Magnetic Insulators
Under Uniform Electric Fields
Naoya YAMAGUCHI
Nanomaterials Research Institute (NanoMaRi), Kanazawa University
Kakuma-machi, Kanazawa, Ishikawa 920-1192
This year, we tried to focus on electric ﬁeld
eﬀects of magnetic insulators. We have developed a linear-combination-of-pseudo-atomicorbital (LCPAO) scheme of a ﬁnite electricﬁeld method based on the modern theory ofpolarization [1] and implemented it to the
OpenMX code [2], a ﬁrst-principles calculation code based on the density functional theory (DFT). Through the scheme, one can consider electric ﬁeld eﬀects even for periodic systems such as bulk insulators. We improved
our implemented code this year. The socalled egg box eﬀect causes numerical errors
due to the real space grid, especially in the
LCPAO method, and it disturbs evaluation of
the forces, dipole moment and stress tensor.
It can be resolved by the grid cell sampling
to repeat the evaluations for the shifted grid
several times based on the frozen LCPAO density matrix, and we implemented the functionin the previous year. We found that a solution was the “one-shot” grid cell sampling, thatis, the forces under the ﬁne grid were evaluated from the density matrix obtained from therough grid without the grid shifts. We calculated electronic and static dielectric constants
and Born eﬀective charges of III-V and II-VI
semiconductors and group IV insulating materials. The calculated values coincided withthe reported computational values even in the
GGA case that the density gradient is sensitive to the egg box eﬀect, and they were anagreement with the experimental values. In
addition, we also debugged the implemented
code for the non-collinear spin density functionals applicable to materials that spin-orbit
interaction (SOI) is important. We also foundthat the SOI has a non-negligible inﬂuence on
the dielectric constants of cases including theheavy elements. For the magnetic insulator
cases, we conﬁrmed that the debugged code
worked well for the antiferromagnetic NiO fordiﬀerent U parameters based on the DFT+U
scheme through the comparison to the previous
study. For some insulators with noncollinear
spins, the self-consistent-ﬁeld (SCF) calculations were diﬃcult to get converges because
the careful mixing during the SCF calculations
were essential. Our implementation will become a powerful tool to expand subjects of researches on materials in investigating the electric ﬁeld eﬀects.
We also developed the new evaluation
scheme for the anomalous Hall and Nernst conductivity without constructing the Wannierfunctions or explicit evaluation of the Kubo
formula [3]. We reproduced the intrinsic contribution of the typical metals such as bcc iron.
Our scheme has advantages of eﬃciency andstability: it is the non-iterative scheme unlike
Wannierization and can avoid numerical instability such as the k-space Dirac monopole. The
scheme is more appropriate for not only large
scale cases but also high-throughput calculations than a Wannier function method.

References[1] N. Yamaguchi and F. Ishii,
https://doi.org/10.48550/arXiv.2203.10441.
[2] http://openmx-square.org.
[3] H. Sawahata, N. Yamaguchi, S. Minami and
F. Ishii,
https://doi.org/10.48550/arXiv.2204.05949.

131

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Optical conductivity of Ca5Ir3O12 by first-principles calculations
Shoya Kawano
Department of Electrical and Electronic Engineering, Kyushu Institute of Technology,
Kitakyushu, Fukuoka, 804-8550

We have studied the title compound

Perdew-Burke-Ernzerhof

type.

Γ-point-

Ca5Ir3O12 which have attracted attention due tocentered 5×5×13 and 10×10×25 k-points

the its strong spin-orbital interaction (SOI) [1].

samplings is set to be compared.. We use theSuch strong SOI is affected to the physicalenergy cutoff of 96 Ry for the wave function, aproperties.

anconvergence criterion for the electronic self-

antiferromagnetic ordering below 7.8 K, aconsistency loop of 10−10 Ry, and the Gaussian

second order phase transition at 105 K and non-smearing method with a smearing width of

linear conductivity along c-axis and so on. We

0.002 Ry. We included the SOI effect. In

performed synchrotron radiation-based infrared

RESPACK,(SR-IR)

its

calculated within random phase approximation.

electronic property for single crystal of

For this calculation, we set cutoff energy for

Ca5Ir3O12.

wepolarization function of 6 Ry. Smearing value

observed reflectivity and optical conductivity.

used in tetrahedron calculation is set to 0.01 eV.

Then, we investigated reflectivity and optical

Lattice parameters of Ca5Ir3O12 is referred to

conductivity of Ca5Ir3O12 by first-principles

previous report [5].

Thiscompoundspectroscopy

From

this

to

shows

revealthemeasurement,

calculations to discuss about our experimental

polarization

functionisFig 1 shows band structure of Ca5Ir3O12
from 5 × 5 × 13 and 10 × 10 × 25 k-point

results.
We

theperformed

densityfunctional

sampling. E = 0 is fermi level. Both results arecalculations by using Quantum ESPRESSO

consistent with previous report []. As showncode [2]. These results were used to calculate

previous report, this material is metal on thisreflectivity and optical conductivity by usinglevel of density functional calculation. ThisRESPACK code [3]. In Quantum ESPRESSO,

metallic trend is different from experimental

we use the norm-conserving pseudo potentials

observation which shows as semiconducting

generated by the code ONCVPSP (Optimized

electrical properties. This is limitation of thisNorm Conserving Vanderbilt PSeudopotential),level calculation. From this result, we use 5×5

and are obtained them from the PseudoDojo [3].

×13 k-point sampling for polarization function

The exchange-correlation function is used

calculation because this calculation is time132

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

consuming.
Fig. 2 shows the calculated reflectivity of
Ca5Ir3O12 parallel to c-plane and c-axis. Thisshows reflectivity R = 1.0 at  = 0 because of
metallic behavior in our results. The broad peakis shown around 5000 cm-1.
Fig.

3

shows

the

calculated

opticalFig. 1 Band structure of Ca5Ir3O12 fromconductivity of Ca5Ir3O12 parallel to c-planedifferent k-point sampling. E = 0 is fermi
and c-axis. These have two peaks at about 1000
level.

cm-1 and about 5000 cm-1 for parallel to c-planeand c-axis. We considered that the peak of
about 1000 cm-1 is shown due to the metallic
behavior in the calculation. Experimental result
has the peak at about 4000 cm-1. This seems to
be good agreement with our 5000 cm-1 peak.
However, we note that the calculation andexperiment have difference of metal or
semiconductor.

Fig. 2 Calculated reflectivity of Ca5Ir3O12
We need to more discussion by using theseparallel to c-plane and c-axis.
results, and also improvement such as metallic
behaviour in the calculation. Using ISSP
Supercomputer, we achieved the first principles
calculation of optical properties such as thecompound Ca5Ir3O12.

References[1] K. Matsuhira et al. J. Phys. Soc. Jpn. 87,(2018).
[2] https://www.quantum-espresso.org
Fig. 3 Calculated optical conductivity of[3] https://sites.google.com/view/kazuma7k6
Ca5Ir3O12 parallel to c-plane and c-axis.
[4] http://www.pseudo-dojo.org[5] M. Charlebois et al. Phys. Rev. B 104,
075153, (2021)

133

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Critical exponent of metal-insulator transition in
doped semiconductors and spin ordering
Yosuke HARASHIMA
Center for Computational Sciences, University of Tsukuba
Tennodai, Tsukuba, Ibaraki 305-8577
Devision of Material Sciences, Nara Institute of Science and Technology
Takayama-cho, Ikoma, Nara 630-0192

Impurity doping have an important eﬀect
on the conduction properties of semiconductors. Evaluating electrical conductivity at azero temperature, the material becomes an insulator at low impurity concentrations, a metal
at high impurity concentrations, and a metalinsulator transition occurs at some concentration in between. This metal-insulator transition is known to occur in many materials regardless of semiconductor or impurity type andis a general and fundamental property of quantum transport.
Electrons in semiconductors are scatteredby randomly aligned impurities and the phaseshifts of wavefunctions are distributed randomly. When those waves overlap, they cancel
each other out and a localized state appears.
This is Anderson localization, and the metalinsulator transition mentioned above is considered to be the Anderson transition between theAnderson localized phase and the delocalized
phase. Continuous transitions such as the Anderson transition can be classiﬁed according to
the critical exponent. The critical exponent νcharacterizes the divergence of the correlation
length ξ ∝ |n − nc |−ν at the transition point(n and nc are impurity concentrations and thecritical concentration). It is universal and independent of the details of the system. The
critical exponent represents the universality ofthe phase transition, therefore, deriving its exact value is an essential problem.

Two diﬀerent values for this critical exponent have been reported from experiments,ν ≈ 0.5 and ≈ 1.0, but the origin of this discrepancy has not been clariﬁed. This problem
is called the exponent puzzle. To solve thisexponent puzzle, the actual situation in the
doped semiconductor needs to be simulated
from ﬁrst-principles.
In this study, we consider a system of randomly distributed P impurity donor ions in
Si. For the analysis of its electronic structure, we used a program we implemented that
self-consistently solves the Kohn-Sham equation based on density functional theory. Experiments suggest that the spin order changes
near this metal-insulator transition point, andthus, the present calculations take into accountthe spin degrees of freedom.
We generated random impurity conﬁgurations. The impurity concentration is ranged
from ≈ 0.8 × 1018 cm−3 to ≈ 2.1 × 1018 cm−3 ,and the system size is taken by 228.6, 285.8,
342.9, and 400.1 Å. The critical concentration has been predicted by convolutional neural network [1]. We sampled ≈ 180, 000 data inthe vicinity of the predicted concentration, andsolved the electronic state self-consistently.

References[1] Y. Harashima, et al.: J. Phys. Soc. Jpn.
90 (2021) 094001.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Exploration of exotic surface sites for catalyst informatics
Yoyo HINUMA
National Institute of Advanced Industrial Science and Technology (AIST)
1-8-31, Midorigaoka, Ikeda, Osaka 563-8577

Surface point defects of metal oxides, forthat are metastable against macroscopic facet

instance O vacancies, have a dominant effectformation and by comparing cleaved surfaces

on heterogeneous catalysis. The Mars-Van

and surfaces suggested by a genetic algorithm

Krevelen mechanism is one of the most(GA) for promising orientations is proposedfrequently encountered catalytic process. In one

and demonstrated using 34 orientations of β-

example, O vacancies on a metal oxide catalyst

Ga2O3

surface act as reaction sites. The energy

terminations

minimum required to remove O from a surface,

accessible are found for β-Ga2O3 and θ- Al2O3,

which is denoted as the surface O vacancy

respectively, where the highest surface energy

formation energy (EOvac), can be used to

was roughly twice of the lowest. The lowest

rationalize and predict catalytic performance insurface O vacancy formation energy (EOvac) insuch a catalytic process. Calculation of EOvac

an accessible surface is 3.04 and 5.46 eV in therequireswith(101) and (20-1) terminations for β-Ga2O3 andsufficient spacing between O vacancies, henceθ-Al2O3, respectively, where the decrease insome estimation of EOvac from less costly

EOvac from the most stable surface is 1.32 andcalculations, such as slab-and-vacuum model

1.11 eV, respectively. The EOvac in accessible

calculations with minimum cell size and evensurfaces showed a good correlation withbulk calculations, will be effective in screening

descriptors

materials for a given purpose.

environment, suggesting that exploiting surfaceaslab-and-vacuum

model

Computational exploration of previously

andθ-Al2O3.

Seven

considered

of

the

local

and

six

experimentally

coordination

O in an unfavorable environment in an

unknown reactive sites is a powerful strategy

accessible

for emergence of new catalytic reactions.

vacancy-related catalyst performance even in

Exoticmaterials that do not show reactivity on thesurfacescanbetheoreticallyinvestigated, but there are very few, if any,
computationalmodelsofhightermination

most stable surface.

indexorientations that considers reconstruction of thesurface. A workflow to efficiently obtain a setof accessible terminations by removing those

135

would

enhanceOActivity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analysis of the electronic structure of ferromagnetic shapememory alloy and ferrimagnetic spinel oxide
Masao OBATA1,2
1

Institute of Science and Engineering, Kanazawa University, Kanazawa, Ishikawa 920-1192
2

Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa,
Ishikawa, 920-1192
We have investigated the electronic andvector length in Fermi surface nesting. The

magnetic structure of the magnetic shapeobtained nesting vector from the generalized

memory alloy of Ni2MnGa and ferrimagnetic

susceptibility

spinel oxide of NiCo2O4. In these materials, theexperimentally observed crystal structure at low

LDA/GGA

showedtemperatures, such as 10M or 14M long-periodinconsistency with experimental facts, such as

modulated structures [2]. We also estimated thethe period of martensite modulation due toeffect of Mn's on-site Coulomb interaction on

Fermi surface nesting and the properties of

the tetragonal phase [3].

electrical resistivity, respectively. Since these(B) NiCo2O4

discrepancies may originate from electron

The NiCo2O4 spinel has drawn much attention

correlation effects, we employed the quasi-

for its material application due to its low cost,

particle self-consistent GW (QSGW) approach,high electronic conductivity, redox reaction, andwhich is one of the beyond LDA/GGA methods,

high electrochemical activity. However, its

to investigate the electronic structure of thoseelectronic structure is not well understood. We

materials.

investigated the inverse spinel β structure by

level

The

investigation

first-principles

calculationisconsistent

with

the

package ecalj [1] is used for this study.

QSGW. We found that the eg orbital of Co(A) Ni2MnGa

tetrahedral site appears on the Fermi-level and

The Ni2MnGa ferromagnetic shape memory

splits due to the uniaxial crystal symmetry,alloys, which have magnetic and shape memory

stabilizing 3z2 and destabilizing x2-y2 orbitals.

properties, have been attracted as magnetic

References

actuator materials. We applied the QSGW to the[1] https://github.com/tkotani/ecalj/

high-symmetry (cubic) and[2] M. Obata, T. Kotani, T. Oda, submitted.

low-symmetry(tetragonal) phases of Ni2MnGa. We found that[3] M. Zelený, P. Sedlák, O. Heczko, H. Seiner,

the Fermi surface of the cubic phase expands

P. Veřtát, M. Obata, T. Kotani, T. Oda, L. Straka,

compared to GGA, resulting in the reduction ofMater. Des., 209, 109917 (2021).

136

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles calculations of complex metallic alloy
surfaces
Kazuki NOZAWA
Department of Physics and Astronomy, Kagoshima University
1-21-35, Korimoto, Kagoshima 890-0065

We studied the adsorption of pentacene on
the 2-fold surface of an icosahedral Ag-In-Yb
quasicrystal [1](QC). An STM experiment reported that pentacene molecules adsorbed in aquasiperiodic manner on this surface[2].
The QC surface has approximated by a diskshaped atomic cluster with a radius of 2.2 nm(Fig. 1). Atomic positions of the QC surface
has extracted from the structural data of an
X-ray diﬀraction experiment for the isostructural Cd5.7 Yb quasicrystal[3], where Ag and
In atoms occupy the Cd sites in the Ag-In-Yb
QC. In the calculations, the molecular axis ofpentacene is constrained to be parallel to thesurface, and all atomic positions, including thesubstrate atoms, are ﬁxed. Calculations arecarried out with the VASP code mainly on thesystem-B as bulk jobs using 72 nodes.

Fig. 2(a)). Comparably stable orientational
conﬁgurations are found when the molecularaxis is aligned to two 5-fold axes on the surface.
Obtained orientational dependence of the adsorption energy well explains the result of statistical analysis from an STM experiment[2].

(a) 2f-90°

First, we carefully checked the cluster thickness dependence of the adsorption energy. And
we conﬁrmed that the thin ﬁlm composed onlyof the top layer atoms well describes the interactions with pentacene. Thus, we describe theresults below using the thin ﬁlm as the substrate.
The adsorption energy of pentacene shows
strong orientational dependence on the molecular axis of pentacene. Figures 2(a) and (b)show the adsorption energies of pentacene withits molecular axis aligned to two diﬀerent 2fold axes, 2f-90◦ and 2f-180◦ , which are parallel to the surface and perpendicular to eachother. It is clearly shown that pentacene favors one of them (2f-90◦ direction shown in(b) 2f-180°

Figure 1: Adsorption energy of pentacene withthe molecular axis parallel to the 2-fold (a) 90◦
and (b) 180◦ directions.
We also studied the adsorption of oxygen
atoms on the (111) surface of the PdZn inter-137

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

metallic compound. We used the VASP codewith a slab model consisting of six atomic layers. Using a 2x2 unit cell containing eightatoms in the top layer, we investigated theadsorption structures for various oxygen coverages between 0.125 - 1.0 monolayer (ML).
Calculations were mainly carried out on thesystem-C as ﬂat MPI jobs with 4-9 nodes. At
high oxygen coverages, we found that Zn atoms
form a Zn-O layer with a hexagonal ring reminiscent of the Wurtzite ZnO. PdZn is known
as a candidate catalyst for the methanol steam
reforming (MSR) because of its higher thermal
stability than the traditional Cu-based catalyst. It has been reported that a ZnO patch isformed on the PdZn catalyst during the MSR
reaction, and considered that the high CO2 selectivity of PdZn in MSR is due to the formation of the ZnO patch[4]. However, there
is still no report of the ﬁrst-principles calculations about the formation of the Zn-O layer.

References[1] M. Sato, Master Thesis (Kagoshima University, 2022).
[2] A. Aloﬁ et al., Mat. Trans. 62, 312(2021).
[3] H. Takakura et al., Nature Matter. 6,58(2007).
[4] M. Friedrich et al., Angew. Chem. 52,
4389 (2013).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Atom exchange of fcc metal surfaces
Tsuneo FUKUDA†
Department of Physical Electronics and Informatics, Graduate School of Engineering,Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-Ku, Osaka 558-8585

The

migration ofan adsorbed atom

vacuum layer for both sides for both the(adatom) impinged from gas phase to a surface

Ni(110) and Ni(100) surfaces. After fully

is one of the fundamental processes for crystal

relaxed atomic structures of slabs for pristine

growth. In some adatom-surface combinations,surfaces, Ni or Cu adatom was located andinstead of migration of an adatom on theadsorbed surfaces were again relaxed bysurface, an adatom may be embedded in the

keeping atomic positions of bottom 4 layers

surface layer by displacing the surface atom,

fixed. Electronic and ionic iteration parameters

and the released atom migrates on the surface,

are listed in Table 1. The NEB method waswhich is often called "displacive adsorption".

performed for 5 images with both the initial and

Such

and

final structures being fixed (IMAGE=4). Near

surface atoms are frequently reported by using

the potential maximum, the migration potential

field ion microscopy (FIM) [1].

was further evaluated by dividing these images.

substitutions

betweenadatoms

We have investigated adatom migration andadatom-surface

atom

substitution

The obtained migration potential barriers

fromare listed in Tables 2 and 3. For the Ni(110)theoretical point of view. We chose the Ni(100)surface, a simple surface diffusion of adatom

and Ni (110) surfaces as model systems andalong [110] direction, path A in Fig. 1(a), had ainvestigated the migration and the substitutionof Ni and Cu atoms based on first-principles
calculations. We employed a popular firstprinciples calculation code VASP, and thenudged elastic band (NEB) method was applied
Fig. 1: Adatom migration pathways for (a) Ni(110) andNi(100) surfaces. The unit cells used in the structural
calculation are shown by the dotted lines. Initialadatom position is indicated by blue circle, and path A,
B, and C on the Ni(110) surface and path A and B on
the Ni(100) surface are indicated by purple, green, andyellow, respectively.

to the evaluation of adatom migration andexchange potentials [2].
Surface models are shown in Figs. 1. We
employed 7-layer slab model with ~0.8 nm†

Present address: Division of Electronics and Physics, Graduate School of Engineering, Osaka
Metropolitan University, 3-3-138 Sugimoto, Sumiyoshi-Ku, Osaka 558-8585

139

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 2 Migration potentials of Ni adatom
corresponding paths shown in Figs. 1

Table 1 Parameters for present calculation
VASP Version
slab geometry
k-points
potential
cut off energy
Fermi level smearing
convergence condition

SCF mixing parameters

5.3.5
Ni(110): 4×2 unit 7 layerNi(100): 3×3 unit 7 layerNi(110): 12×16
Ni(100): 12×12
PBE [3]384.08 eV
Methfessel & Paxton
 = 0.12 eVElectronic:10-6 eVIonic: 0.01 eV/Ang.
AMIX = 0.02
BMIX = 0.0001
AMIX_MAG = 0.08
BMIX_MAG = 0.0001(linear mixing)

Time period

POTIM = 1.0

Number of core576 (192/image)face
Ni(110)Ni(100)path
Path APath B
Path C
Path APath B

Potential energy [eV]
0.321
0.444
0.443
0.728
1.105

Table 3 Migration potentials of Cu adatom
corresponding paths shown in Figs. 1
face
Ni(110)Ni(100)path
Path APath B
Path C
Path APath B

Potential energy [eV]
0.309
0.426
0.428
0.523
1.080

report.[4]In conclusion, the present calculation

lowest energy. Atom exchange processes suchshowed that in addition to the surface migrationas path B and C have higher energy than path A.

of adatom such as Ni and Cu, atom exchange

Experimentally, only path C was seen by FIM

may be possible on the Ni(110) surface, but

study [1]. Although the present calculation ofslightly higher energy, i.e., higher temperature

the energy barrier of path C gave 0.36 mV

is needed for replace surface atom with adatom

lower than that of path B, but we failed toon the Ni(100) surface.

reproduce the experimentally observed large

References

difference in the exchange probability between[1] G. Antezak and G. Ehrlich, Surf. Sci.

path B and C [1]. This seems to indicate theReports 62 (2007) 39.

thermal effect, i.e., collective motion of[2] H. Jonsson, G. Mills and K. W. Jacobsen,

adatoms and surface atoms is crucial to theCondensed Phase Simulations, ed. B. J. Berne,

atom exchange process and molecular dynamic

G. Ciccotti and D. F. Coker (World Scientific,

study should be required for understanding this1998).

discrepancy.

[3] J. P. Perdew, K. Burke, and M. Ernzerhof,
Phys. Rev. Lett. 77 (1996) 3865.

For the Ni(100) surface, adatom diffusion
along the [110] direction, path A in Fig. 1(b),[4] B. Müller, B. Fischer, L. Nedelmann, A.

again had a lower energy than atom exchange

Fricke, and K. Kern, Phys. Rev. Lett. 76 (1996)
2358.

process path B, in agreement with the previous

140

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of the ﬁrst-principles method for
calculating Tc based on density functional theory forsuperconductors
Ryosuke AKASHI
Department of Physics, The University of Tokyo

The ﬁrst-principles prediction of the superconducting transition temperature Tc of metals
is a challenging goal in the condensed matterphysics. For phonon-mediated superconductors, accurate calculation schemes is now available on the basis of the Eliashberg theory anddensity functional theory for superconductors(SCDFT) [1, 2]. In this year, we conducted adevelopment of a ﬁrst-principles method withthe latter theory.
In the conventional superconductors, thephonon-mediated attraction is the dominantsource of the electronic pairing interaction,
where the electron-electron Coulomb repulsion
has only a secondary role that it partially cancels the attraction. On the other hand, as the
Coulomb interaction becomes stronger, there
emerges a chance for it to aﬀect the superconductivity in a diﬀerent way. A prominent example is the plasmon-mediated pairing
mechanism [3, 4]: the frequency dependenceof the screened Coulomb interaction enhances
the pairing. Another is the spin-ﬂuctuation
mechanism, where ferromagnetic ﬂuctuationstrongly suppress the singlet pairing [5, 6, 7, 8].
We have developed an SCDFT based method
to calculate Tc with the plasmon and spin ﬂuctuation eﬀects included. In this project, wemade further progress along this line. In the
SCDFT, the superconducting Tc can be evaluated by solving the following gap equation∆nk = −Znk ∆nk−

1∑tanh[(β/2)En′ k′ ]Knkn′ k′∆n′ k′ .(1)2 n′ k′En′ k′The kernels K and Z represent the eﬀectof the electron-phonon and electron-electron
Coulomb interactions. By developing new
forms of K we can in principle incorporate
novel interaction eﬀects. β is the inverse temperature and Enk is the Kohn-Sham energy
eigenvalue.
First, we constructed a formalism of theexchange-correlation functional in the SCDFT
based on the adiabatic connection formula [9].
We formally conﬁrmed that this formalism reproduces the previous one.
Next, we extended this formalism and derived a formula for the exchange-correlation
kernel beyond the local density approximation. As this is numerically too demanding,
we are continuing exploration of eﬃcient numerical implementation of the newly developed
formula.
We also tested an implementation of the
SCDFT-based Tc calculation in Superconducting Toolkit [10] to see if the previously
published values [8], calculated with anotherin-house code, are well reproduced. The calculated values (Table 1), though fairly agreeing
with the previously published ones, were generally larger. The overestimation is likely attributed to a subtle implementation details likehow to numerically integrate the internal frequencies. These calculation were performed in
System B (Ohtaka) with parallelization within
a single node. The elapsed time for each Tc

141

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

was approximately less than 30 minutes.
Table 1: Superconducting transition temperature Tc (K) calculated with the SCDFT gap
equation Eq. (1) using Superconducting
toolkit, with and without the spin ﬂuctuation eﬀects. In RPA and LDA, the exchange
correlation kernels entering the K formula [7]are ignored and incorporated, respectively.
RPA
LDA
w.o. SF w. SF w.o. SF w. SF
20.5
2.8
18.1
2.5
V
Al
1.2
0.6
0.9
0.4

References[1] M. Lüders, et al., Phys. Rev. B 72 (2005)
024545.
[2] M. A. L. Marques, et al., Phys. Rev. B 72
(2005) 024546.
[3] Y. Takada, J. Phys. Soc. Jpn. 45 (1978)
786.
[4] R. Akashi and R. Arita, Phys. Rev. Lett.
111 (2013) 057006.
[5] N. F. Berk and J. R. Schrieﬀer, Phys. Rev.
Lett. 17 (1966) 433.
[6] F. Essenberger, A. Sanna, A. Linscheid,
F. Tandetzky, G. Profeta, P. Cudazzo,
and E. K. U. Gross, Phys. Rev. B 90
(2014) 214504.
[7] M. Kawamura, Y. Hizume, and T. Ozaki,
Phys. Rev. B 101 (2020), 134511.
[8] K. Tsutsumi, Y. Hizume, M. Kawamura,
R. Akashi and S. Tsuneyuki: Phys. Rev.
B 102 (2020) 214515.
[9] D. C. Langreth and J. P. Perdew, Solid
State Commun. 17 (1975) 1425.
[10] M. Kawamura, R. Akashi and S.
Tsuneyuki, Phys. Rev. B 95 (2017)054506 .

142

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Calculation of photoelectron angle distribution in thephotoexcitation process on the organic molecules adsorbed
surface
Kaori Niki
Graduate school of science
Chiba University, Yayoi-cho, Inage-ku, Chiba 263-8522
In recent years, it has been reported electronic

Burke-Ernzerhof (PBE) formalism. We used aand physical properties of organic molecules

unit cell with lattice constants a = b = 3.53 Å,

which interact with the surface using Wavec = 20.0 Å, α = β = 90° and γ = 120°, and plane-

numberPhotoelectron

wave basis set with the projector augmented

Spectroscopy. We have investigated thewave (PAW) approach with an energy cutoff ofcopper-380 eV. The Brillouin zone integration was

monolayer substrate system. Monolayer TiSe2

performed on a Monkhorst-Pack of 18×18×1

have two typically phases depending on thegrid of k-points. The energy convergencetemperature. A (1 × 1) structure (normal phase)

criterion was chosen for the self-consistency

is shown at room temperature and a (2 × 2)

cycle was 1×10-7 eV. To account for Fermi

superstructure (CDW phase) is realized undersurface broadening, temperature parameter σ

the 200 K. Each phase has band gap of 83 meV

for Methfessel-Paxton smearing was appliedand 153 meV, respectively [1, 2]. We have[5].

adopted this interesting thin film as the

We investigated a local Coulomb repulsion ofsubstrate and reported the structural changes

Ti 3d electrons and the effect of the electronic

depending on the temperature in the previous

smearing parameter σ on the band gap. We

year.

In this year, we investigated thecalculated band gaps with different sets ofelectronic state of a (1 × 1) monolayer TiSe2.

Coulomb repulsion U and σ. Fig. 1(a) show a

Based on these results, we optimized thenegative bandgap without considering U andstructure of CuPc adsorbed on TiSe2.

σ. On the other hand, fig. 1(b) and (c) have

1. Band calculation of TiSe2 monolayer

positive bandgaps close to 0. It is found that

We performed density functional theory

both σ and U increase the gap between the top(DFT) calculations using the Vienna Ab Initio

of Se 4p band (Γ, red point) and the bottom of

Software Package (VASP) version 5.4.4 [3,4].

Ti 3d band (M, blue point). However, the rise

The

were

in σ push up the upper end of the Se4p band

Gradient

above the fermi surface, so Fig. (b) is also

Approximation (GGA) within the Perdew-

excluded. As a result, we find the parameter set

space

(Ⅱ)

exchangedescribed

byresolvedphthalocyanine

correlation
the(CuPc)

effects

Generalized143

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo(U = 3.9 eV and σ = 0.01 eV) which reproduce

structure of the monolayer TiSe2 with lateralexperimental result [6]. We used these

dimensions of 693 Å2. For Cu atom of CuPc,

parameters for optimization of CuPc / TiSe2

U value was adjusted to 4.0 eV which could

structure.

reproduce the qualitative orbital ordering ofisolated CuPc. In addition, CuPc had an
unpaired electron, thus we considered spinpolarization. Ionic positions were optimized
until the residual force on each ion was lessthan 1×10-2 eV/Å. When starting with arandom wave function, it took about 12 hours
to converge one electronic state using 5 nodes
with total 144 cores. From this structure
optimization calculation, it is found that theadsorption distance between molecule andsubstrate is 3.16 Å, resulting in a flat molecule
structure.
We have reached the stage where it is possible
to calculate the Wave number space resolved
Photoelectron Spectroscopy. We are planningto perform this calculation next year.

References[1] J.-P. Peng et. al., Phys. Rev. B 91, 121113(2015).
[2] P. Chen et. al., Nat. Commun 6, 8943
(2015).
[3] G. Kresse and J. Furthmuller, Phys. Rev. B,
54, 11169 (1996).
Figure 1 Band dispersion of the (1×1)[4] G. Kresse and J. Hafner, Phys. Rev. B, 49

monolayer TiSe2 with different electronic

14251 (1994).

smearing parameter σ and effective Hubbard[5] M. Methfessel and A. T. Paxton, Phys. Rev.

parameter U for Ti.

B 40, 3616 (1989).

2. Structural optimization of CuPc/TiSe2[6] R. Bianco et.al., Phys. Rev. B 92, 094107

We expanded above model for an 8 × 8(2015).

144

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Physical properties of layered graphene
Yoshitaka FUJIMOTO
Depertment of Physics, Tokyo Institute of Technology
Oh-okayama, Meguro, Tokyo 152-8551

Graphene is one of the most promissing materials for electronics devices including ﬁeld effect transistors and molecular sensors. Bilayerof graphene would have rich properties because electronic structures of graphene change
depending on how two layers interact witheach other. Here, we study the stackingpattern eﬀects on the electronic transport andmolecular adsoprtion of bilayer graphene using a ﬁrst-principles density-functional calculation [1, 2, 3].
It has been reported that the bilayer
graphenes with three diﬀerent stacking patterns (AA, AA′ , and AB) have been synthesized and observed experimentally. Table 1
lists the adsorption energies and the binding
distances between the B atom and the adsorbed molecule for various molecules on the
B-doped bilayer graphenes with three diﬀerent
stackings. For all stacking patterns, CO andCO2 molecules are adsorbed not strongly but
weakly, whereas NO and NO2 molecules canbind strongly with the large adsorption energies and the short binding distances. O2 andN2 molecules weakly bind with small adsorption energies. Therefore, only NO and NO2
molecules in air are adsorbed with chemicalbonds on the B-doped bilayer graphene without depending on the stacking patterns.
We study electronic transport of the pristine
bilayer graphene for the three diﬀerent stackings. The conductance for the AB stacking has
the linear dispersion near E = 0 eV as in thecase of the monolayer. On the other hand, unlike monolayer, the slope of the conductancecurve between 0 eV and ∼ ±0.25 eV is diﬀerent from that between ∼ ±0.5 eV and ±1.0
eV, respectively. Due to the diﬀerence of theslope of the conductance curve in diﬀerent energy ranges, the transport properties induced

145

by the adsorption of molecules would be diﬀerent from that of the monolayer. The ﬁnite conductivity in the AB-stacked bilayer graphene
was reported theoretically and observed experimentally. The conductance of the AA-stacked
bilayer graphene seems to have constant value
from the energies E = −0.25 eV to +0.25 eV,
and it increases linearly below −0.25 eV andabove +0.25 eV. Unlike the AA-stacked bilayer
graphene, the conductance of the AA′ stacking
shows asymmetric behaviors near the Fermi
energy. Thus, it is interesting that the conductances of the bilayer graphenes with AA,
AA′ and AB stackings are diﬀerent from one
another.
We study the molecular adsorption eﬀects
on the transport of the B-doped bilayer
graphenes for three diﬀerent stackings, anddeﬁne ∆G(E) = (Ga − Gb )/Gb × 100(%),
where Ga and Gb are the conductances of the
B-doped bilayer graphene with and without
molecules, respectively. When NO and NO2
molecules are adsorbed on the AB-stacked bilayer graphene, the conductances at the energy E = 0 eV change with ∆G(0) = +8.2%
and +3.0%, respectively. For the AA stacking,the adsorptions of NO and NO2 molecules can
induce ∆G(0) = +2.1% and −17.4% in the
conductances, respectively. In the case of the
AA′ stacking, there are sizable conductancechanges of −17.2% and −47.7% for the adsorptions of NO and NO2 molecules, respectively.
In summary, the stacking-dependent behaviors of the transport and the adsorption
properties of molecules of bilayer graphene
have been investigated for various molecules
including environmentally polluting or toxic
molecules and common molecules (NO, NO2 ,CO, CO2 , O2 , and N2 ) using a ﬁrst-principles
density-functional study. Irrespective of stack-Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 1: Adsorption energy Ea (eV) and distance d (Å) between molecule and B atom for eachmolecule adsorbed on B-doped bilayer graphenes with AA, AA′ , and AB stackings.
Stacking
NO
NO2
CO
CO2
O2
N2
AA
Ea −1.20 −1.12 −0.12 −0.04 −0.16 −0.28
d
2.15
1.60
2.90
2.87
1.76
2.96
AA′
Ea −1.22 −1.15 −0.12 −0.04 −0.19 −0.28
d
2.15
1.60
2.90
2.87
1.75
2.96
AB
Ea −1.19 −1.13 −0.12 −0.03 −0.20 −0.27
d
2.14
1.60
2.89
2.84
1.75
2.93

Table 2: Percentage of changes in the conductance at the Fermi energy E = 0 [∆G(0)] foreach molecules adsorbed on B-doped bilayer
graphene with AA, AA′ , and AB stackings.
The changes in the conductance are calculatedwith respect to the B-doped bilayer graphene.
AA
AA′
AB
NO
2.1
-17.2
8.2
NO2
-17.4
-47.7
3.0

ing patterns, only NO and NO2 moleculesin air can bind strongly on B-doped bilayer
graphene. It is found that the conductancecurves of bilayer graphenes change depending on the stacking patterns and the presenceof the NO/NO2 molecule, and the variationof the conductances induced by molecular adsorptions could be used by gas sensing devices
such as ﬁeld-eﬀect transistors under low bias
voltages.

References[1] Y. Fujimoto and S. Saito, Appl. Surf. Sci.
Adv. 1, 100028 (2020).
[2] Y. Fujimoto, Mod. Phys. Lett. B 35,
2130001 (2021).
[3] Y. Fujimoto and S. Saito, J. Electrochem.
Soc. 169, 037512 (2022).

146

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Computational materials design of Ag and Cu chalcogenide
based thermoelectric materials
Ho Ngoc Nama) and Kazunori Sato a, b)
a)b)

Graduate School of Engineering, Osaka Univ., Yamadaoka, Suita, Osaka 565-0871

CSRN, Graduate School of Engineering Science, Osaka Univ., Toyonaka, Osaka 560-8531
The development of compact, wearable, andrespectively [2]. The effects of the doping ofespecially self-charging personal electronics

transition metal impurities were investigatedhas become more feasible in recent years. As aand the results were consistent with thecontinuous power supply for an uninterrupted

experimental observations [2]. We have also

operation, it is desirable that these electronic

found that experimental transport properties

devices can convert directly the waste heat ofwere reasonably reproduced by using thethe human body or environment into electricity

electron-phonon coupling method, showing thevia flexible thermoelectric (TE) generators. A

suitability of this scattering model in estimating

recent study discovered the extraordinary

the relaxation time [3].

ductility of the inorganic semiconductor silver

In addition to Ag chalcogenides, we havesulfide (Ag2S) [1] paving the way for flexible

also applied our calculation procedures to Cu

TE developments. In this study, we use first-

sulfide systems and found that the defectprinciples calculations combined with theformation energy and transport properties canBoltzmann transport theory to investigate thebe simulated by using the acanthite-likeelectronic and transport properties of Ag andstructure for this material. Based on these

Cu chalcogenide materials.

knowledges, we will extend our computational

First of all, we have chosen the exchange -materials design for (Ag1-x, Cux) (S1-y, Sey)2

correlation functional SCAN+rVV10 in orderchalcogenides to realize flexible TE materials.

to reproduce band gap energy and lattice

References

constants of a-Ag2S reasonably. According to[1] X. Shi et al., Nat. Mater. 17 (2018) 421.

the calculations of the formation energy of[2] H. N. Nam et al., Phys. Chem. Chem. Phys.

typical intrinsic defects, it is found that the23 (2021) 9773.

intrinsic defects greatly affect the system’s[3] H. N. Nam et al., Appl. Phys. Lett. Accepted.

conductivity where Ag vacancy and interstitial[4] H. N. Nam et al., Phys. Rev. B105 (2022)

Ag

075205.

act

asp-typeandn-typedefects,

147

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Thickness-Dependent Electronic Properties ofAtomically Thin Boron Monosulfide
Masayuki TOYODA
Department of Physics, Tokyo Institute of Technology
Ookayama, Meguro, Tokyo 152-8551

Rhombohedral boron monosulfide (r-BS) isa meta-stable phase of binary boron-sulfersystem obtained under high-temperature andhigh-pressure condition [1]. Recently, Kondo
et al. have succeeded to exfoliate atomicallythin layers of r-BS from its bulk.
We have studied the electronic structures ofthin layers of r-BS using the first-principles
density functional theory calculations. The
calculations have been performed using themassively parallel computers in ISSP, University of Tokyo.
From the electron localization function(ELF) analysis, we have found that B and S
atoms are covalently bonded in each S-B-B-S
unit layer (Fig. 1). The valence-band maximum (VBM) states are consisted of hybridized
B-pz and S-pz orbital states. By the stackingof layers, the VBM states exhibit splitting, resulting in the systematic narrowing of the bandgap (Fig. 2). This band-gap narrowing has also
been observed in the optical experiement [2]and is suggesting the potential application of
r-BS as 2D semiconductos with tunable band
gap.

Figure 1: Electron localization function along
the atomic bonds in (a) r-BS, (b) h-BN, and(c) MoS2 .

References[1] T. Sasaki, H. Takizawa, K. Ueda, and
T. Endo, phys. stat. sol. (b) 223, 29(2001).
[2] H. Kusaka, R. Ishibiki, M. Toyoda, et al.,J. Mater. Chem. A 9, 24631 (2021).

Figure 2: Calculated band gap values of thinlayer (1 < N < ∞) and bulk (N = ∞) r-BS.

148

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Large-Scale Molecular Dynamics Simulations on NonEquilibrium Phenomena Using First-Principles Calculationand Machine Leaning
Masaaki MISAWA
Faculty of Natural Science and Technology, Okayama University
Artificial neural network (ANN) potential,

movement of atoms occurs during the elastic-

which is an interatomic potential constructed bymachine-leaning,a

In order to improve the predicting ability ofpromising method to achieve extra-large-scale

ANN-potential, we introduce a more accurate

molecular dynamics (MD) simulation withtraining method that uses not only potential

first-principles accuracy [1]. Application of thisenergy but also atomic force and pressure as

ANN-MD to far-from-equilibrium phenomena,reference data [4]. Using this improved ANN-such

pressure-induced

potential, it was succeeded that reproducing thetransformation, is important to understandelastic-to-plastic transition behavior and plastic

structural properties of materials under extreme

deformation of α-quartz with an accuracy closeconditions. For this purpose, we have tried to

to FPMD simulation. Thus, the ANN-potential

perform ANN-MD simulation of shock-induced

trained with energy, force, and pressure is a

structural transformation of silica.

potentially powerful tool to investigate wideasattracts

fracture

andattentionas

to-plastic transition process.

To compute shock-compression behaviors

range of far-from-equilibrium phenomena andwithin the framework of MD method, thewill also provide useful information for solid

multiscale-shock technique [2] was employedearth physics field in future.

in our simulations. Potential energy of shockcompressed

α-quartz

obtainedbyfirst-

References

principles MD (FPMD) method is used as a[1] J. Behler and M. Parrinello, Phys. Rev. Lett.

reference data for training of ANN-potential.

98, 146401 (2007); N. Artrith and A. Urban,

As a result of ANN-MD simulation for elastic

Comput. Mater. Sci. 114, 135 (2016).

shock-wave
behaviorsofregion,elastic-deformation[2] E. Reed et al., Phys. Rev. Lett. 90, 235503

α-quartzwas(2003).

successfully

reproduced with high-accuracy [3]. On the[3] M. Misawa et al., J. Phys. Chem. Lett. 11,

other hand, for plastic shock-wave region, the4536 (2020).

ANN-potential[4] K. Shimamura et al., J. Chem. Phys. 153,has

completely

failedon

234301 (2020).

prediction of both structure and energy, becauseof that irregular structure appears and rapid149

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Defect formation energy and band structure of Pb-based
topological insulators
Yuki TOKUMOTO
Institute of Industrial Science,
The University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8505

PbBi2Te4 topological insulator (TI) is

(DFT)

using

Viennaab-initio

simulationconsidered as one of the promising candidates

package (VASP) version 6.2.1. We adopted

for future spintronics material with a large spin

generalized gradient approximation (GGA)

current density. However, experimental studies

proposed by Perdew, Burke, and Ernzerhofof its surface transport properties have not yet(PBE) as the exchange correlation energy

been reported, owing to a lack of bulk

functional. For all calculations, we included

insulating crystals. So far, we achieved bulk

spin-orbit coupling (SOC). We obtained band

insulating states in Pb(Bi,Sb)2Te4 topological

gap of 115 meV for PbBi2Te4, which is muchinsulators by tuning compositional ratio of Bi

lower than experimentally reported value ~230

and Sb [1]. Although such control ofmeV. In order to estimate band gap morecompositional ratio leads to a change in theaccurately,

type and concentrations of intrinsic point(HSE06) and HSE03 hybrid functional was

defects, the Fermi level is not necessarily well

employed. As a result, band gap was further

tuned. For further success in achieving theunderestimated. We found that the HSE is notbulk-insulating state, not only the reduction ofeffective for accurate estimation of band gap of

absolute amount of charged defects but also thenarrow-gap semiconductors.

theHeyd-Scuseria-Ernzerhof

enhancement of the activation energy is

In 2022, we plan to calculate defectrequired. Recently, it was reported that Snformation energies using GGA-PBE including

doping for Bi2Te2Se TI is effective for lowering

SOC.

carrier concentrations and activated resistivities,
with a localized impurity band that acts as aReferencescharge buffer occurring inside the bulk band[1] Y. Hattori, Y. Tokumoto, and K. Edagawa:gap.

Phys. Rev. Mater. 1 (2017) 074201.

We carried out band structure calculation of
PbBi2Te4 based on density functional theory

150

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Electronic structure of the interfaces
between diamond and alkali metals
Toshihiro SHIMADADivision of Applied Physics, Faculty of Engineering
Hokkaido University, Kita-13 Nishi-8, Kita-ku, Sappooro, Hokkaido 060-8628
The interaction between diamond surfaces

functional. The

initialstructure

for

the

and liquid alkali metals has been little

optimization was created considering the bulk

investigated. We observed the etching process

lattice constants of the Li, Na, and K. 3 × 3 × 4

upon heating and the change in fluorescence ofunit cells of the diamond with 4 layers of alkali

DFT

metal atoms on both sides were employed. We

calculations using the ISSP supercomputer

tried several starting structures do the alkali

were performed to investigate the electronic

metals (lattice constant, orientation and shift),structure,theand the final structures were almost the same.

experimental results can be explained by the

The results are shown in Fig. 1. An upwarddifference in band bending.

shift in the density of states of interfacial

nitrogen

impurities

and

it

(NV-

was

centers).

shown

that

Experimental observation revealed that the

carbon is observed, and it is stronger at theetching of diamond occurred in heated lithium.
K and Na did not show etching.

The

fluorescence

was

of

the

NV-

centerinterface with (c) K.

significantly reduced only in contact withmolten K. This is understandable if we consider
that the negatively charged NV- that emits
fluorescence is lost due to upward band
bending. Although the extent of band bending
dependsonthedopingstateofFig.1 Density of states of carbon atthesemiconductor, the amount and direction of

diamondband bending can be estimated by determining

materials [1].

the positional relationship between the Fermi

Referenceslevel of the undoped semiconductor (in this[1] H. Takehana et al. Carbon 182 (2021) 585.

case diamond) and the metal using DFT[2] https://www.vasp.at

calculations. We used VASP[2] with PBE

151

interfaces

withvarious

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Automatic generation of first-principles effective models based on MLO
Hirofumi SAKAKIBARA
Advanced Mechanical and Electronic System Research Center (AMES),
Tottori University, Tottori, Tottori 680-8525

To thematerial informatics,

structure. Historically, we already have theautomatic generation of data is the central part

technique of Maximally Localized Wannierof calculations. According to the density

Functionfunctional theory (DFT) and local density

contains several difficulties or automation

approximation

calculateespecially for the system spanned by s- and p-

electronic structure, which generally controls

orbitals like semi-conductors. Therefore, fortheproperties,

calculating mixed system (superlattice and sosystematically without any empirical inputs.

on) containing not only the localized electrons

The DFT calculation itself is not so much

such as d-electron but also (s- or p-) delocalized

demanding in computational resources as longelectrons, MLWF is not a perfect method.

most

goal

of

(LDA),

part

of

we

can

material(MLWF)[1],

however,

MLWF

as we consider tens of atoms per unit cell.

For the goal of automation, we have already

Therefore, DFT calculations have been taken

constructed a new method named Muffin-tin

advantage of material informatics.

Like Orbital (MLO). MLO is given as a linear

The band structure within few eV measured

combination of atomic basis functions, which isfrom Fermi energy is effective for material

used for the first-principles calculations based

properties at low temperature. In other words,

on LMTO algorithm. Thanks to the PMT

wholeexcessmethod [2], we can take into account the effects

information. Even the drastic development ofof extended electron orbital such unoccupied

computational power, the computational coststates can be considered in the localized basis.

beyond the DFT calculations, for example

Here, PMT is a mixed basis function for first-

many body calculations, are still sometimes

principles calculation between Plane-wave anddemanding.

new

Linear Muffin-Tin orbital. By a kind offunctional material such as magnets and/or

weighted sum method, we can take into accountsuperconductors driven by electronic many

the effect of unoccupied orbital to the low-body effects, it is convenient that we canenergyautomatically construct a model which only

numerically.

band

structure

Therefore,

containsforminingcontains the low-energy part of electronicmodels’senergyeigen

valuesFor the benchmark materials, we have152

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

free electron’s Bloch orbital.

chosen four simple samples: Si(already shown
Fig.1 of the 2020’s report), SiO2(cubic),

For the future work, we have to simplify and

SrTiO3, and graphene. For all samples, thesophisticate MLO algorithm to save theautomation of model construction is succeeded.

computational times and to adopt for more

For SrTiO3, components described by plane-larger system such as superlattice, heterowave (namely, interference of unoccupied

junctions, and surfaces.

orbitals to the low-energy model) bases is few.
This can be interpreted that LMTO is asufficiently accurate basis function for SrTiO3.
For graphene, we can obtain a two-orbital
model which contains only C-pz’ π -bondReferences

orbitals forming the Fermi surface (or, Dirac[1] N. Marzari and D. Vanderbilt, Phys. Rev.

cone). Surprisingly, it is revealed that such π-

B 56, 12847 (1997).

bonds contains much plane-wave components.

[2] T. Kotani, H. Kino, and H. Akai, J. Phys.

For SiO(cubic), we find that an empty sphere inSoc. Jpn. 84, 034720 (2015).

a relatively large interstitial region is necessary
to reproduce the extended orbital shaping like a

153

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical Study on Electronic Properties
in New Nanoscale Surfaces and Interfaces
Katsuyoshi KOBAYASHI
Department of Physics, Ochanomizu University
2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610

References[1] M. Bonilla et al.:(2018) 289.

Nat. Nonotech. 13[2] K. Sumida et al.: Phys. Rev. Materials 6(2022) 014006.

154

Energy (eV)

(a)

Γ

M

Γ

M

(b)
Energy (eV)We theoretically studied the electronic
structures of VSe2 monolayers.
Recentlymonolayers of transition-metal dichalcogenides(TMD) are extensively studied. Much attention is paid to magnetic properties of TMD
monolayers in recent years. Room temperature
ferromagnetism was reported for VSe2 monolayers in 2018 [1]. However, there is a controversy over its emergence. A recent experiment suggested that VSe2 monolayers are on
the verge of ferromagnetism [2]. We performed
a density-functional calculation on this system.
We used the program package VASP for thedensity-functional calculation. Figure 1 shows
the calculated result. Figure 1(a) and (b) show
band structures of the VSe2 monolayer in nonmagnetic (NM) and antiferromagnetic (AFM)
states, respectively. The magnetic structureof the AFM
state is shown in Fig. 1(c). We√√
used a 3 × 3 supercell of the primitive cellin the calculation. Γ is the center in the twodimensional Brillouin zone. M is the point at
the half of a primitive reciprocal lattice vector.
We found that the band structures of NM andAFM states are very similar.
In addition to the VSe2 monolayers we performed calculations of electronic structures of
V5 Se8 . We unfolded the calculated band structures in order to compare with experimental
band structures obtained from angle-resolved
photoelectron spectroscopy.

(c)Figure 1: Band structures of a VSe2 monolayer in nonmagnetic (a) and antiﬀeromagnetic(AFM) (b) states. The magnetic structure of
the AFM state is shown in (c). Red and green
circles show V and Se atoms, respectively. Arrows express the spin structure.

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles calculation of graphitization of diamondsurface and its exfoliation process
Kouji Inagaki
Graduate School of Engineering, Division of Precision Engineering and Applied Physics
Osaka University, Yamada-oka 2-1, Suita, Osaka 565-0871
Diamond has a wide bandgap electronic
property

and

high

mechanicalatoms (shown in (a) and (b)). This is carried out

strength;

by artificially adding a constant value of 0.002

application of diamond to semiconductor

Bohr to z axis of the terminal atoms in every

electronic devices or to mechanical cutting tools

quenched MD step with optimizing along x andare expected [1]. In electronic device appli-

y directions for the atom and other surface atoms.

cations, polishing is required to produce a flat

This procedure is repeated until saturated. The

surface, but diamond is the hardest material andbond breaking energy 2.1eV is obtained by theit is not easy. On the other hand, in toolenergy difference between (b) and (c), while cor-applications, a serious wear property in cutting

responding value of pristine surface is muchiron-based materials is reported. By utilizing thislarger energy of 3.2 eV. This indicates C-C bondwear phenomenon, it may be possible to realize

is effectively weakened by a Fe atom.

a novel diamond surface flattening method.

It is concluded that a Fe atom can play a

Currently, two possible causes of wear arecatalytic role in peeling graphite layer formed on

proposed: graphitization of diamond surface,diamond surfaces. Further investigations will be

and diffusion of C atoms into metal. This issue

required to evaluate metal element, atomic

remains unclear, particularly in the mechanism

environment effect, etc.

how strong C-C bonds break.
In this study, we investigated weakening of
C-C bond by the effect of Fe atom to confirm(a) Pristinegraphite layer peeling. Figure 1 (a) and (b)(b) Fe inserted (c) Peeled

Fig. 1: Peeling of graphite layer formed on dia-shows side views of the surface structures ofmond (221). Bright, dark and small atoms indi-

diamond (221) with and without Fe atom, andcate C, Fe and H atom. Atoms directed by arrow(c) peeled structure with Fe atom. (Peeled inare pulled-up to obtain peeled structures.

pristine structure is also perfomed but not

Reference

shown.) A DFT-based STATE code is employed[1] J.Wang, G.Zhang, N.Chen, M.Zhou, Y.Chen

to obtain stable structures and energies. Peeled

Int. J. Adv. Manufac. Technol. 113 (2021) 3027.

structures are obtained by pulling-up terminal

155

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

AB type 2D materials searchby high-throughput DFT calculations
Masahiro FUKUDA
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
Recent rapid research progress of twodimensional (2D) materials have revealed that
2D materials are expected to be goodcandidates for future applications and devices.
In our previous research, we construct a
structure map [1] and a web-based database [2]of AB2 type monolayers by high-throughput
DFT calculations using OpenMX [3].
In this project, a structure map for AB typemonolayers of 2016 compounds which are all

Fig.1:

the combinations of 63 elements selected from

Examples

of

basic

planarstructures of AB type monolayers.

the periodic table (except for noble gases,

distortion, buckling and so on.

lanthanoids and actinoids) is constructed byhigh-throughput calculations based on the DFT

The genealogical classification helps us to(GGA-PBE) with the symmetry-unconstrained

understand phase transitions caused by latticegeometry optimizations and variational cell

matching with a substrate, stacking layers,

optimizations starting from several structures

external bending, tensile and compressive

such as ferromagnetic planar square lattice andstresses, and so on, when we invent newplanar honeycomb lattice structures as initialdevices.

states. We classified the converged structuresby planarity, the number of atoms in a unit cell,

References

2D Bravais lattice and space-group symmetry.

[1] M. Fukuda, J. Zhang, Y.-T. Lee, T. Ozaki,

The classification makes it clear that most ofMater. Adv., 2, 4392 (2021).

the AB type monoatomic layers are understood[2] Structure map and database of AB2 type 2D

as basic planar structures and their derivationmaterials (www.openmx-square.org/2d-ab2/).

patterns such as the shape of the primitive cell,[3] OpenMX, http://www.openmx-square.org

156

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Charge storage mechanism of Ti3C2Ch2 (Ch = O, S, Se, Te)
Kosuke Kawai, Masashi Okubo
Department of Electrical Engineering and Bioscience, School of Advanced Science andEngineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555

We have investigated the charge storage
mechanismsoftransition

metalof Ti27C18Ch18 (Ch = O, S, Se, Te), all Al atoms

carbidesand a Ti3C2 monolayer were removed from

(MXene) based on density functional theory

Ti6Al2C4, which was obtained from the(DFT) calculations. This year, we focused onMaterials Project (ID: mp-3747), and expanded

the dependence on termination function group

to a superstructure of 3×3×1 (Fig. 1a).

of a Ti3C2Tx monolayer.

Structure optimization calculations were carried

DFT calculations were performed with theout before and after adsorption of Zn atom on

Vienna ab initio simulation package (VASP).

A–C sites (Fig. 1b). Bader charge analysis was

The projected augmented wave method and aperformed using the script provided byplane basis set implemented in the VASP code

Henkelman’s group.3

were utilized with a cutoff energy of 520 eV

Adsorption at A and B sites are preferred toand k-point sampling on a 4×4×2 grid.1 The

that at C site (Fig. 2a) due to more coordination

generalized gradient approximation of thenumber with Ch atoms (3 for A and B site vs. 1

Perdew–Burke–Ernzerhof exchange-correlation

for C site). Averaged adsorption energy, whichfunctional was used.2 To prepare the slab model

would

be

inversely

proportional

Fig. 1 (a) The model structure of Ti27C18Ch18 (Ch = O, S, Se, Te) and (b) absorption
sites on the Ti27C18Ch18 monolayer. These structures were described using VESTA.4

157

to

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

charge/discharge rates, was in the order of Te <References

Se < O < S. Net charge transfer through Zn[1] G. Kresse, J. Furthmüller: Phys. Rev. B 54

adsorption increased in the order of Te < Se < S(1996) 11169−11186.

< O (Fig. 2b), which likely arises from more

[2] J. P. Perdew, K. Burke, M. Ernzerhof: Phys.

electronic interaction with more electronegative

Rev. Lett. 77 (1996) 3865−3868.

atoms. These results imply that Ch = O is the[3] W. Tang, E. Sanville, G. Henkelman:most preferable to achieve both a large

J. Phys.: Compute Mater. 21 (2009)

capacitance and fast charge/discharge rates

084204.

simultaneously in electrochemical capacitors[4] K. Momma, F. Izumi: J. Appl.

using Zn2+ ion as an adsorbed species.

Crystallogr. 41 (2008) 653−658.

Fig. 2 (a) Adsorption energy and (b) net
charge transfer for Zn atom on the
Ti27C18Ch18 (Ch = O, S, Se, Te) monolayer.

158

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Diffusion behavior of hydrogen in tungsten-rhenium alloy
Kazuhito Ohsawa
Institute for Applied Mechanics, Kyushu University,
Kasuga-koen, Kasuga, Fukuoka 816-8580

Introduction

Simulation Method

Tungsten (W) and its alloys are plausible

The stable positions of H in the W-Re alloys

candidates for plasma facing materials (PFMs)

and their energy levels are calculated in terms ofused in fusion reactors because of their excellent

first-principle calculations based on density

properties, e.g. high melting point, low hydrogen

functional theory. We use Vienna ab-initio(H) solubility, and toughness for irradiation.

simulation package (VASP). Large simulation

However, a large amount of H and H isotopes

cell composed of 5x5x5 bcc lattice (250 atoms)

are retained in vacancy (V) and vacancy typeare used to avoid the effects of periodic

lattice defects in the W specimen nucleatedboundary condition imposed on the simulation

under the irradiation circumstance. In particular,

cell. The cut-off energy of plane wave is 350eV.

tritium (T) retention in the PFMs is a serious

Re density is assumed to be low (less than 0.8

problem for safety operation of fusion reactors.

atomic percent) in the W-Re alloys. Besides,

By the way, rhenium (Re) is created in the Wenergy profiles of H along the migration paths in

specimen by nuclear transmutation in thethe W-Re alloys are estimated by nudged elastic

neutron irradiation circumstance in fusion

band (NEB) method.

reactors. The effects of Re addition on the W

We investigate energy profiles of H in two

specimen were investigated. Fortunately, thetype of W-Re model alloys, including one andmaterial properties are improved by the Re

two Re atoms, as shown in FIG. 1 and 2,

addition. For example, the H retention isrespectively.

decreased because

vacancy

nucleationissuppressed by the presence of Re. Besides, theResults

plasticity is also improved. Therefore, theH atom in the pure W and W-Re alloy is suited

application of W-Re alloys are positively

at tetrahedral interstitial site (T-site). Migrationconsidered for the PFMs instead of pure W.

energies are estimated as barrier heights for H to

In the present work, properties of H in W-Re

move to the neighboring T-sites. In pure W

alloys is investigated. In particular, diffusion

lattice, migration energy for H is estimated to be

behavior of H in the W-Re alloys.

about 0.21eV.

159

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

In FIG. 1, T-sites (a-i) in the vicinity of a Re

from the two Re atoms. So, the migration

atom and migration path of H from T-site (a) toenergies of H to move the neighboring T-site are(i) are shown. T-site (a) and (b) situated nearest

estimated to be 0.21-0.22 eV, which is almost

to the Re atom are geometrically equivalent.

same as that in pure W.

Energy profiles of H at the T-sites and along the
migration path A are shown in FIG. 3. H located

Summary and Discussion

at T-site (a) and (b) are about 0.1 eV unstable,

According to H energy profile, H will keepcompared with that located far enough away

away from Re in the W-Re alloys. Therefore, thefrom the Re. Therefore, T-sites close to Re arehigher Re density becomes, the lower H

supposed to be unfavorable for H.

solubility becomes. If Re density is low, theFIG. 2 shows likely migration path of H in the

migration energy of H in the W-Re alloy is

W-Re alloy including two Re atoms. The path isestimated to be about 0.21eV, which is similar toassumed to avoid T-sites close to the Re atoms.

that in pure W. However, the room available for

FIG. 4 shows energy profile of H along the

H diffusion becomes smaller by the Re addition.

migration path B from T-site (1) to (12). The

So, H diffusivity in W-Re alloy would be lower,

migration path B keeps an appropriate distancecompared with that in pure W.

FIG. 1: Schematic view of W-Re alloy
including one Re and H migration path A.

FIG. 2: Schematic view of W-Re alloy
including two Re and H migration path B.

FIG. 3: Energy profile of H along the path A in FIG. 1.

FIG. 4: Energy profile of H along the path B in FIG. 2.

160

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Clarification of atomistic mechanism application of process
design for adhesion interface between metal and plasmatreated fluoropolymers using first principles calculation
Yuji Ohkubo, Misa Nishino, and Kouji Inagaki
Graduate School of Engineering,Osaka University, 2-1 Yamadaoka Suita, Osaka 565-0871
Recently, increasing frequency of the digital

Our calculations were performed using thesignals is necessary because the amount of

STATE (Simulation tool for atom technology)

information

increasing.

code with plane-wave basis and ultra-soft

However, the higher the frequency, the greater

pseudopotential[2, 3]. The wave function and thetheTherefore,charge density of cutoff energies were 36 andpolytetrafluoroethylene (PTFE) which has low

400 Ry, respectively. Generalized gradientrelative dielectric constant and dielectric loss

exchange-correlation

tangent is considered as suitable as dielectrics ofPredew-Burke-Ernzerhof (PBE) was used forhigh frequency printed wiring boards. However,

the exchange-correlation functional and DFT-PTFE has low adhesion property, so adhering

D2 was used for the dispersion correction

PTFE to Cu is difficult. We have achieved

method[2, 3]. Cu surface was modeled Cu(111)

generation of oxygen-containing functional

4×4 slab composed of 3 atomic layers. As thegroups and adhesion strength of 0.94 N/mm

model of as-received PTFE, CF3–CF3 was

between PTFE and Cu when PTFE was He-

calculated. In addition, CF2=CF2, CF3–CF2–OO・,

plasma-treated at over 200℃ under atmospheric

CF3–CF2–OH, and CF3–CF=O were calculatedpressure[1]. However, the factor improving

as the model of plasma-treated PTFE. These

adhesion property, such as the chemical reaction

were the models of molecule containing oxygen-

at PTFE/Cu interface and the value of adsorption

containing functional groups observed by C1s-

energy has not been investigated. Therefore, in

XPS spectrum of the plasma-treated PTFE

this study, in order to explore functional groups

surface. Cu surface, fluorinated molecules, andcontributing to improvement in adhesion

adsorption systems were optimized then total

property, the reaction between Cu(111) surface

energies were calculated. The adsorption energy

and fluorinated molecules was analyzed and thewas defined as the difference between the sum

adsorption energy was calculated by means ofof total energy of Cu surface and fluorinatedfirst-principles calculations.

molecules and total energy of adsorption system.

communicationtransmission

loss

is

is.

161

functional

based

on

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Fig. 1shows theoptimized

Table 1 Value of adsorption energies on
Cu(111).

atomicgeometries for CF3–CF3. CF3–CF3 was notbonded to Cu surface and the value of adsorptionenergy was 0.25 eV in case of both on top siteand on bridge site. This is because C–F bonding
energy of 5.02 eV[4] is large and C–F bond isstable. After optimization for CF3–CF2–OO・, O–

COO・, the adsorption energy was the highest

O bond in CF3–CF2–OO・ was broken and CF3–

and the molecule was stable.

CF2–O・ and O were bonded to Cu surface,In this study, the functional groups

respectively. In this case, the sum of adsorption

contributing to improvement in adhesionenergies of CF3–CF2–O・ and O was calculated

property were explored by calculating theas the adsorption energy of CF3–CF2–OO・.

adsorption energies by means of first-principles

Therefore, the calculation of adsorption energy

calculations. From the result of calculations, theof CF3–CF2–O・ which is broken O–O bond atadsorption energy of molecules containing

initial state was added. Fig. 2 shows the

COO・ was the highest. Therefore, generating the

optimized atomic geometries for CF3–CF2–OO・

functional groups containing COO・ is possible

and CF3–CF2–O・. The adsorption energy wasto generate PTFE surface having high adhesion

3.10 eV, and the highest adsorption energy wasproperty. However, the calculations about Cu

obtained. Table 1 shows the value of adsorption

surface having different miller indices areenergies by calculation. The value of adsorption

needed because Cu surface has not only Cu(111),

energies of CF3–CF3, CF2=CF2, CF3–CF2–OO・,

but also Cu(100) and Cu(110). In addition, theCF3–CF2–O・, and CF3–CF=O was 0.25 eV, 0.68

calculations copper oxide such as CuO andeV, 4.73 eV, 3.10 eV, 0.60 eV, and 0.74 eV,

Cu2O are also needed because Cu surface isrespectively. In case of molecules containing

likely to be oxidized.

References[1] M. nishino et al., INTERFINISH2020
Abstract, C-SEP06-004 (2020) 210.
[2] K. Toyoda et al., J. Chem. Phys. 132 (2010)

Fig. 1 Atomic geometries for CF3–CF3
model (a) on top site and (b) on bridge site.

134703.
[3] K. Toyoda et al., J. Nanosci. Nanotechnol. 11(2011) 2836–2843.
[4] H. O. Pritchard et al., Chem. Rev. 55 (1955)

Fig. 2 Atomic geometries for (a) CF3–CF2–
OO・ model and (b) CF3–CF2–O・ model.

745–786.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles electronic structure calculation of
double-perovskite photocatalyst
Kazume NISHIDATE
Department of Systems Innovation Engineering, Graduate School of Science and Engineering,
Iwate University, 4-3-5 Ueda, Morioka, Iwate, 020-8551

Double-perovskite oxides, A2 B ′ III B ′′ V O6 ,have been extensively studied due to their intriguing physical and chemical properties originating in their mixed valence nature[1]. Above
all, Ba2 B ′ III B ′′ V O6 was found to show an efﬁcient photo catalytic activity to dissolve water molecules into oxygen and hydrogen gases.
While TiO2 has been known to be an practical photo catalyst, it uses only the ultraviolet
rays which is less than 3 % of the sunlight pouring on the earth surface. On the other hand,the catalytic function of Ba2 B ′ III B ′′ V O6 double perovskite is activated under visible lightand hence has a great potential as a photocatalyst in daily use. In this work, we study
the surface electronic properties of Ba2 PrBiO6
double-perovskites. We used the DFT code of
Quantum ESPRESSO throughout our study.
PAW potentials were employed to represent
the core region and the PBE functional wasapplied for exchange correlation. We also usedthe HSE06 hybrid functional to evaluate theband gap values. We constructed slab system with three units along the z-axis exposing(001) surface. The vacuum region was taken to
be 20 Å height. Where two types of surfaces
can be exposed as the (001), namely, the BaO polar-surface and the Pr-Bi polar-surface.
We calculated the surface band structures andidentiﬁed the band gaps as well as their work
functions for these polar-surfaces.

1). Top components of the valence band arecomprised of oxygen orbitals, while the isolated bottom part of the conduction band isderived from the Bi orbitals. The surface bandgap value was estimated to be 1.93 eV within
the HSE hybrid functional level. The band gap
value of the bulk system with the HSE is foundto be 3.70 eV, therefore we think that the bulk
band gap is signiﬁcantly modiﬁed at the surface region. However, experimentally obtained
optical band gap value is 1.07 eV and which isstill half of the surface band gap obtained inthis study. We think the origin of the discrepancy is the B-site disordering (Pr↔Bi). Now,
we have been studying the eﬀect of the B-site
disordering by evaluating the band gap of thesystem.

Figure 1: Ba-O surface band structure.

References
As an example, we show the Ba-O surface band structure calculated within the
PBE exchange-correlation functional (Figure[1] S. Vasala and M. Karppinen: Prog. in
Solid State Chem. 43 (2015) 1.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Electronic structure calculation for a transition-metalmonoxide using a four-atom-configuration model
Takayuki MAKINO
Research Center for Development of Far-Infrared Region,
University of Fukui, Bunkyo, Fukui, 910-8507

We have studied an electronic property of atransition-metalmonoxide.

Recently,

Ry which required a 6×6×6 k-point mesh.

thisAdopted pseudopotentials are based on themonoxide was reported to have an indirect gap

projector augmented-wave method.

whose energy is ca. 0.2 eV [1]. It is well known
that these compounds have been poorly

Introduction of Hubbard U – It should be

described by the density functional theory

noted that in addition to the Hubbard U on the d(DFT) with using commonly used approximate

orbital (Ud) in the transition-metal element, wefunctionals. It was very difficult for us to

introduced that (Up) on the p orbital of the

reproduce this insulating ground state of thisoxygen atom. An additional introduction of Upmonoxide, only with the simple DFT+U

is believed to be useful to open the gap (i.e.,

calculation. The word “simple” means anleading to a correct insulating ground state) due

application of only the on-site Hubbard energy

to the existence of the exchange-inducedon the d electrons. In this work, we explain

splitting. The value of Up (ca. 21 eV) has been

about several extensions [2] that we learned

determinedfrom literatures [2] and used to reproduce theresponse approach. On the other hand, if we

insulating ground state. We used the pwscf

tried to decide the value of Ud self-consistently,

codes included in the Quantum ESPRESSO

we could not reproduce the insulating ground(QE) package [3]. We performed the following

state theoretically. Therefore, as a compromise,jobs to obtain the theoretical electronic andwe set Ud of ca. 4.4 eV. We did not adopt thevibronic properties.

magnetic exchange J parameter for this

by

the

self-consistentlinearcalculation.
Self-Consistent Field Calculation – No matter
what physical quantity is calculated; one must

Spin-polarized DFT+U – The primitive cell offirst determine the electron density. We used a

the rock-salt structure is composed of two

50 Ry energy cutoff for the electronic wave

atoms (one is anion, while the other is cation).

functions and a small smearing width of 0.02

To implement the antiferromagnetic ordering,164

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

we adopted four-atom-configuration including

points. This is qualitatively consistent with thetwo cations with up and down spins. By

experimental observation [1]. The ground state

adopting this configuration, we can expect anobtained in the four-atom cell has slightly lower

effective lowering of the symmetry which may

energy per the cation-anion pair compared to

be useful to open the gap.

thenonmagnetic

andmetallic

two-atomprimitive cell, and thus the antiferromagnetic
Structural optimization – We also optimized

insulating ground state is energetically favored.

the structure by using the Broyden–Fletcher–

The result of the density-of-states calculation

Goldfarb–Shanno method. This turned out to besuggests that both the valence and conduction

essential to make the Fermi energy lie in the

bands are mainly composed of the d electron,

splitting region of the d electrons. Otherwise,

consistent with the narrow Mott-Hubbard gap

one cannot reproduce the insulating ground[1].

structure with the experimental lattice spacings.
atom
1
Tr[ns(na)] (up, down, total) =2.48039 1.01275 3.49314
spin 1eigenvalues:
0.292 0.292 0.448 0.449 1.000⁝
spin 2
eigenvalues:
0.151 0.151 0.192 0.259 0.259⁝

This resulted in the structure with the symmetry
C2h (2/m). It is known that the theoreticalground state depends on the starting eigenstates(occupation) during the spin-polarized DFT+U
calculations.

In

some

of

transition-metalmonoxides such as cubic FeO and CuO, thisFig. 1: An example of the orbital level output

adjustment is essential to reproduce theafter the initial eigenvalue settings are reflected.

insulating ground state [2]. This is also true inour case. The example of the output is shown inReferences

Fig. 1.

[1] K. Kaminaga et al., Appl. Phys. Lett. 108, 1
Band

dispersion

andelectronic(2016).

DOS[2] B. Himmetoglu et al., Phys. Rev. B. 84,

calculations –It should be noted that all of the115108 (2011).

above-mentioned extensions such as non-zero[3] P. Giannozzi et al., J. Phys.: Condens. Matter

Up, the spin polarization, structure optimization,

21, 395502 (2009).

and occupational adjustments turned out to be
essential to open an indirect gap (0.55 eV) in
our case with a transition between L and Γ

165

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Interactions in transition-metal-phthalocyaninemonolayer weakly bound to metal surfaces
Tetsuya ARUGA
Department of Chemistry, Graduate School of Science, Kyoto University
Kitashirakawa-Oiwakecho, Sakyo, Kyoto 606-8502

Phthalocyanine is a π-conjugated planarmolecule with a size of ∼1.2×1.2 nm2 . Two H
atoms at the center of the molecule can be substituted by a variety of transition metal ions
(M 2+ ), yielding a transition metal phthalocyanine (M Pc). The M 2+ ions are coordinatedby lone pairs of four N atoms arranged in aplanar tetragonal geometry. The adsorptionof M Pc on transition metal surfaces [1, 2] hasbeen widely studied experimentally.
We recently have studied experimentally theadsorption and ordering of metal phthalocyanine molecules on a bilayer indium ﬁlm fabricated on Si(111) surface [3, 4, 5] , on which theinteraction of M Pc with the substrate is expected to be weaker than the transition-metals
substrates. Our aim is to establish nearlyfree-standing transition metal phthalocyaninemonolayers eﬀectively decoupled from the substrate.
The experimental studies of M Pc adsorption on metal surfaces commonly show thatthe phthalocyanine molecules form monolayerswith long range order, in which the symmetry
axes of molecules are aligned at a particular
azimuthal angle which is not parallel to theaxes of the translational symmetry of the twodimensional lattice the molecules form. Thishas sometimes been ascribed to the direct interaction of nitrogen atoms (imide N) of themolecule with the substrate metal atoms.
Our computational result suggests that theelectronic interaction between phthalocyanineand In substrate is indeed week due to a large

van der Waals gap between the molecular plane
and the topmost In atomic layer of the substrate and further to the weak electronic interaction of the π orbitals of the molecules withthe sp electrons of the In bilayer.
In order to highlight the intermolecular interaction, we studied the “free-standing” M Pc
monolayer by ﬁrst-principles calculation by
VASP. The molecules were assumed to be ordered in a nearly square translational symmetry which exactly is the one observed on
In/Si(111). Note that the characteristics of themolecular arrangement is more or less similar
on other metal surfaces studied. The total energy of the molecular ﬁlm was calculated as afunction of the azimuthal rotation angle of themolecule. It was found that the total energy
is minimized at an azimuthal angle close tothat observed experimentally for the molecule
adsorbed on many metallic surfaces. This implies that the molecular conﬁguration in the
M Pc monolayer is governed by the intermolecular interaction. We have examined several
possibilities of the physical origin of the inplane intermolecular interaction between M Pc
molecules and succeeded in identifying the interaction that stabilizes the free-standing M Pc
monolayer.
We also studied the d electronic structureof M 2+ ions in the metal phthalocyanine adsorbed on In/Si(111) surface to probe the interaction with the substrate sp electrons. A
good correspondence between the density ofstates measured by photoemission experiments

166

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

with those obtained by the calculation yielded
an insight into the interaction between central
metal ions and metallic substrate in this system.

References[1] H. Koshida, Y. Takahashi, H. Okuyama,
S. Hatta, and T. Aruga, e-Journal of
Surface Science and Nanotechnology, 20(2022) 25.
[2] H. Koshida, H. Okuyama, S. Hatta, T.
Aruga, Y. Hamamoto, I. Hamada, Y.
Morikawa, J. Phys. Chem. C 124 (2020)
17696.
[3] S. Terakawa, S. Hatta, H. Okuyama, T.
Aruga, Phys. Rev. B 105 (2022) 125402.
[4] S. Terakawa, S. Hatta, H. Okuyama, T.
Aruga, Phys. Rev. B 100 (2019) 115428.
[5] J. W. Park and M. H. Kang, Phys. Rev.
Lett. 109 (2012) 166102.

167

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Electronic Structure and Fermiology of d-electroncompounds
Isaki Kinjo, Juno Iraha, Yasutomi Tatetsu1 , and Takahiro Maehira2
Graduate school of Engineering and Science, Nishihara, Okinawa 903-0213
1
Center for Liberal Arts Education, Meio University, Nago, Okinawa 905-8585
2
Faculty of Science, University of the Ryukyus, Nishihara, Okinawa 903-0213

represents that WC is a compensated metal.
We move to discuss the Fermi surface of WC.
Three bands cross the EF , therefore WC has
three Fermi surfaces in Figure 2. The color on
the Fermi surface illustrates the distribution of
the Fermi velocity components. Fermi surfaces
for WC centered at the A, K, and M points,
respectively. The 5th band has one dog’s bonelike hole sheet centered at the each Γ point.
The Fermi surfaces were calculated with FermiSurfer [3].

eVThe monocarbides of transition elementsfrom the group-IVB, -VB, and -VIB columnsof the Periodic Table are well known for theirgreat hardness and strength, high melting temperatures, metal-like thermal and electricalresistivities, nonstoichiometry, and superconducting properties [1, 2]. Most experimental
and theoretical eﬀorts to understand the fundamental properties of these technologicallyimportant materials have focused thus far on
the group-IVB and -VB carbides, all of which
crystallize with the cubic rocksalt structure.
The compound WC has two phases: a low temperature phase is hexagonal WC and a hightemperature phase above 2525◦ C is cubic WC.
We studied simple hexagonal WC with a spacegroup of P6m2 which contains one molecule in
the unit cell. The lattice parameters a and care 2.906 and 2.837 Å, respectively [1]. The
calculation for the energy band structures was
carried out by using the OpenMX code(http://www.openmx-square.org/). First, we discuss the calculated results for WC as shown in
Figure 1, in which we depict the energy band
structure along the symmetry axes in the Brillouin zone, which is shown in Figure 1, in theenergy region from -20.0 to 20.0 eV. The Fermi
level EF is at 0.0 eV. for WC and indicated bydashed lines in Figure 1. With respect to theenergy band structure near EF , we emphasizethat there is always hybridization between the
W 5d and C 2p states in WC. The total number of holes is equal to that of electrons, which

20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15
-16
-17
-18
-19
-20

Γ

M

K

Γ

A

L

H

A,L

M,K

H

Figure 1: The energy band structure for WC,
the symmetry points and axis for the simple
hexagonal-type structure. EF indicates the position of the Fermi level.
ReO3 -type structures can be described as
ABX3 perovskites in which the A-cation site
is unoccupied. They therefore have the general composition BX3 , where B is normally acation and X is a bridging anion. The chem-

168

eV

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 2: The Fermi surface for WC centeredat Γ point. Colors indicate the Fermi velocity
components on the Fermi surface.

25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
- 10
- 11
- 12
- 13
- 14
- 15
- 16
- 17
- 18
- 19
- 20
- 21
- 22
- 23
- 24
- 25

Γ

X

M

Γ

R

M

R

Figure 3: The energy band structure for ReO3 .
EF indicates the position of the Fermi level.
8

T otalRe- s
O 1- s
O2- s
O3- s
Re- p
O 1- p
O2- p
O3- p
Re- d
O 1- d
O2- d
O3- d
Re- f

7

6

5
D(E)(S tates /cell eV .)ical diversity of such structures is very broad,
ranging from simple oxides and fluorides, suchas WO3 and AlF3 , to more complex systems
in which the bridging anion is polyatomic, as
in the Prussian blue-related cyanides such as
Fe(CN)3 and CoPt(CN)6 . We found that theenergy bands near the Fermi level are mainly
because of the hybridization between the Re 5d
and O 2p electrons in Figure 3. Since the lowest twelve bands are fully occupied, as shownin Figure 3, the next three bands are partially occupied, while higher bands are empty.
This compound is compensated metal becauseof having two chemical units in the unit cell.
The calculated total density of states (DOS)for ReO3 is shown in Figure 4, in the energy
region from -25.0 to 25.0 eV. The total densityof states for ReO3 is shown by the solid blackline and the s, p, d and f states are shown by
the solid color lines, respectively. This figuretells us that the DOS of the d states is higher
than that of the f states at the Fermi level.
The Fermi surface of ReO3 is found to consistsof two hole sheets and two electron sheets.

X

4

3

2

1

0

- 20

- 10

0

10

20

Energy ( eV .)Figure 4: The density of states for ReO3 . EF
indicates the position of the Fermi level shownby the dashed line.

References[1] L. E. Toth:Transition Metal Carbides andNitrides., Academic, New York(1971).
[2] E.K. Storms:The Refractory Carbides.,Academic, New York(1967).
[3] M. Kawamura: Phys. Rev. B 89, 094515(2014).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles Study of Defects of Magnesium Alloys
Daisuke Matsunaka
Department of Mechanical Systems Engineering,
Shinshu University, 4-17-1 Wakasato, Nagano 380-8553
atom, consistent with the previous DFT study.

Magnesium (Mg) has been of increasingly
viewpoint,

Several magnesium alloys include long

because of its low density and relatively highperiod stacking ordered (LPSO) structures

specific strength.

which consist of periodic arrangement of basalinterest

from

the

engineering

For molecular dynamics simulation widely

stacking faults and enrichment of solute atoms

used to obtain atomic-level information onin the vicinity of the stacking faults. The solute-strength and deformation of materials, anenriched layers give rise to a significant massinteratomic potential is very important. In thischange as well as local stiffness due to the L12-

study, a highly accurate interatomic potential oftype solute clusters, which affect the lattice

pure magnesium was developed based onvibration properties of the LPSO structures.

artificial

The

Our previous study showed that for a heavyreference data for training the ANN potential

enough mass change, a phonon-mediatedwere systematically constructed using density

interaction of the solute-enriched layers isfunctional theory (DFT) calculations. The

attractive and stabilizes the periodic stacking ofdeveloped ANN potential can accurately

the solute-enriched layers. In this study, we

estimate lattice constants and elastic moduli.

analyze phonon states of LPSO magnesium

Additionally,

generalized

stacking

fault

alloys, using first-principles calculations. We

energiesslipinmagnesium

calculate phonon density of states and phonon

calculated with the ANN potential are also in

dispersion based on the density functional

agreement with the DFT results. We also

perturbation theory.

developed the ANN potentials for several kinds

Referencesof magnesium alloys; Mg-Y, Mg-Ca, Mg-Al,[1] T. Nagata: Master Thesis, Shinshu Univ.

Mg-Zn. The ANN potentials of magnesium(2022).

alloys[2] D. Matsunaka, K. Oboso, Y. Shiihara and H.

neuralof

network

successfullysystems(ANN)[1].

described

interactions

between a basal dislocation and each solute

Mori: Proceedings of CMD2021, 204.

170

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

3.3

Strongly Correlated
Quantum Systems

171

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Tensor-Network Renormalization-Group Study of Critical
Phenomena
Naoki KAWASHIMA
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
We developed efficient methods, algorithms,

operator and the scaling dimensions. Ourparallelized programs, and sometimes new

benchmark calculation on the 2D Ising model

concepts, based on novel numerical techniques

established validity of this basic idea. The newincluding the tensor network (TN) method andscheme may provide a direct method for

applied them to relevant physical problems. To

estimating the scaling dimensions in higher

list subjects of our research in 2021, (1)dimensions.
In [2], we proposed a method for obtaining

development of new numerical methods basedon the TN representation [1,2], (2) study of TN

theground states such as Kitaev spin liquid [3], (3)calculations. In this method, we consider anstudy of spin liquid in frustrated spin systems

imprurity tensor representing a locally excited[4],state, and construct an eigenvalue equation in(4)

developmentof

open-source

excitation

spectrum

based

on

TN

the space of such excited states, which can beapplications [5].
In [1], we re-considered the method forblock-diagonalized by Frourier transformation.

extracting the critical information from the

By diagonalizing each block we can obtain

RSRG calculation with TNs. The most common

excitation spectra of various excitations. We

method for obtaining the scaling dimension isappliedto form a transfer matrix from the scale-quantum spin chain and successfully computed

invariant tensor. Then, we can obtain theits excited states and the dynamical structure

scaling dimensions from its eigenvalues using

factor. We further investigated entanglement

the relationship derived from the conformal

properties of excited states.

thisschemetoone-dimensional

field theory. However, this method has not been

In [3], we considered in the Kitaev model

generalized to three or higher dimensions. In

on the honeycomb lattice and its extention to

our scheme, we construct a super-operator that

S=1. The models with arbitrary spin quantum

represents the RSRG tarnsformation. Without

numbers are not exactly solvable in contrast to

explicitly relying on the CFT, we derive thethe well-known Kitaev spin liquid solution ofrelashion between the eigenvalues of the super-

the spin-1/2 system. To unveil the important172

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

difference between these states, we use theextereme dilution to clarify the validity of thetensor-network wave functions, which proved,

analytical predictions for the universal behavior

in our previous work, to be essential inof the model in this region. We confirmed thecapturing the nature of the Kitaev spin liquid.

universal behaviors. In addition, we estimated

We found that the distinct sign structures of themodel-dependent parameters such as the s-tensor-network wave function for the integer-

wave scattering length in a good agreement

and half-integer-spin quantum spin liquids arewith the prediction as well as the non-universal

responsible for completely different groundcorrection term of the third order in the particle

states in the spatially anisotropic limit.

density, which has never been estimated before.

In [4], we investigated S=1/2 XXZ laddersystem with four-spin interaction. The model

References

can be viewed as a one-dimensional variant of[1] X. Lyu, R. G. Xu and N. Kawashima, Phys.

the J-Q model on a square lattice. By means ofRev. Research 3, 023048 (2021).

variational

state[2] W.-L. Tu, H.-K. Wu, N. Schuch, N.

(VUMPS) calculations and an effective field

Kawashima and J.-Y. Chen, Phys. Rev. B 103,

theory, we determine the phase diagram of the205155 (2021).

model and present evidence that the Néel-VBS[3] H.-Y. Lee, T. Suzuki, Y. B. Kim and N.

transition is continuous and belongs to the

Kawashima, Phys. Rev. B 104, 024417 (2021).

Gaussian universality class with the central[4] T. Ogino, S. Furukawa, R. Kaneko, S.

charge c=1. The full phase diagram consists ofMorita and N. Kawashima, Phys. Rev. B 104,8075135 (2021).

distinct

uniform

phasesmatrixincluding

product

magneticallyordered phases, Haldane-like phases, and VBS[5] Y. Motoyama, K. Yoshimi, A. Masaki-Kato,phases.

T. Kato and N. Kawashima, Comput. Phys.

In [5], we developed DSQSS, an open-

Commun. 264, 107944 (2021).

source software for quantum Monte Carlo[6] A. Masaki-Kato, Y. Motoyama and N.

simulation of lattice system. In [6], we applied

Kawashima, J. Phys. Soc. Jpn. 90, 034711

it to the Bose-Hubbard model in the case of(2022).

173

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical studies of Mott transitionsin quantum spin liquid candidates
Youhei YAMAJI
Center for Green Research on Energy and Environmental Materials,
National Institute for Materials Science
Namiki, Tsukuba-shi, Ibaraki 305-0044

The Kitaev model is a unique solvable twodimensional quantum system [1]. As shown byKitaev, the ground state of the model hamiltonian is a quantum spin liquid. Later, Jackeli
and Khaliullin proposed that the effective lowenergy hamiltonian of Mott insulating phasesof honeycomb iridium oxides such as Na2 IrO3
could be the Kitaev model [2]. Although theground state of Na2 IrO3 was found to show
a magnetic long-range order, the dominant
terms in the ab initio effective spin hamiltonian of Na2 IrO3 are given by the Kitaev-typeexchange couplings [3].
Even though there emerge new candidate
materials represented by α-RuCl3 on the frontof the search for the spin-liquid ground states,
an important question has not been solved yet:
It has not been clarified yet whether the small
Mott gaps of these candidate materials affectthe properties of them or not. To elucidate an
impact of the itinerant nature of electrons on
the properties of a spin-liquid candidate, we
studied the original ab initio itinerant hamiltonian consisting of iridium t2g orbitals [3], instead of the spin hamiltonian.
In the present research, we studied the abinitio t2g hamiltonian of Na2 IrO3 [3]. The t2g
hamiltonian consists of the kinetic energy andthe intra-atomic and inter-atomic Coulomb repulsions as,plings, ĤU denotes the intra-atomic Coulombinteractions, and ĤV is the inter-atomic
Coulomb repulsion.
Naı̈vely, ĤV is expected to be relevant tocharge channels but irrelevant to spin degrees
of freedom. However, it is not true. Wheninter-atomic exchange couplings are estimatedby the second-order perturbation theory, theintra-atomic and intra-orbital Coulomb repulsion U in the energy denominator is replaced
by U −V , where V is the inter-atomic Coulomb
repulsion. Therefore, when the inter-atomic
Coulomb repulsions are controlled as parameters, not only the charge but also the spin
degrees of freedom are affected.
We controlled the nearest-neighbor, second nearest-neighbor, and 1/r long-range
Coulomb interactions to examine the competition among the magnetic and charge orders
and suppression of the magnetic orders, by using an open-source code mVMC [4].

References[1] A. Kitaev: Ann. Phys. (Amsterdam) 321(2006) 2.
[2] G. Jackeli and G. Khaliullin: Phys. Rev.
Lett. 102 (2009) 017205.

(1)[3] Y. Yamaji, et al.: Phys. Rev. Lett. 113(2014) 107201.

where ĤK represents the kinetic terms including trigonal distortion and spin-orbit cou-

[4] T. Misawa, et al.: Comput. Phys. Commun. 235 (2019) 447.

Ĥt2g = ĤK + ĤU + ĤV ,177

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical study of symmetry breaking and quantum
transport phenomena in charge-spin-orbital coupled systems
Yukitoshi MOTOME
Department of Applied Physics,
The University of Tokyo, Bunkyo, Tokyo 113-8656

We have theoretically studied a variety ofthe effect of randomness on the spin dynamics

intriguing phenomena in correlated electronin the Kitaev quantum spin liquid [13]. We alsosystems

elucidatedwithcharge-spin-orbital

coupling

linearandnonlinearthermal(project numbers: 2021-Ca-0050 and 2021-Cb-transport in the presence of both uniform and0014). During the last fiscal year, we havestaggered magnetic fields [14]. We have madeachieved substantial progress on the following

collaborations with experimental groups on the

topics. We summarize the main results below.

topological nature in an external magnetic field(i)

Regarding[15,16]. In addition, we showed how to create

topological spin crystals, such as skyrmion andand control fractional excitations by analyzing

hedgehog lattices, as moiré interferences

the effect of local lattice distortions [17]. We

between spin helices, we clarified how theiralso proposed that iridium ilmenites can bemagnetic and topological properties can begood candidates for Kitaev magnets [18].

modulated by changing twist angles between(iii) Multipole physics: We collaborated withthe directions of the constituent spin density

experimental groups on a chiral magnet

waves [1] and shifting relative phases [2,3,4].

Pb(TiO)Cu4(PO4)4 to clarify the control of

We also elucidated charge modulation on suchmagnetic domains [19] and nonreciprocal

topological spin crystals [5]. In addition, we

directional dichroism [20,21].

clarified the ground state phase diagrams [6](iv) Development of new theoretical methods:

and spin excitations [7] for effective spin

We developed a many-body numerical methodmodels with long-range interactions. We also

for quantum spin systems based on theclarified linear and nonlinear optical responses

Lefschetz thimbles technique [22]. We alsoin quasi-one-dimensional chiral magnets [8,9].

developed new methods based on machine

We have collaborated with experimental groups

learning techniques: determinant-free fermionic[10,11]. We wrote a review article on the

wave function approach [23] and inverse design

itinerant frustration mechanism [12].

of(ii) Kitaev quantum spin liquids: We clarified

differentiation [24].

Topologicalspin

crystals:

178

Hamiltonians

by

using

automatic

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[14] K. Nakazawa, Y. Kato, and Y. Motome,[1] K. Shimizu, S. Okumura, Y. Kato, and Y.

preprint (arXiv:2201.04274), accepted for Phys.

Motome, Phys. Rev. B 103, 184421 (2021).

Rev. B.

[2] S. Hayami, T. Okubo, and Y. Motome, Nat.

[15] T. Yokoi, S. Ma, Y. Kasahara, S. Kasahara,

Commun. 12, 6927 (2021).

T. Shibauchi, N. Kurita, H. Tanaka, J. Nasu, Y.

[3] K. Shimizu, S. Okumura, Y. Kato, and Y.

Motome, C. Hickey, S. Trebst, and Y. Matsuda,

Motome, preprint (arXiv:2201.03290).

Science 373, 568 (2021).

[4] K. Shimizu, S. Okumura, Y. Kato, and Y.

[16] S. Suetsugu, Y. Ukai, M. Shimomura, M.

Motome, J. Phys.: Conf. Ser. 2164 012069

Kamimura, T. Asaba, Y. Kasahara, N. Kurita, H.

(2022).

Tanaka, T. Shibauchi, J. Nasu, Y. Motome, and[5] S. Hayami and Y. Motome, Phys. Rev.

Y. Matsuda, preprint (arXiv:2203.00275).

B 104, 144404 (2021).

[17] S.-H. Jang, Y. Kato, and Y. Motome, Phys.

[6]

Y.

Kato

and

Y.

Motome,preprint

Rev. B 104, 085142 (2021)(arXiv:2202.04407).

[18] S.-H. Jang and Y. Motome, Phys. Rev.

[7] Y. Kato, S. Hayami, and Y. Motome, Phys.

Materials 5, 104409 (2021).

Rev. B 104, 224405 (2021).

[19] K. Kimura, Y. Kato, S. Kimura, Y.

[8] S. Okumura, T. Morimoto, Y. Kato, and Y.

Motome, and T. Kimura, npj Quantum Mater. 6,

Motome, Phys. Rev. B 104, L180407 (2021).

54 (2021).

[9] S. Okumura, T. Morimoto, Y. Kato, and Y.

[20] T. Katsuyoshi, K. Kimura, Z. Yang, Y.

Motome, J. Phys.: Conf. Ser. 2164 012068

Kato, S. Kimura, Y. Motome, Y. Kohama, and T.

(2022).

Kimura, J. Phys. Soc. Jpn. 90, 123701 (2021).

[10] K. Fujiwara, Y. Kato, T. Seki, K. Nomura,[21] M. Akaki, K. Kimura, Y. Kato, Y. Sawada,

K. Takanashi, Y. Motome, and A. Tsukazaki,

Y. Narumi, H. Ohta, T. Kimura, Y. Motome,

Commun. Mater. 2, 113 (2021).

and M. Hagiwara, Phys. Rev. Research 3,[11] N. D. Khanh, T. Nakajima, S. Hayami, S.

L042043 (2021).

Gao, Y. Yamasaki, H. Sagayama, H. Nakao, R.

[22] P. A. Mishchenko, Y. Kato, and Y. Motome,

Takagi, Y. Motome, Y. Tokura, T. Arima, and S.

Phys. Rev. D 104, 074517 (2021).

Seki, Adv. Sci. 2105452 (2022).

[23] K. Inui, Y. Kato, and Y. Motome, Phys.

[12] S. Hayami and Y. Motome, J. Phys.:

Rev. Research 3, 043126 (2021).

Condens. Matter 33, 443001 (2021).

[24][13] J. Nasu and Y. Motome, Phys. Rev. B 104,

(arXiv:2203.07157).

045116 (2021).

179

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Low-energy excitations of skyrmion crystals in acentrosymmetric spin-charge coupled magnet
Masahito MOCHIZUKI
Department of Applied Physics, Waseda University
Okubo, Shinjuku-ku, Tokyo 169-8555

In this project, we have theoretically studied the low-energy dynamics of skyrmion crystals in a centrosymmetric Kondo-lattice magnet with conduction-electron-mediated magnetic interactions (project ID: 2021-D-0002).
We computed the dynamical spin- andcharge-structure factors of skyrmion crystals ina centrosymmetric spin-charge coupled magnet by taking the Kondo-lattice model witha classical treatment of localized spins. Ourlarge-scale adiabatic molecular dynamics simulations revealed four Goldstone modes in theabsence of an external magnetic field [Figure1]. Three of the four Goldstone modes are associated with the spontaneous breaking of theSO(3) symmetry in spin space, and thus linearly dispersing. The remaining one is the socalled phonon mode associated with the displacement of skyrmions, and thus quadratically dispersing. Surprisingly, we observed
clear segregation of spin and charge excitations: the three linearly dispersive Goldstone
modes have full contribution from the spin sector and the quadratically dispersive Goldstone
mode has full contribution from the charge sector [1]. Note that the dynamical structure factors obtained with the adiabatic molecular dynamics simulations perfectly coincide with thedispersion relations obtained with the linearspin-wave calculation.
In our adiabatic molecular dynamics simulations, instead of repeated full diagonalizations of the quadratic form Hamiltonian,
we utilized the kernel polynomial method in

combination with the automatic differentiation technique to evaluate the local physicalquantities, for example, expectation values ofitinerant electron spins and local charge occupations. The Chebyshev moments are evaluated using the combination of processing andthreaded parallelization techniques on 18,432
cores (144 nodes) of System B Ohtaka.
(a) S(q,ω)(b) N(q,ω)

Figure 1: Dynamical (a) spin- and (b) chargestructure factors of the skyrmion crystal in theabsence of an external magnetic field.

References[1] R. Eto, R. Pohle, and M. Mochizuki,
preprint [arXiv:2203.01496].

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical study on the photodriven spin andcharge dynamics of topological materials
Masahito MOCHIZUKI
Department of Applied Physics, Waseda University
Okubo, Shinjuku-ku, Tokyo 169-8555

We have theoretically studied the dynamics
of topological magnetism and topological electron states under periodic driving (project ID:
2021-Ba-0015, 2021-Cb-0009). The main results of these projects are listed below.
(i) Dynamical magnetic topology switching ofskyrmion crystals: We revealed novel dynamics of skyrmion crystals in a centrosymmetric spin-charge coupled system under the microwave magnetic field [1]. By taking the
Kondo-lattice model with a classical treatmentof localized spins, we clarified the dynamic
topological phase transitions of the skyrmion
crystals among their skyrmion number Nsk =2, 1, and 0 through the large-scale spin dynamics simulations in combination with the kernel polynomial method and the automatic differentiation technique. The topological phasetransitions are induced by the effective magnetic field perpendicular to the rotating planeof the circularly polarized microwave magnetic
field. In our numerical simulations with thekernel polynomial method and the automaticdifferentiation technique, we utilized our own
hybrid parallelization code using both the processing parallelization with the message passing interface and the threaded parallelization
with OpenMP. Moreover, in the automatic differentiation process, we reduced the computational cost for the evaluation of Chebyshev
moments by using the relation 2Tm (x)Tn (x) =Tm+n (x) + T|m−n| (x) where Tm (x) denotes them-th order first-kind Chebyshev polynomial.
(ii) Spin-wave eigenmodes of the quadruple-Q

magnetic hedgehog lattices in chiral magnets:
We studied the spin-wave eigenmodes of thequadruple-Q hedgehog lattices which appear
in the Kondo-lattice model on the cubic lattice by the spin-dynamics simulations in combination with the kernel polynomial method[2]. As a result, under the [001] magnetic field,
we clarified two eigenmodes with counterclockwise fashion for the ac magnetic field perpendicular to [001] and four eigenmodes for theac magnetic field parallel to [001]. Three ofthe four eigenmodes parallel to [001] are localized around point defects of magnetic textures,and the remaining one is closely related to thephase degrees of freedom.
(iii) Photodriven dynamical phase transitionsin the α-type organic salt: We clarified the
dynamical phase transitions in the charge ordered organic salt α-(BEDT-TTF)2 I3 under
the irradiation of laser by the time-dependentmean-field calculation and the Floquet theory[3]. The suﬀicient intensity of laser melts the
charge order and induces the semimetal phase.
A much stronger laser induces the Chern insulator phase with nonzero Hall conductivity.

References[1] R. Eto and M. Mochizuki, Phys. Rev. B
104, 104425 (2021).
[2] R. Eto and M. Mochizuki, in preparation.
[3] Y. Tanaka and M. Mochizuki, preprint[arXiv:2203.04542].

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Topological phases, excitation modes, effects of exceptional
points and transport phenomena in strongly correlated
systems
Norio KAWAKAMI
Department of Physics,
Kyoto University, Kitashirakawa, Sakyo-ku, Kyoto 606-8502
and hold the possibility of being applied indiodes or high-frequency optical devices. Whilenonlinear responses in noninteracting models
have been explored widely, the effect of strong
correlations on the nonlinear response is still
poorly understood. In [2], we first derive aformula for calculating the nonlinear response
at finite temperatures that is entirely based on
single-particle
Green’sfunctions.
Wefurthermore analytically show that nonlinear
responses are significantly enhanced by therenormalization of the band structure and nonHermiticity in the Green’s function. Finally, we
confirm our analytical prediction by performing
numerical calculations for several strongly
correlated models.
In [3], we use this Green’s function method
to study the nonlinear Hall effect in Ce3Bi4Pd3.
Experiments measured a huge nonlinear Hall
effect in this material. From symmetry analysis,
we develop a model describing Ce3Bi4Pd3 as a
Weyl-Kondo semimetal. Performing dynamical
mean-field calculations for this model, we findthat below the Kondo temperature, Weyl points
emerge close to the Fermi energy in the band
structure; at high temperatures, this material isa metal. Due to strong correlations, the band
structure is strongly renormalized. We thendirectly calculate the nonlinear longitudinal
conductivity andthenonlinear Hall
conductivity and find that the nonlinear Hall
resistivity is strongly enhanced compared to anoninteracting system. We find good agreement
between our numerical calculations and theCorrelated materials have appeared as anarena to study non-Hermitian phenomena, suchas exceptional points emerging in the singleparticle Green’s function. Exceptional points
are degeneracies of eigenvalues due to the nonHermiticity of a matrix. Contrary to Hermitiandegeneracies, the eigenvalues and theeigenvectors coalesce at an exceptional point,
giving rise to novel phenomena.
In [1], we show that topological Kondo
insulators are an ideal platform for studying
these phenomena due to a combination ofstrong correlations and surface states. Using
numerical simulations, we demonstrate theemergence of exceptional points in the singleparticle Green’s function on the surface of thematerial while the bulk is still insulating. We
believe that this situation is perfect forexperimental observation of exceptional points.
In particular, we reveal how quasiparticle stateswith long lifetimes are created on the surface
by non-Hermitian effects while the Dirac cones
are smeared. This effect is related to the surface
Kondo breakdown at which heavy Dirac cones
disappear from the single-particle spectrum andare replaced by light states.
Furthermore, we study nonlinear responses
in strongly correlated systems, specificallyanalyzing the effect of renormalization andnon-Hermiticity on the second-order nonlinear
response.
Nonlinear responses in condensed matterare recently intensively studied because they
provide rich information about the materials

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

experimental observations.
In [4], we analyze the effect of strong
correlations on fragile topological insulators.
Fragile topological insulators (FTIs) offer
obstruction to the formation of exponentiallylocalized Wannier functions, but they can betrivialized by adding certain trivial degrees of
freedom. For the same reason, FTIs do not hostsymmetry-protected flow of edge states
between bulk bands in cylindrical boundary
conditions. Still, they are expected to have aspectral flow between the fragile bands andother bands under certain twisted boundary
conditions. We analyze commonly observed
effects of strong correlations, such as the Mott
insulator transition and magnetism, on a known
model hosting fragile topology. We show thatfragile topology, along with the twisted
boundary states, is stable with interactions
below a critical interaction strength in thenonmagnetic case. Above this interaction
strength, a transition to the Mott insulatingphase occurs, and the twisted boundary states
disappear. Furthermore, the fragile topology is
destroyed by a homogeneous magnetic field.
However, we show that a magnetic field can
induce a topological phase transition whichconverts a fragile topological insulator to a
Chern
insulator.
Finally,we
study
ferromagnetic solutions of the fragile
topological model.
In [5], we investigate magnetic instabilities
in charge-neutral twisted bilayer graphene close
to so-called “magic angles” using a
combination of real-space Hartree-Fock anddynamical mean-field theories. We find that
localized magnetic states emerge for values of
the Coulomb interaction U that are significantly
smaller than what would be required to render
an isolated layer antiferromagnetic. Ourfindings shed new light on perspectives forexperimental realization of magnetic states incharge-neutral twisted bilayer graphene.

In [6], we analyze the impact of criticalnematic fluctuations on the low energy
properties of phonons. We propose how to
identify the three-state Potts nematicfluctuations by ultrasound attenuation. The
Landau damping term becomes isotropic due tofluctuations of the C3-breaking bond-order, andthe nemato-elastic coupling is also isotropic.
The transverse sound attenuation coefficient
diverges isotropically, in contrast to the case of
the C4-breaking bond-order that shows strong
anisotropy. The shift of the first order transitionline at low temperatures toward the secondorder line renders the transition a weak firstorder in a wide range of parameters.

References[1] R. Peters, K. Kimura, Y. Michishita, T.
Yoshida, and N. Kawakami: “Surface
exceptional points in a topological Kondo
insulator” Phys. Rev. B 104 (2021) 235153.
[2] Y. Michishita and R. Peters: “Effects ofrenormalization and non-Hermiticity on
nonlinear responses in strongly-correlated
electron systems” Phys. Rev. B 103 (2021)
195133.
[3] A. Kofuji, Y. Michishita, and R. Peters:“Effects of strong correlations on the nonlinear
response in Weyl-Kondo semimetals” Phys.
Rev. B 104 (2021) 085151.
[4] A. Joshi and R. Peters: “Mott transition andmagnetism in a fragile topological insulator”
Phys. Rev. B 103 (2021) 165130.
[5] J. Vahedi, R. Peters, A. Missaoui, A.
Honecker, and G. T. de Laissardière:“Magnetism of magic-angle twisted bilayer
graphene” SciPost Phys. 11 (2021) 083.
[6] K. Kimura, M. Sigrist, and N. Kawakami:“Probing three-state Potts nematic fluctuations
by ultrasound attenuation” Phys. Rev. B 105(2022) 035130.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Finite-temperature methods for quantum many-body systems
using Boltzmann machines
Yusuke NOMURA
RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, 351-0198

The

thermalbehaviorofnumericallymany-body

optimizemachinesstatistical mechanics provides a theoretical

Hamiltonian evolution as accurately as possible

framework for describing finite-temperature

within the representability of deep Boltzmann

properties. However, in quantum many-bodymachines. We apply the methods to thesystems, due to the "curse of dimensionality" oftransverse-field Ising model and the two-

Hilbert space, it is very difficult to capture thedimensional J1-J2 Heisenberg model. The

complex competition between thermal andnumerical benchmarks show that our scalable

quantum

variousapproach can successfully simulate the finite-

numerical methods have been developed, suchtemperature properties of the quantum spinas quantum Monte Carlo, diagrammatic, andproblems.

Althoughreproduce

Boltzmannsystems is a fundamental problem. Celebrated

fluctuations.

to

deep

imaginarytimetensor network methods, it is challenging toestablish a reliable methodology that can beextended to the most exotic and interestingregions in quantum many-body physics.
Here, we take a novel approach using
artificial neural networks. In particular, we
employ deep Boltzmann machines that haveflexible representability. We propose twodifferent approaches, offering paths to encode
many-body

thermalphysics

into

deep

Fig. 1: Structure of deep Boltzmann machine

Boltzmann machines. In the first method, we
findaconstructcompletely
deep

deterministic

Boltzmannwaymachines

employed in the present study.

toReferences

that

reproduce the exact purified expression of finite[1] Y. Nomura, N. Yoshioka, and F. Nori, Phys.

temperature states. In the second method, we

Rev. Lett. 127, 060601 (2021)

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Exotic phenomena induced by strong correlations andnon-Hermitian topology
Tsuneya Yoshida
Department of Physics,
1-1-1 Tennodai, Tsukuba, Ibaraki, JAPAN 305-8571
In this year, we have mainly studied non-interacting level.

Hermitian topological phenomena by

Furthermore, we have explored thefocusing on exceptional points [1-4]. In

topological structure of the classicalparticular, we have analyzed exceptional

systems[5-7]. In particular, we havepoints at surfaces of topological Kondo

observed Hermitian and non-Hermitian

insulators[1].

havetopological physics in systems of the headapplied the dynamical mean-filed theory

conduction and the evolutionary gamecombinedtheory. The topological properties ofSpecifically,withrenormalization

the

group

we

numerical

methodtoasuperconductors are also discussed [8,9].

variant of the periodic Anderson model
which describes the topological Kondo
insulator

SmB6.

Our

numerical

simulation has elucidated that finite
lifetimeofquasi-particles

induces

exceptional points at surfaces of the
topologicalKondo

insulator.

These

exceptional points induce additional low
energy excitations and change the spin
structure of surface states (see Fig. 1).
Fig.1 Spectral weight for a surface of a

We also have analyzed correlations

topological Kondo insulator. The emergence ofeffects on the non-Hermitian topology inzero

dimension[4],

where

we

have

-

exceptional

pointsinduceslowenergyexcitations and affects the spin structure of theobserved that the classification of the***point-gap topology is reduced to Z2 while***

surface states (The figure is taken from Ref. [1])the classification is Z at the non-

185

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[6] S. Makino, T. Fukui, T. Yoshida, and Y.

[1] R. Peters, K. Kimura, Y. Michishita, T.

Hatsugai, Phys. Rev. E 105, 024137

Yoshida, and N. Kawakami, Phys. Rev. B(2021)

104 235153 (2021).

[7] T. Yoshida, T. Mizoguchi, and Y.

[2] T. Yoshida, R. Okugawa, and Y.

Hatsugai, Sci. Rep. 12, 1-7 (2021)

Hatsugai, Phys. Rev. B 105, 085109[8] T. Yoshida, T. Mizoguchi, Y. Kuno, and[3] H. Wakao, T. Yoshida, and Y. Hatsugai

Y. Hatsugai, Phys. Rev. B 103, 235130

arXiv:2203.05773(2021)[4] T. Yoshida and Y. Hatsugai, Phys. Rev.

[9] Y. Yanase, A. Daido, K. Takasan, andB 104, 075106 (2021).

T. Yoshida, Physica E, 140, 115143 (2022)[5] T. Yoshida, T. Mizoguchi, and Y.
Hatsugai, Phys. Rev. E 104, 025003

186

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Extreme response of isotropic spin ﬂuctuations
emerging from anisotropic antiferromagnets undermoderate spin dilution
Hidemaro SUWA
Department of Physics, University of Tokyo, Tokyo 113-0033

The stability and response of magnetic
materials to external stimuli are determined by spin ﬂuctuations dictated by magnetic anisotropy. The two-dimensional (2D)
isotropic antiferromagnet is one of the ideal
cases to pursue an extreme magnetic response. However, magnetic anisotropy is signiﬁcant in most materials, reducing the magnetic response. As a perturbation, magnetic
anisotropy introduces a characteristic lengthscale ξani . The signiﬁcance of anisotropy follows from the fact that the correlation length
increases rapidly with decreasing temperatureand easily reaches ξani . In contrast, the Zeeman energy from a typical achievable magnetic
ﬁeld is weaker, and the length scale ξext introduced by the external ﬁeld is much larger, i.e.,ξext > ξani . Moreover, the Zeeman ﬁeld in antiferromagnets must be a staggered ﬁeld thatis linearly coupled to the staggered magnetization, which is diﬃcult to realize.
Our primitive 2D antiferromagnet is realized on a pseudo spin-1/2 square lattice embedded in a [(SrIrO3 )1 /(SrTiO3 )2 ] superlattice, with the adjacent IrO2 planes well separated by non-magnetic spacers. Strong spinorbit coupling of iridium stabilizes the Jeﬀ =1/2 moment antiferromagnetically coupled toeach other via the Heisenberg super-exchangeinteraction. An essential feature of such a
Jeﬀ = 1/2 square lattice is that the large
Dzyaloshinskii–Moriya interaction arising fromthe staggered rotation of the IrO6 octahedronaround the c axis is canceled throughout thelattice, and the pseudospins tend to be almost
completely isotropic, which is called a hidden
SU(2) symmetry. This phenomenon allows thein-plane uniform magnetic ﬁeld to act as aneﬀective staggered ﬁeld. Nevertheless, higherorder super-exchange paths due to Hund’s coupling cause small easy-plane anisotropy, eﬀectively reducing the spin symmetry from SU(2)to U(1).
We have theoretically and experimentallydemonstrated that we can switch the orderof ξext and ξani utilizing magnetic dilution.
Using ISSP System B in class C projects(ID: 2021-Ca-0117) and the ALPS/looper(http://github.com/wistaria/alps-looper)
code, we simulated large-scale 2D AFM
systems of more than one million quantum spins.
We calculated the Berezinskii–Kosterlitz–Thouless transition temperatures for several dilution fractions. Using
the crossover argument with multiple perturbations, we have shown that the response
to magnetic ﬁelds changes from the U(1)model to the SU(2) model above the thresholddilution fraction because of the length-scale
switch (ξext < ξani ). The theoretical calculation successfully accounts for the experimental
observations, conﬁrming the extreme response of isotropic ﬂuctuations emerging fromanisotropic antiferromagnets under moderate
spin dilution.

187

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Research of Multi-Channel Kondo Eﬀect
Emerging from Heavy Rare-Earth Ions
Takashi HOTTA
Department of Physics, Tokyo Metropolitan University
1-1 Minami-Osawa, Hachioji, Tokyo 192-0397

We have discovered the three-channel Kondo
eﬀect in the cubic Ho compound [1]. We haveanalyzed a seven-orbital impurity Andersonmodel hybridized with Γ8 and Γ7 conduction
electrons for a case with ten local f electrons
corresponding to a Ho3+ ion by using a numerical renormalization group (NRG) method.
Then, we have found a residual entropy of log ϕ√with the golden ratio ϕ = (1 + 5)/2 as a signal of the three-channel Kondo eﬀect for the
local Γ5 triplet ground state.
For the construction of the local f -electron
Hamiltonian Hloc , we introduce one f -electronstate, deﬁned by the eigenstate of spin-orbit
and crystalline electric ﬁeld (CEF) potential
terms. Under the cubic CEF potential, we obtain Γ7 doublet and Γ8 quartet from j = 5/2
sextet, whereas we ﬁnd Γ6 doublet, Γ7 doublet,and Γ8 quartet from j = 7/2 octet. By using
those one-electron states as bases, we obtain
Hloc asHloc =∑†(λj + Bj,µ )fjµτ
fjµτ + nEf

j,µ,τ

+

∑ ∑ ∑

j1∼j4 µ1∼µ4 τ1∼τ4

Iµj11jτ21,jµ32jτ42 ,µ3 τ3 µ4 τ4 (1)× fj†1 µ1 τ1fj†2 µ2 τ2fj3 µ3 τ3fj4 µ4 τ4 ,where fjµτ is the annihilation operator of a localized f electron in the bases of (j, µ, τ ), j
is the total angular momentum, j = 5/2 and7/2 are denoted by “a” and “b”, respectively,µ distinguishes the cubic irreducible representation, Γ8 states are distinguished by µ = α
and β, while the Γ7 and Γ6 states are labeledby µ = γ and δ, respectively, τ denotes thepseudo-spin, which distinguishes the degeneracy concerning the time-reversal symmetry, n
is the local f -electron number at an impurity
site, and Ef is the f -electron level to control
n. Here we set h̄ = kB = 1 and the energy unit
as eV.
Concerning the spin-orbit term, we obtain
λa = −2λ and λb = (3/2)λ, where λ isthe spin-orbit coupling of f electron. In thisstudy, we set λ = 0.265 for the Ho ions.
Concerning the CEF potential term for j =5/2, we obtain Ba,α = Ba,β = 1320B40 /7
and Ba,γ = −2640B40 /7, where B40 denotes
the fourth-order CEF parameter for the angular momentum ℓ = 3. For j = 7/2, we
obtain Bb,α = Bb,β = 360B40 /7 + 2880B60 ,Bb,γ = −3240B40 /7 − 2160B60 , and Bb,δ =360B40 − 3600B60 /7. In the present calculations, we treat B40 and B60 as parameters.
For the Coulomb interaction terms, we do notshow the explicit forms of I here, but they
are expressed by the four Slater-Condon parameters, F 0 , F 2 , F 4 , and F 6 . These values should be determined from experimental
results, but here we simply set the ratio as
F 0 /10 = F 2 /5 = F 4 /3 = F 6 = U , where U indicates the Hund’s rule interaction among thef orbitals and the magnitude is set as unity inthis study.
In Fig. 1, we show the local CEF groundstate phase diagram for n = 10. The groundstate multiplet for B40 = B60 = 0 is characterized by the total angular momentum J = 8.
Under the cubic CEF potentials, the sept-188

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

0.005
B60 [meV]

1.5

n=10
U=1
l=0.265

G5 triplet
W=10-3G1 singlet

0.0

ublet
G 3 dot-0.005
iple
G tr
4

-0.01
-0.1

-0.05

W=-10-3G3 doublet
0.0
B40 [meV]

0.05

f-electron entropy

0.01

0.1

1

Ho3+ (f10)x=0.0, W=10-3eV
V=0.805eV
U=1eV
l=0.265eV

0.5

log φ
0 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1
10 10 10 10 10 10 10 10 10 10 10 10

Temperature [eV]
Figure 1: Local CEF ground-state phase diagram on the (B40 , B60 ) plane for n = 10 with
U = 1 and λ = 0.265.
dectet of J = 8 is split into four groups as one
Γ1 singlet, two Γ3 doublets, two Γ4 triplets,
and two Γ5 triplets. Then, we obtain fourkinds of local ground states for n = 10, as
shown in Fig. 1. The dashed rhombus denotes the trajectory of B40 = W x/15 and
B60 = W (1 − |x|)/180 for −1 ≤ x ≤ 1 with
W = ±10−3 . Roughly speaking, the Γ5 triplet
appears widely for B60 > 0, whereas the Γ3
doublet is found for B60 < 0. In the region of
B60 ≈ 0 and B40 > 0, the Γ1 singlet was stabilized. For B40 < 0, we ﬁnd the Γ3 doublet andΓ4 triplet in a narrow region between the Γ5
triplet and Γ3 doublet.
Now we include the Γ7 and Γ8 conduction
electron bands. Here we consider only the hybridization between the conduction and j =7/2 electrons. The Hamiltonian is given byH =∑εkc†kµτckµτ +k,µ,τ

+ Hloc ,∑Vµ(c†kµτ fbγτ +h.c.)

k,µ,τ

(2)

where εk is the dispersion of conduction electron with wave vector k, ckγτ is an annihilation operator of conduction electrons, and Vµdenotes the hybridization between f electronin the µ orbital and conduction electron of theµ band. Here we set Vα = Vβ = Vγ = V .
In this research, we analyze the model by
employing the NRG method [2]. We introduce

Figure 2: Entropy vs. temperature for n = 10with x = 0.0 and W = 10−3 , corresponding tothe Γ5 triplet ground state.
a cut-oﬀ Λ for the logarithmic discretizationof the conduction band. Due to the limitationof computer resources, we keep M low-energy
states. Here we use Λ = 8 and M = 5, 000.
In the NRG calculation, the temperature T isdeﬁned as T = DΛ−(N −1)/2 , where D is half
the conduction band width, which was set as
1 eV, and N is the number of renormalization
steps.
Here we brieﬂy discuss the typical result forn = 10 [1]. In Fig. 2, we show entropy vs. temperature for the Γ5 triplet ground state. We
observe a residual entropy of log ϕ at low tem√
peratures with the golden ratio ϕ = (1+ 5)/2,
which is characteristic of the three-channel
Kondo eﬀect. We conﬁrm the residual entropy of log ϕ in the wide region of the local Γ5
triplet ground state. Thus, we conclude thatthe three-channel Kondo eﬀect occurs in theΓ5 triplet ground state of Ho3+ ions.

References[1] T. Hotta, J. Phys. Soc. Jpn. 90, 113701(2021).
[2] H. R. Krishna-murthy, J. W. Wilkins, andK. G. Wilson, Phys. Rev. B 21, 1003
(1980).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical study of topological thermal transport in
Kitaev-related systems
Joji NASU
Department of Physics, Tohoku University
Sendai 980-8578

The Kitaev quantum spin model has been
intensively investigated since the proposal by
A. Kitaev as a canonical model exhibiting
quantum spin liquids. This model is considered to describe the magnetism of iridium oxides and α-RuCl3 where the strong spin-orbit
coupling and electron correlations are present.
However, these materials show a magnetic order at low temperatures due to magnetic interactions additional to the Kitaev term. As additional terms, eﬀects of the Heisenberg interaction and oﬀ-diagonal symmetric term (Γ term)
have been examined intensively. Moreover, recent experiments in α-RuCl3 clariﬁed that an
applied magnetic ﬁeld induces nonzero thermal
Hall conductivity, whose sign depends on themagnetic ﬁeld direction. However, the ﬁeldangle dependence of the Kitaev-Heisenberg
and Kitaev-Heisenberg-Γ models remains unclear in the presence of magnetic orders.
In this project, we systematically examine
the ﬁeld-angle dependence of magnetic orders
and excitation spectra in these models. To address the case with arbitrary spin directions ina magnetic order, we have newly developed thecalculation technique by extending the conventional spin-wave theory [1, 2]. In this method,
we can implement large-sublattice calculations
straightforwardly. Our spin-wave theory needs
the Cholesky decomposition. We use the LAPACK library to perform it. First, we examine the ground-state spin conﬁguration bychanging the magnetic ﬁeld direction and obtain the phase diagram. Based on the ob-tained ground-state magnetic orders, we calculate the energy and Berry curvature of themagnon bands. Furthermore, we calculate thetemperature dependence of the thermal Hall
conductivity. To compute the thermal Hall coeﬃcient, we need to sum up the Berry curvature for the wave-number vector in the Brillouin zone. We parallelize the k-summation in
the ISSP supercomputer to perform this procedure eﬃciently. The thermal Hall conductivity is enhanced in magnetically ordered stateswith noncoplanar spin conﬁgurations. Moreover, we also ﬁnd that the thermal Hall eﬀect
originating from the topological nature of themagnon dispersion is absent when the ﬁeld isapplied along with one of the spin axes in the
Kitaev-Heisenberg model. We also ﬁnd that
this feature disappears by introducing the oﬀdiagonal symmetric Γ interaction. In addition,
we clarify that the Γ interaction suppresses thethermal Hall conductivity because of enhancing the low-energy magnon gap.

References[1] S. Koyama and J. Nasu: B 104 (2021)
075121.
[2] S. Koyama and J. Nasu: J. Phys.: Conf.
Ser. 2164 (2022) 012071.

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Searching for meron crystal in itinerant magnets
Satoru Hayami
Department of Applied Physics, The University of Tokyo, Tokyo 113-8656

Topological spin textures, such as a magnetic skyrmion, meron, and hedgehog, have attracted considerable attention, since they giverise to fascinating physical phenomena, suchas the topological Hall eﬀect. The fundamental understanding of the stabilization mechanisms for these nontrivial spin textures would
be useful for potential applications to nextgeneration electronic and spintronic devices.
In the project with number 2021-Ca-0042, wehave theoretically investigated the possibilityof such topological spin textures based on anitinerant electron model and its eﬀective spinmodel. We have presented the main results
this year below.
(i) Skyrmion crystals in trigonal systems:
We have theoretically investigated a new stabilization mechanism of the skyrmion crystals
in itinerant trigonal systems [1]. By focusing on the anisotropic exchange interactionthat originates from the lack of horizontal mirror symmetry and twofold rotational symmetry along the threefold axis, we obtained two
types of skyrmion crystals with the skyrmion
number of one and two. We have shown that
two SkXs are transformed with each otherby changing the magnetic ﬁeld. Our ﬁndings
suggest itinerant trigonal systems as a newskyrmion-hosting system in addition to conventional hexagonal and tetragonal systems.
(ii) Mechanism of skyrmion crystals in EuPtSi: We have theoretically studied the stabilization mechanism of the skyrmion crystals
in the f -electron compound EuPtSi based onan eﬀective spin model [2]. We found two
important ingredients to induce the skyrmion
crystal: (1) the multiple-q superpositions of

the spirals with low-symmetric ordering vectors and (2) the synergy between spin-charge
and spin-orbit couplings in itinerant magnets.
We have clariﬁed that the model to satisfy two
conditions well describes the skyrmion physics
in EuPtSi by performing unbiased simulated
annealing.
(iii) Meron-antimeron crystal on a triangular lattice: A meron-antimeron crystal consisting of the periodic array of merons andantimerons with a half skyrmion number has
attracted growing attention since its observation in Co8 Zn9 Mn3 and Gd2 PdSi3 . Nevertheless, its origin has not been fully identiﬁed owing to the lack of a stabilization mechanism
and an appropriate model. To understandthe origin of the meron-antimeron crystals on
the basis of metallic magnets, we theoretically
performed simulated annealing for an eﬀective spin model derived from the Kondo lattice model on a noncentrosymmetric triangular lattice [3]. As a result, we showed that several types of meron-antimeron crystals are stabilized by the synergy among the biquadraticinteraction, the single-ion anisotropy, and the
Dzyaloshinskii-Moriya interaction. The emergent meron-antimeron crystals are owing to thenature of itinerant electrons, which have notbeen obtained in localized spin models. We
also found other topological spin textures including the skyrmion crystal can be realized by
the same eﬀective model at zero ﬁelds.
(iv) Charge density waves in multiple-Q spinstates: We elucidated the charge density wave
formation in the presence of the spin density
wave [4]. Based on the perturbation in termsof the spin-charge coupling, we theoretically191

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

derived a useful formula for the relationshipbetween charge density waves and spin density waves, which can be applied to any typeof magnetic texture and lattice structure. We
have tested the obtained formula for several
single-Q and double-Q magnetic orderings including the skyrmion crystal on a square lattice. We have also shown the eﬀects of large
spin-charge coupling beyond the perturbative
regime and the spin-orbit coupling to comprehensively understand the charge density wave
formation in itinerant magnets.
(v) Phase shift in skyrmion crystals: We
have theoretically studied the possibility ofcontrolling the skyrmion crystals by using thephase degree of freedom among the spin density waves [5]. We have shown that a phaseshift can occur in the skyrmion crystals to stabilize a new type of vortex crystals with a different pattern of an emergent magnetoelectricﬁeld through local scalar spin chirality, which
gives rise to nonreciprocal transport phenomena without the spin-orbit coupling. Analyzing the Kondo lattice model and its eﬀective
spin model, we found three mechanisms tocause the phase shift: exchange interactions
between the localized spins, thermal ﬂuctuations, and long-range chirality interactions.
(vi) Skyrmion crystal in centrosymmetric bilayer magnets: We proposed a stabilization
mechanism to realize the skyrmion crystal incentrosymmetric bilayer magnets [6]. By performing the simulated annealing on the bilayer
triangular-lattice spin model, we have shownthat the interplay between the layer-dependent
Dzyaloshinskii-Moriya interaction and interlayer exchange interaction gives rise to theskyrmion crystal even without the frustrated
exchange interaction and multiple-spin interactions. In addition, we have obtained two
triple-Q states with a uniform scalar chirality
while increasing and decreasing the magnetic
ﬁeld in the skyrmion crystal phase that has notbeen obtained in the single-layer system.

onal magnets: We theoretically investigatedthe possibility of realizing multiple skyrmion
crystals against an external magnetic ﬁeld in
tetragonal itinerant magnets [7]. By focusing
on multiple peaks at bare susceptibility of itinerant electrons, we found that three types ofskyrmion crystals with the skyrmion numbersof one and two, which are characterized by different superpositions of helices, are stabilized
in the ground state. Moreover, we found thatthey are transformed with each other by an
external magnetic ﬁeld.

References[1] R. Yambe and S. Hayami, Sci. Rep. 11,11184 (2021)[2] S. Hayami and R. Yambe, J. Phys. Soc.
Jpn. 90, 073705 (2021).
[3] S. Hayami and R. Yambe, Phys. Rev. B
104, 094425 (2021).
[4] S. Hayami and Y. Motome, Phys. Rev. B
104, 144404 (2021).
[5] S. Hayami, T. Okubo, and Y. Motome,
Nat. Commun. 12, 6927 (2021).
[6] S. Hayami, Phys. Rev. B 105, 014408(2022).
[7] S. Hayami, J. Phys. Soc. Jpn. 91, 023705(2022).

(vii) Multiple skyrmion crystals in tetrag-

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Analysis of string excitations in the opticalconductivity of doped Mott insulators
Takami TOHYAMA
Department of Applied Physics, Tokyo University of Science, Tokyo 125-8585

The optical conductivity has provided important information on the nature of the holedoped Mott insulators. The most striking
feature is dynamical spectral-weight transfer
upon chemical doping and photodoping appearing at mid-infrared (MIR) region. The
weights at MIR are sensitive to dimensionality and are found in two dimensions but not in
one dimension. MIR weights are expected tocontain essential information on the dynamical properties of holes in the two-dimensional
Mott insulators. A hole moving in antiferromagnetic (AFM) spin background creates misarranged spins with respect to their sublatticeand consequently induces string-type excitation of spins. MIR weights may have a relation to string structures. However, it is unclear how MIR weights actually are related tostring excitations that are the result of a complex process due to spin-charge coupling. If ahole moves in an AFM state, it leaves tracesof spin mismatches with sublattice magnetization called Sz strings. The Sz strings are
inadequate to describe a hole surrounded by
AFM spins since the hole picks up a nontrivial
U (1) phase when it hops in an AFM spin background. This phase generates another type ofstrings, called phase strings, caused by transverse spin component.
In this project, we demonstrate howmuch Sz and phase strings contribute to
MIR weights.
We calculate the optical conductivity of the Hubbard model inthe strong-coupling regime and the t-J
model by using time-dependent Lanczos andtime-dependent density-matrix renormalization group (tDMRG) methods. We focus on
doped Mott insulators with a single hole andconsider two-leg ladders up to a 20×2 sites [1]and square lattice up to 6×6 sites [2] underopen boundary conditions. Turning on and oﬀ
the eﬀect of phase strings, we examine how
they contribute to MIR weights. We ﬁnd thatphase strings play an essential role in MIR
weights. MIR weights are crucially suppressed
for both the Hubbard and t-J models if we remove phase strings. Although Sz strings also
contribute to MIR weights, their contribution
is smaller than phase strings. We consider that
this is because Sz strings can be self-healed
via quantum spin ﬂips, while phase strings are
not reparable. Our ﬁndings suggest that a mutual Chern-Simons gauge ﬁeld, which is an elementary force between spin and charge in thephase-string theory, is signiﬁcant for obtaining
MIR weights. This indicates that a hole does
not pick up a U (1) phase when moving in AFM
spin background if we remove this gauge ﬁeld.
As a result, we can characterize a doped holesurrounded by AFM spins via a spin-polaron
quasiparticle, which has a cosinelike energy
dispersion in the single-particle spectral function.

References[1] K. Shinjo, S. Sota, and T. Tohyama:
Phys. Rev. B 103 (2021) 035141.
[2] K. Shinjo, S. Sota, and T. Tohyama: inpreparation.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical Calculation on Coulomb Repulsionof EDXT Oligomer Charge Transfer Salts
Tomoko FUJINO
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
typical low molecular weight 1D conductors

We have synthesized discrete oligomer
modelsfor

dopedpoly(3,4-(TTF•TCNQ: 4tTTF ≈ 0.2–0.4 eV, 4tTCNQ ≈ 0.5

ethylenedioxythiophene) (PEDOT) [1,2]. DopedeV), revealing the origin of the high conductivity

PEDOT is a commonly employed conductiveof doped PEDOT. Interestingly, the elongation

polymer in organic electronic devices owing toof characteristic oligomer length from dimer totheir flexibility, lightness, transparency, andtrimer exhibited decreased W (≈ 0.90 eV), while

concisetheir

it improved the conductivity with 70%

complicated packing structures based on a non-activation energy (0.20 eV) of that for dimer.

uniform molecular weight distribution severely

These data indicated that extending thelimit structural data acquisition, especiallyconjugation lengths of the oligomers markedly

electronic structural data, requisite for further

lowered effective Coulomb repulsion (Ueff),

improving the physical properties.

thereby decreasing the ratio of Ueff/W andsynthetic

routes.

However,This study calculated the band structures

improving the conductivity [2]. The details on

based on the single-crystal structures of charge

Ueff by theoretical calculations will be discussed

transfer salts of the dimer as the shortest models

in near future.

for doped PEDOT [1]. The band calculations
functional theory (DFT)-based by OpenMX

References

software revealed their one-dimensional (1D)

[1]. R. Kameyama, T. Fujino, S. Dekura, M.

metallic

Kawamura, T. Ozaki, and H. Mori: Chem. Eur.

band

structures

with

a

strongintracolumnar orbital interaction (calculated

J. 27 (2021) 6696.

band width W ≈ 1 eV). This interaction was[2] R. Kameyama, T. Fujino, S. Dekura, and H.

significantly stronger than that observed for

Mori: Phys. Chem. Chem. Phys. 24 (2022), 9130.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Studies of the superconductivity and magnetic statesin the strongly correlated electron systems based on
Hubbard models.
Atsushi Yamada
Department of Physics, Chiba University
Chiba 263-8522, Japana, Chiba 277-8581

A spin liquid state, which is a purely
nonmagnetic Mott insulator without spontaneously broken spatial or spin symmetry, has
attracted a lot of interest. This state is realized in geometrically frustrated systems likethe charge organic transfer salts κ-(BEDTTTF)2 X[1] and Cs2 CuCl4 .[2]study larger systems, we need to revise ourprogram using MPI technique. We are now
improving our programs, even though we encounter a lot of diﬃculties.

A spin liquid could arise also in the intermediate coupling region of strongly correlated
systems between a semi-metal and orderedstate, because in this case a correlation-driven
insulating gap might open before the system
becomes ordered. This possibility might be realized in the half-ﬁlled Hubbard model on thehoneycomb lattice, where a semi-metal is realized at U = 0, and in fact is studied, for example, using Quantum Monte Carlo (QMC) simulations. Meng et al[3] found that a spin liquidstate is realized in the Honeycomb lattice Hubbard model. But suqsequent QMC studies[4]with larger lattice size ruled out this possibility.

[1] Y. Shimizu, K. Miyagawa, K. Kanoda,
M. Maesato, and G. Saito, Phys. Rev.
Lett. 91, 107001 (2003); Y. Kurosaki, Y.
Shimizu, K. Miyagawa, K. Kanoda, and
G. Saito, Phys. Rev. Lett. 95, 177001(2005).

We have studied the magnetic and metal-toinsulator transitions by variational cluster approximation using 10-site and 16-site clusters
as a reference system. Parts of numerical calculations were done using the computer facilities of the ISSP. We found that UAF = 2.7 and
UMI = 3.0 for 10-site cluster, and UAF = 2.7
and UMI = 3.2 for 16-site cluster.[5] This result
also rules out the existence of the spin liquid inthis model. Our results agree with recent large
scale Quantum Monte Carlo simulations.[4] To[4] S. Sorella, Y. Otsuka, and S. Yunoki, Sci.
Rep. 2, 992 (2012); F. F. Assaad andI. F. Herbut, Phys. Rev. X 3, 031010(2013); F. Parisen Toldin, M. Hohenadler,
F. F. Assaad, and I. F. Herbut, Phys. Rev.
B 91, 165108 (2015).

References[2] R. Coldea, D.A. Tennant, A.M. Tsvelik,
and Z. Tylczynski, Phys. Rev. Lett. 86,
1335 (2001); R. Coldea, D.A. Tennant,and Z. Tylczynski, Phys. Rev. Lett. 68,
134424 (2003).
[3] Z. Y. Meng et al., Nature 464, 08942(2010).

[5] A. Yamada, Int. J. Mod. Phys. B 30,
1650158 (2016).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Non-Abelian anyons trapped in vacancies of theKitaev model and non-local spin correlations
Masahiro O. TAKAHASHI and Satoshi FUJIMOTO
Department of Materials Engineering Science, Osaka University
Machikaneyama 1-3, Toyonaka, Osaka 560-8531

We have clariﬁed, using massive parallel
computer simulations, that a non-local spinspin correlation exists between speciﬁc spatially well-separated sites in the Kitaev spin
liquid with some point vacancies, which reveals the realization of Majorana zero modes(MZMs) strongly trapped in vacanceis.
The Kitaev model [1] is a spin-1/2 model deﬁned with bond-dependent Ising interactions
on the honeycomb lattice and it is exactly solvable with the use of an itinerant Majorana
fermion and a Z2 ﬂux deﬁned on each plaquette. In a chiral spin liquid phase MZMs
can appear exhibiting a non-local correlation
and Z2 ﬂuxes binding them obey non-Abelian
statistics, in principle. It is expected to exploit
the composite particles for topological quantum computation. It is diﬃcult, however, tointroduce and control the composites in the
ground state of the pure Kitaev model since
they are thermal excitations. To avoid the difﬁculty, we focus on point vacancies in the system. It is well known that each vacancy binds
Z2 ﬂux in the ground state, or the boundﬂux sector [2], while MZMs strongly trappedin them are not yet reported.
In this study, we reveal the importance of
localized Majorana fermions caused by vacancies, which have not been properly taken into
account in previous studies. In the Kitaev’s
notation, a spin operator at j-site, Sjγ (γ =x, y, z), is represented as Sjγ = ibγj cj /2, using an itinerant Majorana fermion operator
cj and a localized Majorana fermion opera-

tor bγj (Fig. 1). The former behaves as afree Majorana fermion described as a tightbinding model while the latter forms a Z2 gageﬁeld with the other localized Majorana fermion
from the nearest site on each bond. Then, if avacancy exists, the localized Majorana fermion
from the nearest site of the vacancy site loses
the partner and it can couple with itinerant
Majorana fermions, as shown in Fig. 1, whenan external magnetic ﬁeld is applied. This nontrivial Majorana hopping term, or b-c hopping
term, contributes to realizing MZMs bound inZ2 ﬂuxes that should be naturally found in thebound-ﬂux sector.

Figure 1: Majorana fermions for each spin andnontrivial Majorana hoppings between bγj andck around a vacancy vA, represented as arrows.
The eﬀective Majorana Hamiltonian Heﬀ forthe Kitaev model with vacancies, which are
spatially well-separated, works well to host
MZMs. We assume two vacancies, vA and vB,for simplicity and the direction of a magnetic
ﬁeld parallel to the in-plane a-axis. At nonzero

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

magnetic ﬁelds, a pair of MZMs appears in thebulk gap and is stable against an increase ina magnetic ﬁeld strength unless the boundﬂux ground state is valid. This property is
not conﬁrmed without b-c Majorana hopping
terms: the Majorana gap grows as increasing
the strength whereas pseudo-MZMs [3] disappear rapidly to form the bulk gap. Moreover,
it is discovered that more than 99% of the realspace amplitudes of MZMs are on the localized
Majorana fermions, which implies that they
are strongly trapped in Z2 ﬂuxes in the groundstate.
To approach a pair of MZMs by a physicalobservable using a non-local property, we consider a non-local spin correlation between thenearest sites of each vacancy, say jA and jBsite. Our interest is written as below at inverse temperature β,⟨SjzA (t) SjzB (0)⟩ ≡[]Tr PF SjzA (t) SjzB (0) e−βHeﬀ
Tr [PF e−βHeﬀ ](1)

where PF is a projection operator to
the physical subspace.
Especially theas shown in Fig. 2. Indeed, the structure factor in the zero-ﬂux sector diﬀers from the one
in the bound-ﬂux ground state in a point thatthe signal comes from b-Majorana excitations
shift to a higher ω region, very close to the
Majorana bulk gap, which implies the absenceof MZMs.
In summary, non-Abelian anyons composedof MZMs and Z2 ﬂuxes, both of which aretrapped in vacancies, can stably exist in the
ground state of the vacancy-induced Kitaev
model with a magnetic ﬁeld. They exhibit the
non-local spin-spin correlation in a chiral spin
liquid phase, and this system may become thenew platform for topological quantum computation.

References[1] A. Kitaev, Ann. Phys. 321 (2006) 2.
,[2] A. J. Willans et al., Phys. Rev. Lett. 104(2010) 237203.
[3] W.-H. Kao and N. B. Perkins, Ann. Phys.
435 (2021) 168506.

Figure 2: The structure factor of a non-local
spin-spin correlation and the Majorana spectrum structure.
Fourier-transformed dynamical structure fac∫ ∞ i(ω+iδ)t z
tor Ψzz⟨SjA (t) SjzB (0)⟩jA jB (ω) ≡0 eclearly reveals the contribution from MZMs
and b-Majorana excitations inside the bulk gap

197

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Discrete time crystals in solids
Tatsuhiko Ikeda
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

We have studied a discrete time crystal(DTC) in solid-state materials using Supercomputer System B at the ISSP. This year, apaper on this project was published [1]. We
will report this project below.
A DTC is an exotic nonequilibrium phasein periodically driven dissipative quantum systems that breaks the discrete time translation
symmetry. The DTC had been well studied
and experimentally demonstrated in artificial
quantum systems without dissipation, such as
trapped ions, NV centers in diamond, andquantum computers. However, it had not been
explored in natural materials, like solids, with
dissipation. Nonetheless, if we create the DTC
in natural materials, it could oﬀer a new possibility of time crystals in material science.
In this study, we have investigated the DTC
in solid-state materials. To uncover the mechanism and properties of the DTC in solids, wehave considered a periodically driven quantum
Ising model with dissipation using the FloquetRedfield equation that describes a periodicallydriven quantum system subject to dissipation.
The Floquet-Redfield equation is much harder
to solve than the usual Schrödinger equation
because we need to treat a D × D density matrix rather than a D-dimensional wave function in the Floquet-Redfield equation (D is theHilbert space dimension). Therefore, in thisstudy, we have employed the mean-field theory
and numerically solved the DTC order parameter self-consistently.

the phase diagram of the DTC in solids (seeFig. 1). This phase diagram highlights a nontrivial behavior that the separate two DTC regions appear. Also, we have shown that this
DTC is robust against any perturbation. We
believe that these results pave the way for a
new research field of time crystals in materialscience.

DTCτNormalT
Figure 1: Phase diagram of the DTC in solids.
The horizontal (vertical) axis denotes the temperature of the bath (the period of the Hamiltonian).

References[1] K Chinzei and TN Ikeda: Phys. Rev. Research 4, 023025 (2022).

Performing a massive numerical calculation
with the supercomputer, we have obtained198

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Interaction-induced quantum spin Hall state in the
Dirac electron system α-(BEDT-TSeF)2I3
Akito KOBAYASHI
Department of Physics, Nagoya University
Nagoya 464-8602

We have constracted extended-Hubbard
model using first-principles calculations todeal with spin-orbit and non-local repulsive interactions and have shown that aninteraction-induced quantum spin Hall (QSH)
state is stabilized, focusing on the recentlydiscovered candidate topological insulator
α-(BEDT-TSeF)2 I3 having two-dimensionalcharge-neutral Dirac cones.[1, 2, 3, 4] In the absence of repulsive interactions, a topological insulator characterized by a nonzero spin Chern
number appears by the spin-orbit coupling. By
considering up to next-nearest neighbor repulsions at Hartree-Fock level, the intrinsic spinorbit gap is found to grow and a QSH state
appears that has both a nonzero spin Chern
number and order parameter as shown in Fig.
1. The loops ϕi shown in Fig. 1 represents
the spin current flowing between BEDT-TSeF
molecules. The spin currents between nextnearest neighboring molecules also exist, butthey are omitted in Fig. 1 for simplicity. These
spin currents increase at low temperatures below 50 K and widen the gap. Transport coeﬀcients and spin susceptibility have been calculated and found to be consistent with most of
the experimental findings, including the metalto-insulator crossover occurring at ∼ 50 K as
well as the Berry phase change from 0 to pi under hydrostatic pressure. We argue that such a
QSH state does not necessitate a sizeable spinorbit interaction to generate a large insulating gap, which is highly advantageous for the
search of novel topological phases in genericmaterials having small spin-orbit coupling.

References[1] S. Kitou, et al., Phys. Rev. B 103, 035135(2021).
[2] T. Tsumuraya et al., Eur. Phys. J. B, 94,
17 (2021).
[3] Y. Suzumura et al., JPSJ 90, 124707(2021).
[4] D. Ohki, K. Yoshimi, and A. Kobayashi,
arXiv:2110.05010

Figure 1: Interaction-induced quantum spin
Hall state in α-(BEDT-TSeF)2 I3 .

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study of cuprate high-temperature superconductors
using a four-band d-p model
Hiroshi WATANABE
Research Organization of Science and Technology, Ritsumeikan University
1-1-1 Noji-Higashi, Kusatsu-shi, Shiga 525-8577

The discovery of superconductivity incuprates [1] has brought about the significant
progress in strongly-correlated electron systems. However, we have not yet reached aunified understanding of their properties, including their material dependence of the superconducting transition temperature Tc . Recent
development of theories and experiments sheds
light on the importance of the orbital degree of
freedom in cuprates [2, 3]. To obtain the unified description of cuprate high-temperature
supercondctors, we study the four-band d-p
model that properly includes the orbital degreeof freedom [4]. We construct the tight-binding
model for La2 CuO4 and HgBa2 CuO4 systems
based on the first-principles calculation and examine the effect of Coulomb interactions withthe variational Monte Carlo (VMC) method.
The Gutzwiller-Jastrow type wave function isused for the VMC trial wave function. The system size for the calculation is N =24×24=576
unit cells (and thus 576×4=2304 orbitals in total), which is large enough to avoid finite size
effects.
The superconducting correlation function
vs hole doping rate x for the La2 CuO4
system is shown in Fig. 1. At x = 0, thesystem is insulating and the superconductivity is completely suppressed: P dd = 0. As x
increases, mobile carriers are introduced into
the system and the mobility of the Cooper pairincreases. On the other hand, the strengthof the d-d pairing itself is reduced by doping because the electron correlation is also re-duced. The balance between these two factors results in the dome-shaped behavior of
P dd . The Ud /t1 dependence of P dd can bealso understood with this picture. We consider that Ud /t1 ∼ 8 is a realistic value for the
La2 CuO4 system. For the HgBa2 CuO4 system, while the dome-shaped behavior is observed for Ud /t1 = 7 and 8, P dd monotonicallydecreases with x for Ud /t1 = 6. This is because the system is metallic for Ud /t1 = 6 andthe picture of “doped Mott insulator” is nolonger valid. It results from the smaller ∆dp
in the HgBa2 CuO4 system that leads to theweaker electron correlation compared with the
La2 CuO4 system. The difference between two
systems are well described in our four-band d-p
model.

P dd

Figure 1: Superconducting correlation function P dd vs hole doping rate x for the La2 CuO4
system.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[1] J. G. Bednorz and K. A. Muller, Z. Phys.
B 64, 189 (1986).
[2] H. Sakakibara et al., Phys. Rev. Lett. 105,
057003 (2010).
[3] C. E. Matt et al., Nat. Commun. 9, 972(2018).
[4] H. Watanabe et al., Phys. Rev. Research
3, 033157 (2021).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Superconductivity in correlated electron systems
Takashi YANAGISAWA
National Institute of Advanced Industrial Science and Technology (AIST)
1-1-1 Umezono, Tsukuba 305-8568

1

2Introduction

Our computations are mainly based on the
optimized variational Monte Carlo method[1].
We also employ the Gutzwiller-Jastrow wave
function where the doublon-holon correlation
is taken into account. We have investigated
the ground-state phase diagram of the twodimensional Hubbard model and the twodimensional d-p model. We performed parallel computation in Monte Carlo calculations.
In order to reduce statistical errors, we carried out ∼ 500 parallel calculations. Parallel
computing is very important to reduce Monte
Carlo statistical errors.
The many-body wave function is written in
the form ψ (1) = exp(−λK)PG ψ0 , where K denotes the kinetic energy part (non-interactingpart) of the Hamiltonian and PG = PG (g) is
the Gutzwiller operator to control the double occupancy with the variational parameterg. ψ0 indicates a trial wave function which
is usually taken as the Fermi sea, the BCS
wave function or the state with some magnetic(or charge) orders. We can improve the wave
function systematically by multiplying by operators PG and e−λK repeatedly. We can consider ψ (2) = exp(−λ′ K)PG (g ′ )ψ (1) for different
variational parameters λ′ and g ′ . This wave
function is a very good many-body wave function because the ground-state energy is lowered greatly and the ground-state energy islower than those that are evaluated by anyother wave functions. We also employ the
Jastrow-type wave function which is written
as ψJ = PG PQ PJ ψ0 where PJ indicates anearest-neighbor number correlation operator
and PQ controls the nearest-ngighbor doublonholon correlation.

202

Why does the pairing state
become stable?

We have shown that the superconducting
phase exists in the strongly correlated region of electronic models[2].
We investigated kinetic-energy effect in superconductivity in the strongly correlated phase of the twodimensional Hubbard model. Let us examine why the superconducting state becomesstable in the strongly correlated region. The
Gutzwiller-BCS state is stabilized as a potential energy driven superconductivity because the Coulomb interaction energy is lowered while the kinetic energy increases in thisstate. In contrast, we showed that in the ψλ BCS wave function ψλ−BCS = e−λK PG ψBCS ,the Coulomb energy increases and instead the
kinetic energy is lowered in the strongly correlated phase where the Coulomb repulsive interaction U is large. The correlated superconducting state is realized as a kinetic energy
driven pairing state and this indicates the enhancement of superconductivity due to kineticenergy effect.
We estimate the kinetic energy in the superconducting state ψλ−BCS [3]. We define theSC condensation energy ∆Esc as a sum of twocontributions ∆Ekin−sc and ∆EU −sc :∆Esc = E(∆ = 0) − E(∆ = ∆opt ),∆Ekin−sc = Ekin (∆ = 0) − Ekin (∆ = ∆opt ),∆EU −sc = EU (∆ = 0) − EU (∆ = ∆opt ),where ∆ = ∆sc is the SC order parameter and∆opt is the optimized value which gives the energy minimum. We have
∆Esc = ∆Ekin−sc + ∆EU −sc .

(1)

The kinetic energy in ψλ−BCS is lower than
the kinetic energy in the normal state ψλ . The

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

0.5

Coulomb energy expectation value increases as∆sc increases. The results show

3

Kinetic energy enhancement of superconductivity

We define the difference of the kinetic energyas∆Ekin = Ekin (ψG ) − Ekin (ψλ ),
(3)

sc

∆E

kin-sc

/N

0.012

0.2

0.008

0.1

0.004

0

sc

0.3

∆E /N

for ψλ−BCS with U = 18t and the hole density
x = 0.12.

∆E /N
U

(2)

0.016

U

kin

∆EU −sc < 0,

kin

/N

E /N

0.4

∆E /N, E /N

∆Ekin−sc > 0,

0.02

∆E

0

-0.1

-0.004
0

5

10

15

20

U/t

where Ekin (ψG ) and Ekin (ψλ ) indicate the kinetic energy for ψG and ψλ , respectively. We
can write ∆Ekin = Ekin (λ = 0) − Ekin (λ) for
the optimized value of λ. ∆Ekin has the close
relation with the SC condensation energy ∆Escand its kinetic part ∆Ekin−sc .
We show ∆Ekin /N in Fig. 1 for x = 0.12
where x is the hole doping rate. The Coulomb
energy EU /N and the superconducting condensation energy ∆Esc /N are also shown in
Fig. 1. ∆Ekin begins to increase after the
Coulomb energy EU reaches the peak whenU ≈ 8t. The y axis on the right shows∆Ekin−sc /N in Fig. 1. ∆Ekin−sc shows a similar behavior to ∆Ekin . ∆Ekin−sc may change
sign as a function of U , which is consistent withthe analysis for Bi2 Sr2 CaCu2 O8+δ [4]. Thisshows the kinetic energy enhancement of superconductivity.

Figure 1: Kinetic-energy difference ∆Ekin /Nand the kinetic-energy gain ∆Ekin−sc /N in the
superconducting state ψλ−BCS as a functionof U on a 10 × 10 lattice where Ne = 88 andt′ = 0. The Coulomb energy EU /N for ψλ andthe condensation energy ∆ESC are also shown.
We use the periodic boundary condition in one
direction and antiperiodic one in the other direction. The y axis on the right shows the superconducting condensation energy ∆Esc andthe kinetic condensation energy ∆Ekin−sc /Nfor ψλ .

4[2] T. Yanagisawa, J. Phys. Soc. Jpn. 85,
114707 (2016).
T. Yanagisawa, J. Phys. Soc. Jpn. 88,
054702 (2019).
T. Yanagisawa, Condensed Matter 4, 57(2019).

Summary

We examined the kinetic energy effect in SC
states. The Gutzwiller-BCS state is the potential energy driven SC state, because the SC
condensation energy comes from the Coulombinteraction energy. This is the same as theoriginal BCS state where the superconductivity appears due to the attractive interaction.
We evaluated the kinetic energy in the improved SC state (ψλ−BCS ) to find that the kinetic energy gain stabilizes SC state while theexpectation value of Coulomb interaction energy increases. This indicates that superconductivity is enhanced due to the kinetic energy
effect.

203

References[1] T. Yanagisawa et al., J. Phys. Soc. Jpn.
67, 3867 (1998).
T. Yanagisawa, Phys. Rev. B75, 224503(2007) (arXiv: 0707.1929).

[3] T. Yanagisawa, Phys. Lett. A403, 127382(2021).
T. Yanagisawa et al., EPL 134, 27004(2021).
[4] G. Deutscher, A. F. Santander-Syro, N.
Bontemps: Phys. Rev. B 72, 092504(2005).

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Photoinduced nonequilibrium dynamics in correlated
electron systems
Atsushi ONO
Department of Physics, Tohoku University,
Sendai 980-8578

Antiferromagnets are promising for spintronics applications owing to their robustness
against a perturbative ﬁeld and to a higher
energy scale compared with that of ferromagnets. Recently, a current-induced staggered
torque, called Néel spin-orbit torque (NSOT),
has been recognized as an eﬃcient mechanismthat rotates the Néel vector in antiferromagnets. However, since most of the previous
studies considered the electrical switching of
the antiferromagnets, it is not fully understoodwhether and how the NSOT is generated by
optical pulses.
We have studied the real-time dynamics induced by a static electric ﬁeld and a terahertz electric-ﬁeld pulse [1]. We considered aminimal tight-binding model of antiferromagnetic Dirac semimetals, where a nonsymmorphic symmetry associated with the direction of
the Néel vector protects the crossing of doubly
degenerated energy bands, i.e., Dirac points.
The time evolution is governed by the Landau–
Lifshitz–Gilbert equation for the localized moments and the von Neumann equation for theitinerant electrons. We solved these coupledequations by using the ISSP supercomputer
system.
Figure 1 shows the real-time dynamics induced by a mono-cycle electric-ﬁeld pulse. We
found that the Néel vector rotates in a picosecond timescale, depending on the amplitude and polarization of light, and the Néelvector rotation accompanies the change in theenergy gap at the Dirac points. Our analy-

sis revealed that the Néel vector is canted by
optical NSOT and then rotated by a magneticanisotropy torque. We also showed that in thissystem a magneto-optical eﬀect can be used toobserve the direction of the Néel vector in realtime.

Figure 1: Time evolution of the Néel vector n, uniform magnetization m, excited electron density, and bandgap [1]. A mono-cycle
electric-ﬁeld pulse F (t) is applied.

References[1] A. Ono and S. Ishihara, npj Comput.
Mater. 7, 171 (2021).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

3.4

Cooperative Phenomena
in Complex Macroscopic Systems

205

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Effects of cavitation on soundwaves
Yuta ASANO, Hiroshi WATANABE, and Hiroshi NOGUCHI
Institute for Materials Research, Tohoku University Katahira, Aoba-ku, Sendai, Miyagi 9808577
Department of Applied Physics and Physico-Informatics,
Keio University, Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 233-8522
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581

Cavitation is a flow phenomenon involving

experiments and numerical calculations, thethe formation of bubbles, caused by local

mechanism remains thoroughly understood. In

pressure-drop in a liquid. Cavitation causes

this project, we investigate the effect of phase

performance degradation, noise, vibration, andtransitions on sound waves by molecularerosion in fluid machinery such as ship

dynamics (MD) simulations [1]. In particular,

propellers and turbomachinery. On the other

we clarify the differences in the effects of first-

hand, the shock waves and localized high-and second-order phase transitions on soundtemperature and -pressure fields generated bywaves.

the bubble collapse are applied to a wide range

The fluids are modeled by a monoatomic

of applications, including cleaning, processing,molecule whose interaction is defined by thechemical reaction acceleration, and medicine.

smoothed-cutoff Lennard-Jones potential. The

Therefore, it is vital to understand thesystem is a rectangular parallelepiped, and thecavitation mechanisms for many fields using

periodic boundary conditions are applied to y-liquid-gas multi-phase flows. In particular,

and z-directions. In x-direction, the oscillating

understanding the effects of cavitation on soundand stationary walls are placed at both ends.

waves is essential for the development of

The total number of particles is about 10

applied technology, such as the realization of

million. We investigate the differences in thehighly efficient chemical reactors. However,waveform change by approaching the phasecavitation

complextransition temperature for the liquid near thephenomenon in which a tremendous number offirst-order transition region and supercriticalbubbles repeatedly generate, grow, split andfluid near the critical point. These waveforms

coalesce, and disappear, making its analysis aare compared with the numerical solution ofchallenging

Burgers' equation.

isanproblem.

extremely

Despitenumerous

206

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

In the first-order transition region, thewaveform varies continuously until just above

References

the phase transition point, in good agreement[1] Y. Asano, H. Watanabe, and H. Noguchi,

with the Burgers' equation. When the phase

arXiv:2112.07139.

transition

occurs,thewaveformchanges

discontinuously due to the appearance of thegas phase, and the Burgers' equation is notapplicable. On the other hand, in the continuoustransition region, no discontinuous changes
occur. Soundwave decay due to the density
fluctuations are significant near the criticalpoint. However, the Burgers' equation isapplicable

even

for

such

large

densityfluctuations.
Finally, we investigated the bubble effects on
the soundwaves by using 60 million particles.
We observed a bubble generation and growthnear the oscillating wall, movement in thesoundwave propagation direction, and thendisappearance. Bubbles repeat this long time(about 30-million-time steps) cycle. We foundthat the bubble motion affects the pressurewave.
The present computational scale could only
treat the interaction between a single bubble
and sound wave. The bubble generation causes
a drastic change in soundwave, known as achange in sound speed, which is caused by theappearance of many bubbles. In order to reveal
the peculiar phenomena, it is necessary to
perform calculations for much larger systems.

207

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Coarse-Grained Molecular Dynamics Study of Biomolecular
Assemblies and Nanocolloids
Wataru SHINODA
Research Institute for Interdisciplinary Science,
Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530
a series of membrane protein assemblies,

We have extended the molecular library
within the SPICA coarse-grained (CG) force

scramblases,

andpoliovirus

capsids

field (FF), which was originally developed fordemonstrated the good performance of SPICA

lipids and surfactants. In this year, we haveFF.

added a new class of lipids, proteins, andA series of MD simulations of Hepatitis B

nucleic acids to the library. Especially, we

virus (HBV) capsid have also been carried out

improved the CG protein model to facilitate

at AA and CG resolutions.[2] In this year, wemolecular dynamics (MD) simulation with ahave constructed a molecular model of the

reproduction of multiple properties from both

entire HBV virion particle including theexperiments and all-atom (AA) simulations.[1]envelope.

The side chain analogs reproduced the transfer

membrane protein within the envelope and thefree energy profiles across the lipid membrane

capsid spike protein plays an important role in aand showed reasonable association free energy

strong anchoring of envelopes around the(potential of mean force) in water compared tocapsid. Due to a significant amount of

those from AA-MD. The CG-MD study of themembrane proteins in the envelope reduces theadsorption

150

lipid diffusion within the envelope, which is

peptides/proteins into the membrane gave

supposed to help increasing the stability ofcorrect predictions of the penetration depth andvirion particle.

orpenetration

of

about

The

interaction

betweenthe

We also analyzed the role of surfactants ininclination angle of peptides/proteins at thetransmembrane

the colloidal stability of nanoparticles in oil byregions, consistent with the OPM (Orientation

CG-MD.[3] Again, SPICA FF was used toof protein in membrane) database. The

observedimerization

nanoparticle aggregation through simulation. A

membrane

periphery

free

and

energies

of

some

the

pathwayofdetailsaggregationoftransmembrane helices in the lipid bilayer werefreefound to be comparable to those obtained fromdetermined for diﬀerent surfactant types andexperimental estimates. Application studies on

system conﬁgurations. The deformation of the208

energymolecular-levelisActivity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

surfactant layer surrounding the nanoparticle

M. Dixit, R. DeVane, C. MacDarmaid, G.

was shown to be the major source of colloid

Fiorin, M. L. Klein, W. Shinoda: J. Chem.

stabilization.

the

Theory Comput. DOI:10.1021/acs.jctc.1c01207.

surprising result that as the packing density of[2] K. Fujimoto, Y. Yamaguchi, R. Urano, W.

the surfactants is reduced, the role of the

Shinoda, T. Ishikawa, K. Omagari, Y. Tanaka, A.

surfactant is reversed from stabilizer to

Nakagawa, S. Okazaki: J. Chem. Phys. 155

nucleation agent.

(2021) 145101.

This

is

evidencedby[3] M. Griffiths and W. Shinoda: J. Phys. Chem.

References

B 125 (2021) 6315. [cover title][1] S. Kawamoto, H. Liu, Y. Miyazaki, S. Seo,

209

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Finite temperature properties of generalized Kitaev
modelsTsuyoshi OKUBO
Institute for Physics of Intelligence, The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 133-0033

The Kitaev model on the honeycomb lattice
has been widely investigated as a fundamental
model to investigate the nature of the quantum spin liquid in two dimension[1, 2]. In the
Kitaev model, the interactions are Ising type,Siγ Sjγ , and the spin component γ = x, y, z isdetermined from the direction to the neighboring site. The ground state is known to be agapless spin liquid state, in which the nature
is described by Majorana fermions[1]. When
we apply a magnetic ﬁeld to the Kitaev system, the excitation spectrum described by themobile Majorana fermions opens a gap, andthe ground state changes to a topological spin
liquid, where a half-integer thermal Hall conductivity emerges in the low-temperature limit[1]. In the recent experiment on α-RuCl3 under a moderate magnetic ﬁeld, a similar halfinteger thermal Hall conductivity was observed
at a ﬁnite temperature [3], although its groundstate seems to be a magnetically ordered state
at zero magnetic ﬁeld due to oﬀ-diagonal and(long-range) Heisenberg interactions.
In this year’s project, we investigated a ﬁnite
temperature properties of the Kitaev modelwith oﬀ-diagonal interactions, in paticular concerning the possible thermal Hall conductivity
at a ﬁnite temperature. The model Hamiltonian is given asH=∑γ∈x,y,zHγ − ⃗h ·

∑
i

⃗i ,
S

(1)

Figure 1: A typical lattice setup and a mappting to a one-dimensional matrix product operator.
where for γ = z,∑
Hz =[KSiz Sjz + Γ(Six Sjy + Siy Sjx )⟨i,j⟩z+ Γ′ (Siz (Sjx + Sjy ) + (Six + Siy )Sjz )].
(2)
In the cases of γ = x, y, we consider similarinteractions with cyclic rotation of x, y, z components. To numerically calculate the thermal
Hall conductivities at a ﬁnite temperature, we
consider several ﬁnite-size clusters with open
edges and represent their density matrix as amatrix product operator (MPO), as shown in
Fig. 1.
The MPO representing a density matrix at agiven temperature was obtained by the exponential tensor renormalization grope (XTRG)
algorith [4], where we calculate the density matrix at an inverse temperature β, ρ(β), throughthe relationship ρ(β) = ρ(β/2)ρ(β/2) with theinitial condition ρ(β0 ) = exp(−β0 H) ≃ 1−β0 H

210

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

for the suﬃciently small β0 . Thus, when we
have an MPO representation of the Hamiltonian, a stadard compression algorithm for thetensor network can be used. When the bonddimension of the MPO is D, both of the computation cost and the memory consumption of
XTRG algorithm scale O(D4 ).
By such an MPO representation of the density matrix, we have successfully calculated thethermal Hall conductivity for various magnetic
ﬁelds and temperatures up to N = 72 spins(see Fig. 1) with a typical bond-dimension
D = 500. Our calculation showed that thethermal Hall conductivity typically has a peak
as a function of the temperature, and it overshoots the half quantized value expected in thezero-temperature limit. Such an overshooting
is consistent with the experimental observation[3].
We also investigated Γ and Γ′ dependenceof the thermal Hall conductivity. We foundthat depending on the sign of Γ and Γ′ , thethermal Hall conductivity is largely modiﬁed
from that of the pure Kitaev model. Some ofthem could be explained by the increase of thegap, previously calculated through the perturbation theory [5], while overall ﬁnite temperature behaviors might not be explained only by
Majorana fermion pictures.
A part of this work has been done in collaboration with J. Nasu, T. Misawa, and Y. Motome.

[5] D.
Takikawa
andS.
Fujimoto,
Phys. Rev. B 102 (2019) 174414.

References[1] A. Kitaev, Ann. Phys. 321 (2006) 2.
[2] Y.
MotomeandJ.
Nasu,
J. Phys. Soc. Jpn. 89 (2020) 012002.
[3] Y. Kasahara, T. Ohnishi, Y. Mizukami, etal., Nature 559 (2018) 227.
[4] H. Li, D.-W. Qu, H.-K. Zhang, et al.
Phys. Rev. Research 2 (2020) 043015.

211

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Membrane shape deformation by binding ofcurvature-inducing proteins
Hiroshi NOGUCHI
Institute for Solid State Physics, University of Tokyo

In living cells, biomembrane shapes are controlled by curvature-inducing proteins. We
have studied the binding of these proteins using mean-field theories and compared their results with simulation results. Clathrin andcoat protein complexes bend membranes in alaterally isotropic manner and generate spherical buds. In contrast, Bin/Amphiphysin/Rvs(BAR) superfamily proteins bend the membrane anisotropically and generate cylindricalmembrane tubes. The former and latter proteins can be modeled as laterally isotropic objects and anisotropic objects of a banana or
crescent shape, respectively.
For isotropic proteins, we derived the freeenergy including the Gaussian curvature andarea expansion by the protein insertion [1].
Then, we investigated the formation of spherical buds [1] and binding onto a tethered vesicle [2]. A narrow membrane tube (tether) is
elongated from a spherical vesicle by an external force imposed by a micropipette and optical tweezers. A first-order transition occurs between a small number of large buds and a large
number of small buds with increasing chemical
potential of protein binding [1]. For the tethered vesicle, interestingly, a first-order transition occurs twice between low and high protein
densities in the tube. The force-dependence
curves of the protein density in the membrane tube and the tube curvature are reflection symmetric and point symmetric, respectively, from the force point, in which the tube
curvature matches the protein (sensing) curvature [2]. This theory reproduces the meshless
membrane simulation results of the homogeneous phases very well. In addition, beadednecklace-like tubes with microphase separation
are formed in the simulation.

212

For anisotropic proteins, an orientationaldependent excluded volume interaction is included in the free energy. We studied binding onto membrane tubes [3]. The proteins
exhibit a second-order or first-order nematictransition with increasing protein density forintermediate and small radii of the membrane
tube, respectively. The tube curvatures for the
maximum protein binding (sensing) and orientational order are differently varied by theprotein density and rigidity. As the external
force along with the tube axis increases, a firstorder transition from a large tube radius withlow protein density to a small radius with highdensity occurs once, and subsequently, the protein orientation tilts to the tube-axis direction.
The density-dependent sensing curvature andthe number of transitions are characteristics
due to the anisotropic bending energy. Eachisotropic protein has a constant sensing curvature. This density-dependent sensing curvature has been measured in the experimentof BAR proteins. This theory quantitatively
reproduces the results of meshless membrane
simulation for short proteins. For long proteins, the formation of protein clusters generates a quantitative deviation from the theory,
although qualitative agreements still hold.

References[1] H. Noguchi, Phys. Rev. E 104, 014410(2021).
[2] H. Noguchi, Soft Matter 17, 10469 (2021).
[3] H.
Noguchi,C.
Tozzi,
M. Arroyo,
Soft Matter
DOI:10.1039/D2SM00274D.

and(2022)

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of Thermal Functional Materials Based on Firstprinciples Simulations
Junichiro SHIOMI
Department of Mechanical Engineering,
The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan
We have studied thermal functional

properties and the compositional dependencematerials using massive parallel computerof ternary alloys were studied by first-principle

system. This year, we focused on thecalculation. Fig. 1 shows the predicted energy

thermoelectric performance of a ternary alloy

by cluster expansion and ZT of alloy of asystem and a nanostructured multiphasecomposition. For the multiphase material, thematerial.

grain size dependence of thermoelectric

The main content of these two studies isproperties was studied by first-principle

briefly introduced as below. For the ternary

calculation for two phases to enhancealloys, lattice structures were predicted bythermoelectric performance by nanostructure

Monte Carlo simulation, then thermoelectricengineering. Fig. 2 shows the nanostructured

Fig. 1: (a) Formation energies from cluster

Fig. 2: (a) Thermal conductivity versus grain

expansion; (b) ZT of one of the alloys.

size; (b) ZT of a nanostructured material.

213

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

thermal conductivity at room temperature andPhys.-Condens. Mat. 26 (2014) 225402.

ZT of a nanostructured phase.

[4] G. Kresse and J. Furthmüller: Comp. Mater.
Sci. 6 (1996) 15.

To conduct these studies, the usage ofsupercomputer system was described asfollowing. ICET package [1] was employed to
predict lattice structures through performing
Monte Carlo simulation and cluster expansion
based on element substitution and formationenergy prediction. BoltzTrap2 package [2] wascarried out to calculate electrical transport
properties by solving semiclassical linearized
Boltzmann transport equation. ALAMODE
package [3] was used to fit interatomic force
constants by atomic displacements and forcesfrom first-principle calculation, as well as
calculate phonon thermal conductivity byrelaxation time approximation method. VASP
[4] was carried out to perform first-principle
calculation

forformationenergy,band

structure and atomic forces. By running ourown python script, thermoelectric properties
were

calculated

fromphononthermalconductivity and electrical properties.

References[1] M. Ångqvist, W. A. Muñoz, J. M. Rahm, E.
Fransson, C. Durniak, P. Rozyczko, T. H. Rod,and P. Erhart: Adv. Theor. Simul. 2 (2019)
1900015.
[2] G. K. H. Madsen, J. Carrete, and M. J.
Verstraete: Comput. Phys. Commun. 231(2018) 140.
[3] T. Tadano, Y. Gohda, and S. Tsuneyuki: J.

214

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Feasibility study of Kitaev quantum spin liquid byfunctional renormalization approach
Kiyu FUKUI and Yusuke KATO
Department of Applied Physics, University of Tokyo, Bunkyo, Tokyo 113-8656
Department of Basic Science, University of Tokyo, Meguro, Tokyo 153-8902

The Kitaev model is an S = 1/2 quantum spin model defined on the honeycomb lattice [1]. In spite of its strong frustration due
to the bond-dependent interaction, this modelis exactly solvable, and its ground state is aquantum spin liquid state. Here we address
the feasibility of the Kitaev quantum spin liquid (KQSL) for two extensions of the model,
by using the pseudofermion functional renormalization group (PFFRG) method [2].
The first one is for ultracold polar molecules
trapped in an optical lattice.
While experimentally accessible implementation of
the Kitaev-type interaction was proposed in2013 [3], the stability of the KQSL has not been
investigated so far. In this proposal, the bonddependent anisotropic interactions are mimicked by angle-dependent dipole interactions
between molecules. However, the interactions
are long ranged with a spatial decay of r−3 ,where r is the distance between the molecules,
it is left as an open question whether the
KQSL can survive against such long-range interactions. We studied the ground state ofa quantum spin model with long-range angledependent Kitaev-type interactions, which was
proposed as an implementation of the Kitaev
model in ultracold polar molecules, by using
the PFFRG method. We clarified that, regardless of the spatial anisotropy of the interactions, the ground state is magnetically orderedin both FM and AFM cases: we found magnetic instabilities toward the FM and zigzag
ordered states in the FM and AFM models, re-215

spectively. By calculation of the anisotropy parameter dependence of the critical cutoﬀ scale,
we concluded that the system is most frustrated and closest to the realization of the
KQSL when the interaction is isotropic in bothcases. Our findings indicate that the QSL
ground state arising from the nearest-neighborbond-dependent anisotropic interactions in the
Kitaev model is destroyed by the long-range interactions. By varying the range of the interactions, we unraveled that the KQSL is unstableeven for the third-neighbor interactions. Thisis the first time that the stability of the KQSL
within the above proposal has been revealed.
The other is the extension to higher-spin systems. Although the Kitaev model was originally introduced for the S = 1/2 moments, its
higher-spin generalization has also attracted
attention. While candidate materials with S =1 [4] and 3/2 [5] have begun to be proposed inrecent years, the stability of the KQSL has notbeen systematically clarified for general spin
S in the presence of non-Kitaev interactions,which are inevitably present in the candidate
materials. In this study, we present our numerical results on the ground state of higher-spin
generalization of the Kitaev model including
the Heisenberg interaction, the spin-S KitaevHeisenberg model, which we consider to be oneof the minimal models for the higher-spin candidate materials, by using an extension of thePFFRG method [6]. Performing the calculations for the models with S = 1, 3/2, 2, 5/2,
and 50 in addition to S = 1/2, we elucidate

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

the ground-state phase diagram by systematically changing the ratio between the Kitaev
and Heisenberg interactions and S. We found
four magnetically ordered phases: Néel AFM,
zigzag AFM, FM, and stripy AFM for all S,
and the phase boundaries between these ordered phases are consistent with the previous
studies for S = 1/2, 1, and ∞. Our results
indicated that the ground state is short-range
QSL for arbitrary S at the ferromagnetic andantiferromagnetic Kitaev points. It is consistent with an analytical result in the previous
study [7]. We clarified that the QSL regions
near these Kitaev points are quickly shrunk
by increasing S, namely, the KQSL is fragile
against the Heisenberg interaction for S ≥ 2.
However, we find the KQSL remains stable forS ≤ 3/2 around the both Kitaev points. Ourfindings will provide the search and design ofthe candidate materials with S > 1/2.

References[1] A. Kitaev, Ann. Phys. 321, 2 (2006).
[2] J. Reuther and P. Wölfle, Phys. Rev. B
81, 144410 (2010).
[3] S. R. Manmana et al., Phys. Rev. B 87,
081106 (2013); A. V. Gorshkov, K. R.
Hazzard, and A. M. Rey, Mol. Phys. 111,
1908 (2013).
[4] P. P. Stavropoulos, D. Pereira, and H.-Y.
Kee, Phys. Rev. Lett. 123, 037203 (2019);
A. M. Samarakoon et al., Phys. Rev. B
104, 184415 (2021).
[5] C. Xu et al., npj Comput. Mater. 4, 57(2018); M. Kim et al., Nat. Electron. 2,457 (2019); I. Lee et al., Phys. Rev. Lett.
124, 017201 (2020); C. Xu et al., ibidem,
087205 (2020).
[6] M. L. Baez and J. Reuther, Phys. Rev. B
96, 045144 (2017).

216[7] G. Baskaran, D. Sen, and R. Shankar,
Phys. Rev. B 78, 115116 (2008).

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Quantum effects on chiral magnets
SOHEI KODAMA and YUSUKE KATO
Department of Basic Science, the University of Tokyo, Tokyo 153-8902, Japan,

We consider the ground state of quantum

complementary to earlier studies on quantum

spin chain of monoaxial chiral ferromagnet.

effects on Ising domain wall [2] and skyrmions

The Hamiltonian is given by[3] based on semiclassical treatment of̂𝑖 ∙ ̂
̂𝑖 × ̂
𝐻 = ∑𝑖 [−𝐽𝑺
𝑺𝑖+1 − 𝐷(𝑺𝑺𝑖+1 )𝑦 −quantum spin taking account of the Berry phase2𝐻𝑆̂𝑖𝑧 + 𝐾(𝑆̂𝑖𝑦 ) ],term.

where, J, D, H, and K, respectively, denoteexchange interaction, Dzyaloshinskii-Moriya(DM)interaction,themagnetic

field

perpendicular to the chiral axis (y -axis) andsingle ion anisotropy.
The magnetization curves for finite-sized
systems obtained by exact diagonalization are
distinctly different between half-odd-integer
and integer spins; The level crossings occur for
S=1/2,3/2, accompanied by  shift of the crystal
momentum k while the magnetization process
is continuous and k is always zero for S=1,2.
These behaviors are commonly observed for

References

arbitrary values of J/D. We argue that in the[1] S. Kodama, A. Tanaka, and Y. Kato, in

limit J=0 with D finite, single soliton has the

preparation.

minimum energy for k= (k=0) for half-odd[2] H. B. Braun, Adv. Phys. 61, 1 (2012).

integer (integer) S, based on the Perron-[3] R. Takashima, H. Ishizuka, and L. Balents,

Frobenius theorem within the subspace spanned

Phys. Rev. B 94, 134415 (2016).

by a single soliton basis. Our approach [1] is217

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

New scaling analysis for graph percolations
Y. Ozeki and K. Hagiwara v
Graduate School of Informatics and Engineering, The University of Electro-Communications

We investigate the transition point and the critical exponent β for graph percolations. A new sizeindependent scaling analysis is proposed, which enables us to analyze numerical data without finitesize effects. This means that the results are equivalent to those in the infinite system. Such a scaling analysis has been applied as dynamical scaling
analysis in the nonequilibrium relaxation method[1] for phase transitions and critical phenomena.
In graph percolations, a number of vertices areprepared instead of a lattice. Each edge between
two of these vertices is considered to be connected
or not. In the Erdős-Rényi (ER) model, a classical graph percolation, a new edge is connected to agraph at random. The probability of a vertex belonging to the infinite cluster, which is denoted by
P (r), is recognized as the order parameter, wherer is the average number of edges per vertex. The
function P (r) can be written as [2]X
P (r) ≡ 1 −
sns ,
(1)
s

where ns is the number of clusters with size s
divided by N . P (r) is expected to behave algebraically as
P (r) = a|r − rc |β ,(2)where β is referred to as a critical exponent. In thepresent study, we define a new function P (x, r) byextending P (r),and introduce a new parameter x
representing the maximum cluster size:X
P (x, r) ≡ 1 −
sns .
(3)
s<x

This function P (x, r) represents the probability
that a randomly selected vertex belongs to a cluster
greater than or equal to x. We expect the following
asymptotic (x → ∞) behaviors for every r case:(r < rc ) A exp(−x/ξ)P (x, r) ∼x−λP
(r = rc ) (4)
p∞ + A′ exp(−x/ξ) (r > rc )where we introduce a function ξ depending on ras ξ = ξ(r) and exponent λP . The asymptotic
behavior of ξ is expected to beξ(t) = b|r − rc |−ν ,

(5)

218

where we define a new exponent ν satisfying therelation
λP = β/ν.

(6)

In the asymptotic regime in r ∼ rc , P (x, r) is
expected to satisfy the following scaling form:
P (x, r) = ξ −λP Ψ(x/ξ).

(7)

The transition point rc and critical exponent β canbe estimated from the behavior of P (x, t). Appropriate values of rc and β as well as a, b, ν in Eqs.
(2) and (5) should be chosen such that ξ λP P (x, t)
is fitted as a function of x/ξ(r) on a scaling function Ψ. In order to carry out such a scaling plot
efficiently, we apply the method introduced for the
dynamical scaling, in which the Bayesian inference
and the kernel method are used [3].
Here, we demonstrate the above scaling analysis
to the ER model, for which the analytic solution is
known; rc = 1/2, β = 1. For precise analysis, weneed to check the size dependence. We have foundthat, for x ≤ 3000, no size dependence appears in
the data for the system with N = 1 × 108 or larger.
The simulation is performed using these parameters, and 2240 independent samples were used for
averaging. The results for P (x, r) are plotted inFig. 3, and the resultant scaling plot is shownin Fig. 4. The transition points and the critical exponent are evaluated as rc = 0.49978(7) and
β = 1.010(9), respectively, where the error bars are
estimated by the bootstrap method [3]. The deviations from the analytic values rc = 1/2, β = 1
are approximately 0.044% and 1.0%, respectively,
demonstrating that the present analysis is reliable.
We apply the above scaling method to thedCDGM model [4], in which a vertex is selectedfrom randomly chosen m vertices so that the size ofthe connected cluster is smallest and the new edge
connects two vertices selected twice with the aforementioned process; the integer value m is fixed anddistinguishes the model as the dCDGM(m) model.
We investigate the dCDGM(m = 2) model. The
same analysis was performed. It is confirmed thatthe simulation for the system with N = 1 × 108
to x ≤ 3000 is sufficiently large. The simulation is
performed using these parameters, and 4480 inde-

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo
0.1

0.5
0.4
0.3
0.2
0.1

P(x,r)

P(x,r)

r = 0.480
r = 0.482
r = 0.484
r = 0.486

r = 0.9197

r = 0.488
r = 0.490

r = 0.9202

r = 0.492
r = 0.494

r = 0.9212
r = 0.9217

r = 0.496
r = 0.498

r = 0.9222

r = 0.9207

r = 0.9227

100

1000

1000

x

x

Figure 3: Results of P (x, r) for the dCDGM(2)model.

Figure 1: Results of P (x, r) for the ER model.
100

10

10

Y = ξλPP(x,r)

Y = ξλPP(x,r)

1

1

0.1

0.1

0.01

0.01
0.001

0.01

0.1

0.001

1

1

X = x/ξ

X = x/ξ

Figure 2: Scaling plot of P (x, r) for the ER model.
pendent samples are used for averaging. The transition points and the critical exponent are evaluated as rc = 0.923211(5) and β = 0.056(1), respectively, which are consistent with those of Da Costa(rc = 0.923207509297(2) and β = 0.05557108(1))[4].

References[1] Y. Ozeki and N. Ito, J. Phys.: Math. Theor.
40 R149 (2007).
[2] D. Stauffer and A. Aharony, “Introduction topercolation theory”, (Taylor & Francis,1994)[3] Y. Echinaka and Y. Ozeki, Phys. Rev. E94
043312 (2016).

219

Figure 4: Scaling plot of P (x, r) for the dCDGM(2)model.
[4] R. A. Da Costa, S. N.Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Phys. Rev. E89
042148 (2014); Phys. Rev. E90 022145 (2014).

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Computational design of proteins useful for medical andindustrial applications
Masataka YOSHIMURA1, Sairi MATSUMOTO1, Mizuki TERANISHI1,
Hirotaro SHIMAMURA2, Rina AOYAMA1, Koji OOKA2, Shino MASUOKA1,
Shunji SUETAKA1, Nao SATO1, Yuuki HAYASHI1, and Munehito ARAI1,2
1

Department of Life Sciences, Graduate School of Arts and Sciences, and2

Department of Physics, Graduate School of Science,

The University of Tokyo, Komaba, Meguro, Tokyo 153-8902

ProteinsasSevere acute respiratory syndrome (SARS)

therapeutics for various diseases and as enzymes

coronavirus 2 (SARS-CoV-2) is an emerging

for industrial production of useful substances.

virus that causes the pandemic of the

Recently, theoretical design of proteins has

coronavirus disease 2019 (COVID-19). Since

attracted much attention; however, it is still

the viral infection is caused by the binding of the

difficult to theoretically design useful proteins.

receptor binding domain (RBD) of the spike

To solve this problem, we have designed various

proteinuseful proteins using the Rosetta 3.13 suite [1]angiotensin-converting enzyme 2 (ACE2) [3],and have experimentally checked the validity of

we computationally designed a single-chain

the computational design.

variable fragment (scFv) of an antibody against

Magnets

have

are

been

widelyoptogenetic

used

tools

of

SARS-CoV-2

to

the

human

for

the SARS-CoV-2 RBD using the scFv against

manipulating protein-protein interactions (PPIs)

the SARS-CoV RBD as a template. Experiments[2]. They consist of pMag and nMag, whichshowed that the designed antibody has a highheterodimerize upon exposure to blue light.

affinity to SARS-CoV-2 RBD comparable to

However, improvement of their binding affinitythat of the antibody medicines for SARS-CoV-2.
Formation

has been demanded. Here we computationallyofaternary

complexbydesigned the Magnets mutants with higher

interleukin-33 (IL-33), interleukin-1 receptor

pMag/nMag affinity than the original ones byaccessary protein (IL-1RAcP), and the ST2

theoreticalmutagenesis

Rosetta.

receptor of type 2 innate lymphoid cells isExperiments

confirmed

mutants

responsible for allergic asthma [4]. To develop aenhanced the dimer affinity. Thus, these

therapeutic agent for the disease, we are trying

Magnets mutants may be useful for in vivo

to computationally design a protein that tightly

manipulation of PPIs.

binds ST2 but does not bind IL-1RAcP using IL-

using
that

the

220

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

33 as a template. We have finished designing aand product-bound form of ADO. We found that

protein that tightly binds to ST2. Further design

the product has higher flexibility than theof the IL-33 mutant that abolishes the binding

substrate inside the protein molecule, thereby

with IL-1RAcP is under way.

facilitating the product release.

The interaction between the programmed cell

Finally, to predict the folding processes ofdeath protein 1 (PD-1) and the programmed

proteins, we calculated free energy landscapes

death-ligandinof multi-domain proteins using the Wako-Saitô-suppressing T-cell inflammatory activity [5]. To

Muñoz-Eaton model, which is an Ising-like,develop an inhibitor of the T-cell activity, we

structure-based statistical mechanical model [8].

computationally designed the mutants of a PD-

By introducing modifications to the model, we

L1 fragment that tightly bind PD-1. Experiments

succeeded in obtaining the folding pathways andconfirmed that some mutants have improved

intermediates that are fully consistent withaffinity with PD-1. We are trying to further

experimental results. Thus, our method may

improve the affinity by multiple mutations.

pave

1

(PD-L1)isimportant

Alkane biosynthesis has attracted much

the

way

for

solvingthefoldingmechanisms of multi-domain proteins that are

attention as a promising way of producing

abundant in proteomes.

carbon-neutral bioenergy. A key enzyme forcyanobacterial alkane biosynthesis is aldehyde

References

deformylating oxygenase (ADO) [6]. We[1] J. K. Leman, et al.: Nat Methods, 17 (2020)

computationally designed ~10 mutants of ADO

665-680.

that are expected to have high activity. The[2] F. Kawano, et al.: Nat Commun. 6 (2015)

experimental test of the ADO activity is ongoing.

6256.

Understanding protein dynamics is essential[3] J. Shang, et al.: Nature, 581 (2020) 221-224.

for improving catalytic activity of enzymes. We[4] X. Liu, et al.: Proc Natl Acad Sci USA. 110

performed molecular dynamics simulations of(2013) 14918-14923.

ADO using the Gromacs 2021.4 program[5] C. N. Bryan, et al.: Proc Natl Acad Sci USA.

package [7]. An initial structure was constructed

118 (2021) e2102164118.

using the AmberTools21 package. The force[6] M. Arai, et al.: Adv Exp Med Biol. 1080

fields for the substrate (aldehyde) and the(2018) 119-154.

product[7] M. J. Abraham, et al.: SoftwareX, 1-2 (2015)(alkane)were

obtainedusing

Antechamber module. The simulations were

19-25.

performed for ~800 ns each for the apo form,[8] M. Sasai, et al.: Biophys Physicobiol. 13

holo (iron-bound) form, substrate-bound form,(2016) 281-293.

221

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Topological order and quantum operation inquantum many-body systems
Synge TODO
Department of Physics, University of Tokyo, Tokyo, 113-0033
Institute for Solid State Physics, University of Tokyo, Kashiwa, 277-8581

We developed novel numerical methods by
combining quantum Monte Carlo methods,
tensor-network algorithms, and other optimization techniques and investigated topological quantum phase transitions in strongly correlated many-body systems and optimizationof quantum operations in quantum computing.
Phase transition in quantum dimer model:
Based on the idea of stochastic series expansion, we implemented a Monte Carlo algorithm for investigating the phase transition of the quantum dimer model in an efﬁcient way to simulate with shorter CPU
time and extended it to simulation on larger
Hilbert space, including monomer-dimer andmonomer-monomer interaction. We obtained
the phase-transition temperature between thecritical and columnar phases by diﬀerent order parameters by simulations at ﬁnite temperatures. We found it vanishes at around
Rohksar-Kivelson (RK) point, while the classical limit merges smoothly to the value obtained by the classical Monte Carlo.
Tensor-network Markov-chain Monte Carlo:
We developed a novel quantum-inspired
method that combines the tensor-network representation of weight function and the sampling scheme based on the Markov-chain
Monte Carlo method. We can remove thesystematic bias due to the ﬁniteness of thebond dimension in tensor network representation from the Markov-chain sampling. Furthermore, the statistical error of the sampling
reduces exponentially as increasing bond di-mension, and we can avoid the negative-sign
problem in quantum lattice models by adopting a high-precision tensor network renormalization scheme.
Many-body localization in random spin chain:
We study the many-body localization of therandom-ﬁeld Heisenberg chain using the nested
shift-invert Lanczos method with an iterative
linear solver. We use the minimum residual
method (MINRES) inside each Lanczos iteration. As a probe of many-body localization transition, we propose a unitary operator
called the twist operator, which has a straightforward interpretation in the real space. We
estimate the transition point of the randomﬁeld Heisenberg chain precisely [1].
Decomposition of multi-qubit gate: We obtaineﬃcient decompositions of CCZ and CCCZ
gates, typical multi-qubit gates, under several qubit connectivities, using the sequential
quantum-circuit optimization algorithm. We
can construct the CCZ gate with only four
CZ-depth when the qubit is square-shaped,
including one auxiliary qubit. In T-shaped
qubit connectivity, which has no closed loop,
we can decompose the CCCZ gate with 17 CZ
gates [2].

References[1] T. Kutsuzawa and S. Todo, preprint:
arXiv:2203.09732.
[2] K. M. Nakanishi, T. Satoh and S. Todo,
preprint: arXiv:2109.13223.

222

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

O(N) algorithm for the Monte Carlo simulation of
the Kitaev model
Masahiko G. YAMADA1
Yutaka AKAGI2
Masafumi UDAGAWA3
1
Department of Materials Engineering Science, Osaka University
Machikaneyama-cho, Toyonaka, Osaka 560-8531
2
Department of Physics, University of Tokyo
Hongo, Bunkyo-ku, Tokyo 113-0033
3
Department of Physics, Gakushuin University
Mejiro, Toshima-ku, Tokyo 171-8588

The thermodynamics of the Kitaev model isof great interest, especially after the characteristic specific heat behavior called a double
peak has been discovered by the Monte Carlosimulation [1].
We extend their simulation using a newO(N ) calculation method for the Kitaev
model Monte Carlo [2]. We newly employed
the infinite product expansion (iPE) method
instead of the previous Trotter decomposition
method. By this iPE method, we succeededin reducing the calculation cost of the Kitaev
model drastically from O(N 4 ) to O(N ). Asa benchmark, we did a simulation for the
Kitaev model on the honeycomb lattice andcomputed the heat capacity and its doublepeak structure. Using the new algorithm anda supermassive parallelization in the ISSP
supercomputer, we succeeded in reproducing
the results in [1] within the errorbar (seeFig. 1). Though currently the calculation
is limited up to the 54-site cluster with anopen boundary, we will eventually extend
this to the large-scale Monte Carlo simulation
up to O(1000)-site simulations. If we also
extend the calculation to three dimensions,
we can potentially discuss the thermodynamic
properties of the vaporization transition in

the three-dimensional Kitaev model, which
was suggested in Ref. [1].

Figure 1: Specific heat data for the N = 54
cluster simulation.

References[1] J. Nasu, M. Udagawa, and Y. Motome:
Phys. Rev. Lett. 113 (2014) 197205.
[2] M. G. Yamada, Y. Akagi, and M. Udagawa: to appear.

223

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoDMRG algorithm with a full SU(N) implementation
Masahiko G. YAMADA
Department of Materials Engineering Science, Osaka University
Machikaneyama-cho, Toyonaka, Osaka 560-8531

The density matrix renormalization group(DMRG) is one of the most powerful numerical methods for strongly correlated condensed
matter systems. Following the previous work,
we extended DMRG to the case with the
SU(N ) symmetry with N > 2, even for twodimensional systems. As a killer application,
we simulated the ground state of the SU(4)Heisenberg model on the honeycomb lattice,which can potentially be realized in cold
atomic systems and solid state systems like
α-ZrCl3 [2]. We keep up to 12800 SU(4) statesequivalent to more than a million U(1) states.
This supermassive DMRG simulation reveals
the quantum spin-orbital liquid ground state,
which has dubiously been expected for morethan a decade. The methodology developed
here can be extended to any classical Liegroups, paving the way to a next-generation
DMRG with a full symmetry implementation [3].

References[1] P. Nataf, and F. Mila: Phys. Rev. B 97(2018) 134420.
[2] M. G. Yamada, M. Oshikawa, and G.
Jackeli: Phys. Rev. Lett. 121 (2018)
097201.
[3] M. G. Yamada, K. Penc, and F. Pollmann: to appear.

224

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Efficient Sampling Simulation of
the Soft Modes Significantly Contribute to Protein Properties
K. TAKEMURA, D. TRAN, M.M. SOBEH, Y. MIYAZAWA, R. KIUCHI, T.N.
WIJAYA, T. OGAWA, Y. TAIRA, R. MISU, R. Osawa, M. Yoshioka, H. NAKAYA and
A. KITAO
School of Life Science and Technology, Tokyo Institute of Technology
Ookayama, Meguro, Tokyo 152-8550
Previously, we developed parallel cascadetransitions from the bound to unboundselection molecular dynamics (PaCS-MD)

states. Finally, we repeated the cycles until

as an enhanced sampling strategy that uses

d = 70 Å to complete the dissociation, as

cycleswe can see in the PaCS-MD flowchart inofmultiple

independentMD

Fig. 1

simulations done in parallel to improve thechance of biologically rare events occurring
without external perturbation [1]. PaCSMD

consistsofcyclesofseveralindependent parallel short all-atom MD
simulations followed by selecting initialstructures for the next cycle according to a
specified quantity. We conducted thedissociation simulation of the p53 DNA
binding domain (p53DNA) from DNA [2].
We used the inter-center of mass distance(inter-COM distance, d) between p53-DBD

Fig. 1 The flowchart of PaCS-MD

and DNA as a quantity for ranking thesnapshots generated in each cycle. By

We successfully generated 75 different

repeating a series of cycles for the selecteddissociation pathways of p53-DBD from

top-ranked snapshots (top 10 snapshots),DNA. We used the COM positions of the

dissociation PaCS-MD generates structures

p53-DBD interface residues relative to thosewith larger inter-COM distances than those

of

found

which

pathways, as shown in Fig. 2. Inspection ofsignificantly enhances the probability ofthe dissociation pathways indicates that the

in

the

previous

cycle,

225

DNA tovisualize

thedissociation

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

sampled space formed a cone-like shapebinding free energy (ΔG°) for this system

around the DNA. Around 93% of thepredicted at 11.8 kcal/ mol. This value is very

sampling pathways (70 pathways) dissociatedclose to the binding free energy of p53-DBD

along the +X and −Y directions (namely, the(residues 94−312) with the consensus DNA−Y directions), while the other pathways

sequence of −11.1 kcal/ mol measured by

moved along +X and +Y directions, whichisothermal titration calorimetry, suggesting

only occupy 7% (5 pathways), hereafterthat the calculated free energy profile iscalled the +Y directions.

reasonable.

Fig. 2 Dissociation pathways of 75 PaCS-

Fig. 3 Free energy profile mapped onto the

MD trials of p53-DBD from DNA.

XY-plane

Using the Markov state model (MSM), We
obtained the free energy profile of p53-DBD
dissociation from DNA and showed the
projections onto the XY planes, as shown in
Fig. 3. The global minimum of this profile
represents the bound state. As discussed
above, dissociation mainly (93%) occurredalong the −Y directions on the XY-plane, andFig.4 PMF as a function of X coordinate.

other dissociations (7%) occurred along the+Y directions. As we can see in Figure 4,

References

during the dissociation process, the PMF[1] R. Harada and A. Kitao. J Chem Phys 139,

increased at a higher rate in the bound state to

035103 (2013).

achieve convergence (became flat) in the[2] M.M. Sobeh and A. Kitao J. Chem. Inf.

unbound region (d ≥ 45 Å). We calculated theModel, 62, 1294–1307 (2022).

226

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Molecular dynamics simulations for assembly anddisassembly of protein aggregates
Hisashi Okumura
Exploratory Research Center on Life and Living Systems,
Institute for Molecular Science, Okazaki, Aichi 444-8585

Proteins are normally folded correctly andthe RPM and RSPM into LAMMPS [1].

perform functions that are necessary to sustain

LAMMPS is an open-source classical MD

life. However, when the concentration ofsimulation package that can be applied fromproteins increases due to aging or other reasons,material to biomolecular systems. We used thethey can aggregate and cause a variety ofsupercomputer at the Supercomputer Center,diseases. For example, Alzheimer’s disease,

the Institute for Solid State Physics, thewhich is one type of dementia, is caused by

University of Tokyo to perform benchmark

amyloid-β (Aβ) peptides, which aggregate into

calculations for this program.

spherical

oligomersoramyloidfibrils.

In addition, continuing from the last year,

Molecular dynamics (MD) is nowadays awe performed non-equilibrium MD simulations

standard tool to investigate these systems.

of the destruction process of amyloid fibrils by

However, once a conformation gets trapped in aan infrared laser. We first revealed the

local-minimum free-energy state, it is hard to

disruption process of Aβ amyloid fibrils [2]. We

escape from there within the time scale of theare now performing MD simulations of poly-

simulation.

alanine amyloid fibrils. We found that poly-

The replica-exchange method (REM), isalanine amyloid fibril is less easily destroyed

widely used to overcome this difficulty because

by infrared laser than Aβ amyloid fibrils. Weof its convenience. Recently, we proposed thewill try to clarify this difference.

replica-permutation method (RPM) and thereplica sub-permutation method (RSPM) to

References

improve the transition ratio of replicas in the[1] M. Yamauchi, G. La Penna, S. G. Itoh, andtemperature space. However, the RPM andH. Okumura, Comput. Phys. Commun. 276,

RSPM are not available for general users

108362 (2022).

because these methods are implemented only in[2] H. Okumura, S. G. Itoh, K. Nakamura, andour own molecular simulation programs and

T. Kawasaki, J. Phys. Chem. B 125, 4964–4976

not in open-source packages. We implemented(2021).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Critical phenomena in novel Anderson transitions
TOMI OHTSUKI1
TOHRU KAWARABAYASHI2
KEITH SLEVIN3
1) Dept. Phys., Sophia University, Chiyoda-ku, Tokyo 102-8554, Japan
2) Dept. Phys., Toho University, Miyama 2-2-1, Funabashi 274-8510, Japan
3) Dept. Phys., Osaka University, Toyonaka, Osaka 560-0043, Japan

Random quantum systems have no translational/rotational symmetries, but can havetime reversal, spin rotation, chiral andparticle-hole symmetries. According to thesesymmetries, the random quantum systems areclassiﬁed to 10 symmetry classes. The threeof them, the so-called Wigner-Dyson classes,
were discovered in 1950’s and 1960’s and havebeen well studied. Recent experimental discoveries of topological insulators and Weyl
semimetal (WSM) have inspired extensive research of random systems other than WignerDyson classes. These 7 new classes containdiscrete chiral or particle-hole symmetries.
Here we have introduced a set of Hamiltonians for these new classes, where the high accuracy numerical studies of the three dimensional Anderson transition is possible [1]. We
have also studied the novel two dimensional
systems, corresponding to a topological superconductor, both analytically [2] and numerically [3]. We especially focused on the criticalbehaviors near the tricritical point, where ordinary insulator, topological insulator and thermal metal phases meet.
When we introduce the non-Hermiticity
to the Hamiltonian, the classiﬁcation is extended and the systems are categorized to 38
classes. We have shown that adding the nonHermiticity changes the universality class [4],and show that the transfer matrix method
widely used in the Anderson transitions also
works for non-Hermitian systems [5]. We havefurther shown that the critical behaviors of 38
classes are mapped to universality classes forthe 10 Hermitian symmetry classes [6].
Machine learning is now widely used in con-densed matter physics. We have studied thevarious quantum phase transitions by analyzing the wave functions via convolutional neural network (CNN). The method is adopted
to classify wave functions obtained via density
functional theory, which is applied to study themetal-insulator transitions in doped semiconductors [7]. In addition, using the long-shortterm memory network (LSTM), we have analyzed the time series of diﬀusion motion ofquantum particles in kicked rotors. The model
is equivalent to the Anderson model, where thedimensions of the Anderson transition is controlled by the modulation of the kick strength.
We have drawn the phase diagram of higher dimensional Anderson transitions by LSTM [8].

References
1. T. Wang, T. Ohtsuki, and R. Shindou, PhysicalReview B 104, 014206 (2021).
2. Z. Pan, T. Wang, T. Ohtsuki, and R. Shindou,,
Physical Review B 104, 174205 (2021).
3. T. Wang, Z. Pan, T. Ohtsuki, I.A. Gruzberg,
and R Shindou, Physical Review B 104, 184201(2021).
4. X. Luo, T. Ohtsuki, R. Shindou, Physical Review Letters 126, 090402 (2021).
5. X. Luo, T. Ohtsuki, and R. Shindou, PhysicalReview B 104, 104203 (2021).
6. X. Luo, Z. Xiao, K. Kawabata, T. Ohtsuki, and
R. Shindou, arXiv:2105.02514
7. Y. Harashima, T. Mano, K. Slevin, and T. Ohtsuki, Journal of the Physical Society of Japan 90,
094001 (2021).
8. T. Mano, and T. Ohtsuki, Annals of Physics
435, 168500 (2021).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Non-equilibrium relaxation analysis on the J1 − J2
frustrated Ising model
Keisuke Iikura and Hiroshi WATANABE
Department of Applied Physics and Physico-Informatics, Keio University
Yokohama, Kanagawa 223-8522, Japan

We consider frustrated J1 -J2 Ising model on
the square lattice which Hamiltonian is givenby∑∑
H = J1σi σj + J 2
σi σj ,
⟨i,j⟩⟨⟨i,j⟩⟩

where ⟨i, j⟩ and ⟨⟨i, j⟩⟩ denote the summation
over the nearest and the next-nearest neighborpairs, respectively. Spins are Ising-like variable, σi = ±1 and J1 < 0 and J2 > 0 denote ferromagnetic and antiferromagnetic interactions, respectively. The parameter of thesystem is given by g = J2 /|J1 |. This model
exhibits criticality with varying exponents as
the parameter g changes. This behavior isbelieved to be Ashkin-Teller (AT) universality class. The AT-like behavior will end atsome points g ∗ , and the phase transition becomes the ﬁrst-order for 1/2 < g < g ∗ . The
end-point is predicted to be 4-state Potts universality class. However, the localtion of theend-point g ∗ varies from study to study. Furthermore, whether the phase transition in therange 1/2 < g < g ∗ is a ﬁrst-order transition
or a continuous transition is under debate [1].
Since the interactions of this model involves
frustration, the cluster algorithm cannot beapplied. Therefore, we apply non-equilibrium
relaxation (NER) method to analize the criticality of this model.
We ﬁrst observe the non-equilibrium relaxation of the order parameter. The stripe orderof this system is deﬁned as follows,
mx ≡

1 ∑
(−1)xi σi ,
N i

my ≡

where (xi , yi ) are the coordinates of the i-th
spin on the lattice. Then the magnetizaiton is
given by m2 = m2x + m2y . The order parameter
decays exponentially in the disordered phase,converges to a constant in the ordered state,
and exhibits power-law decay at the criticalpoint. Then we can identify the critical pointfrom the non-equilibrium behavior of the parameter. We determine the critical exponents
from the non-equilibrium ﬂuctuation of obervables [2]. The location of Potts point is determined to be g ∗ ∼ 0.58. From the numericalanalysis, the phase transition is continuous for
1/2 < g < g ∗ and we did not ﬁnd any signs of
the ﬁrst order transition. We are currently analyzing the behavior of ordered structure underthe ﬁelds, and we conﬁrm the existence of a nematic phase. The identiﬁcation of the natureof the phase transition is a subject for future
work.

References[1] S. Jin, A. Sen, and A. W. Sandvik, Phys.
Rev. Lett. 108, 045702 (2012).
[2] Y. Ozeki and N. Ito, J. Phys. A: Math.
Theor. 40, R149 (2007).

1 ∑(−1)yi σi ,
N i

229

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Structure and mechanical properties of crystalline
polymers absorbing water molecules
Yuji HIGUCHI
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581
Research Institute for Information Technology, Kyushu University
Motooka Nishi-ku, Fukuoka 819-0395

We have studied soft matter by molecularsimulations and revealed the fracture processesof semicrystalline polymers [1] for the improvement of the toughness and dynamics of lipid
bilayers [2] as a model system for biologicalmembranes.
This year, self-assembly processes of amphiphilic molecules were studied by dissipative particle dynamics (DPD) [3] simulations
on systems B and C using the LAMMPS
program [4]. We revealed that two diﬀerent molecules were self-sorted or mixed andthe processes depended on the hydrophobic
length [5].
Furthermore, we studied the adsorption andabsorption processes of water molecules tocrystalline polymers by coarse-grained molecular dynamics simulation. Water molecules are
represented as a sphere in the simulation. The
attractive interaction between water and polymer spheres is suﬃciently strong to treat polymers as hydrophilic. Figure 1 shows a snapshot
at 10 ns and the number of adsorbed watermolecules to polymers along the cell axis. Water molecules selectively attach to and absorb
into amorphous layers. The tendency is thesame as that in the diﬀerent surfaces, where
the water sphere selectively absorbs into amorphous parts. In the hydrophilic semicrystalline
polymers, the absorption of water into amorphous parts leads to the gain of attractive interaction compared to that into crystal parts.

Figure 1: Adsorption and absorption processesof water molecules to polymers. Number ofadsorbed water molecules to polymers along
the cell axis.

References[1] Y. Higuchi: Phys. Rev. E 103 (2021)
042502.
[2] Y. Higuchi, Y. Asano, T. Kuwahara, and
M. Hishida: Langmuir 37 (2021) 5329.
[3] R. D. Groot and P. B. Warren, J. Chem.
Phys. 107 (1997) 4423.
[4] S. Plimpton:(1995) 1.

J. Comput. Phys. 117[5] R. Wakabayashi, R. Imatani, M. Katsuya,
Y. Higuchi, H. Noguchi, N. Kamiya, and
M. Goto: Chem. Commun. 58 (2022) 585.

230

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Majorana-mediated spin transport in Kitaev modelAkihisa Koga
Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551

Spin transport has recently attracted muchinterest. One of the interesting examples is thespin transport in the Kitaev model [1]. In themodel, quantum spins are fractionalized intoitinerant Majorana fermions and local fluxes
due to quantum many-body eﬀects. Due to theexistence of the local conserved quantities, spin
moments never appear in the ground state.
Nevertheless, the itinerant Majorana fermionscarry the spin excitations and the spin transport is realized without spin oscillations. Since
Majorana and flux excitations have distinct energy scales, it is highly desired to clarify how
stable such a Majorana-mediated spin transport is against thermal fluctuations.

quantum state method to the 28-site cluster,
we examine the dynamics of the system after the magnetic pulse is introduced at theleft edges. When T ∼ TL , where TL corresponds to an energy scale of local flux, larger
oscillations in the spin moments are induced in
the other edge, compared to the results at the
ground state. At higher temperatures, excitedZ2 fluxes disturb the coherent motion of theitinerant Majorana fermions, which suppresses
the spin propagation. Our results demonstratea crucial role of thermal fluctuations in the
Majorana-mediated spin transport [2].
T/J=0.5

T/J=0.2

T/J=0.1
T/J=0∆Sz

T/J=0.01

T/J=0.05
T/J=0.03

tJ

Figure 2: Real-time evolution of the change inthe local magnetization in the right edge.
Figure 1: Kitaev model with armchair edges.
Green, red, and blue lines indicate x-, y-, andz-bonds, respectively. The static magnetic
field hR is applied in the right region, and nomagnetic field is applied in the middle region.
Time-dependent pulsed magnetic field is introduced in the left region.
Motivated by this, we deal with the Kitaev
model with armchair edges, which is shown in
Fig. 1, and consider the spin transport at finite temperatures. Applying the thermal pure

References[1] T. Minakawa, Y. Murakami, A. Koga, and
J. Nasu, Phys. Rev. Lett. 125, 047204(2020).
[2] H. Taguchi, Y. Murakami and A. Koga,
Phys. Rev. B 105, 125137 (2022).

231

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of COMPutation ARchive of Exact
Diagonalization (COMPARED)
Kota IDO
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
Development of accurate numerical solvers

highly efficient simulations on supercomputers.

for quantum many-body systems is one of the

Although this parallelization is efficiently done

central issues in the field of computational

for large system sizes such as 36 sites ofmaterials sciences. To achieve this goal, thequantum spin systems, it is not for single

exact diagonalization method has been widely

parameter set for small system sizes. To generateused for benchmarks on the systems smaller thandata for small system sizes, we develop a python

50 sites because this method enables us to obtain

tool

numerically exact results in the systems withparallelly. This tool parallelizes input parameter

arbitrary interactions. Although most numericalsets and performs the simulations independently

data obtained by the exact diagonalizationfor each parameter set. Now we have released

methodthesemore than 20 million data focused on the

representations such as definition of theenergies of the ground state and the first excited

Hamiltonians and the display digits of the results

state on quantum spin systems with small system

are dependent on the articles. Therefore, it issizes [2]. We will upload the results for large

desirable for construction of database to easilysystems and electron systems.

areavailableonarticles,which

performs

HPhi’ssimulations

This project has been done in collaboration

check and obtain the exact diagonalization

with Kazuyoshi Yoshimi and Yuichi Motoyama.

results without definition of notations.

References

In this project, we have constructed an open
database for exact diagonalization results, which[1] K. Yoshimi, K. Ido, Y. Motoyama, R.

is called “COMPutation ARchive of Exact

Tamura, T. Fukushima, Y. Nakanishi-Ohno:

Diagonalization

https://datarepo.mdcl.issp.u-tokyo.ac.jp/repo/3(COMPARED)”[1]. This

database has been available on the ISSP data

[2] https://isspns-gitlab.issp.u-

repository under the CC BY 4.0 license [2]. As a

tokyo.ac.jp/compared/compared

generator of the exact results, we use open-[3] M. Kawamura, K. Yoshimi, T. Misawa, Y.

source software HPhi [3], which supports

Yamaji, S. Todo, and N. Kawashima: Comp.

MPI/OpenMP hybrid parallelization to achieve

Phys. Commun. 217 (2017) 180.

232

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ground state and dynamical properties of the
J1-K-Heisenberg model on the square lattice
Matthias GOHLKE, Tokuro SHIMOKAWA
Theory of Quantum Matter Unit, Okinawa Institute of Science and Technology
1919-1 Tancha, Onna-son, Okinawa 904-0495

H = J1
+ K

X
hi,ji

S·S

X 
(i,j,k,l)

(1)


−1
Pijkl + Pijkl
+ hz

X

Siz ,

i

where J1 represents dominant ferromagneticiDMRG Ly = 4

hSiz i0.5

iDMRG Ly = 6

hf-ED N = 6x6
hf-ED N = 8x8
hf-ED N = 10x100.0hSi⊥ i0.2

0.0
1

q = (π, 0)

⊥
SDP
(q)

q = (0, π)01q = (2π, 0)

⊥
SQP
(q)

In the absence of conventional magnetic order of spin-dipolar moments, ordering withhigher-order moments like spin-quadrupoles
may occur. Such spin-quadrupolar—or spinnematic (SN)—order was found theoretically in spin-1 model with biquadratic spinexchange [1].
Magnets with spin- 12 degrees of freedom,
however, can only exhibit a SN states if two
spin- 12 are combined into an effective spin-1 [2].
In fact, such SN states on bonds has theoretically been observed in frustrated ferromagnets
on the square lattice with dominant ferromagnetic Heisenberg exchange, J1 , antiferromagnetic next-nearest neighbor exchange, J2 , andcyclic permutation, K. It was found that thecondensation of a two-magnon bound state, atstrong magnetic fields along the z-axis, can stabilize a phase with bond-nematic order [3].
Experimentally, the nature of such a groundstate is intrinsically difficult to verify, due tothe lack of probes that couple directly to thespin-quadrupole moments. Instead, it is necessary to examine the dynamics of a SN: A
continuous symmetry for the director of a spinquadrupole remains, that give rise to a gapless
Goldstone mode [4, 5].
We started by studying the square-latticefrustrated J1 -K model [2],

0
0.0

0.2

0.4

0.6

0.8

1.0

hz

Figure 1: Ground-state of the square-lattice
J1 -K-model in a magnetic field at fixed K/|J1 |.
Different system sizes, geometries, and methods (iDMRG,high-field ED) are compared.
Heisenberg exchange between nearest neighbor spins, K the cyclic ring exchange aroundsquares, and hz the Zeeman coupling to a magnetic field along the z-axis.
Using iDMRG and the matrix product states(MPS) framework as well as a recently developed exact diagonalization method near saturation [6], we confirm the existence of thebond-nematic phase in an extended range of
K/|J1 |. In utilizing different methods combined with different geometries, we can assess
possible finite-size effects, cf. Fig. 1. Overall we find a good agreement between highfield ED on symmetric clusters and iDMRG
on cylindrical geometries with a circumferenceof Lcirc = 6 sites.
A significant amount of computational resources has been spent on mapping out the233

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

non-magnetichz /|J1 |

0.1

ω

0.8
0.6 0.0

0.36

0.38

0.40

101

102
QP
S⊥
(q, ω)S DP (q, ω)

1.2 0.2
1.0

101

0.42

3

3

2

2

ω

1.4

100

hc ED
hc 1-magnon

bond-nematic
4-AF
2-AF Neél

1.6

1

1

0.4
0.2

0

0.0
0.35

0.40

0.45

0.50
K/|J1 |

0.55

0.60

0

Γ

X

Γ0 Γ

X

Γ0

0.65

Figure 2: Phase diagram of the square-lattice
J1 -K-model in a magnetic field obtained withiDMRG using Lcirc = 6 sites circumference.
entire phase diagram using a cylinder with
Lcirc = 6, cf. Fig. 2. The bond-nematic
phase is sandwiched between high-field polarized and 4-sublattice AF phase. Additional
phases (Neél, non-dipolar) occur for large K.
Given the ground state wave function as an
MPS, dynamical properties can then be studied by applying a time-evolution unitary U (dt)represented as a matrix product operator. In
doing so, we observe the condensation of twomagnon bound state at the corresponding wave
vector of the SN state. Within the SN phase,
we observe (1) the magnon-like excitation thatremains fully gapped, and (2) a gapless modewith vanishing spectral weight in the dipolarstructure factor and in the q → 0 & ω → 0
limit as predicted by prior mean-field studies, cf. Fig. 3. We do, however, observe relevant qualitative differences most prominent in
the dynamical quadrupole-structure factor. Its
origin is currently under investigation.

Figure 3: (a) Dynamical spin-structure factorand (b) dynamical quadrupole-structure factor.
[4] R. Shindou, S. Yunoki, and T. Momoi,
Phys. Rev. B 87, (2013) 054429.
[5] A. Smerald, H. T. Ueda, and N. Shannon,
Phys. Rev. B 91 (2015) 174402.
[6] H. Ueda, S. Yunoki, and T. Shimokawa,Comp. Phys. Comm. 277 (2022) 108369.

References[1] K. Harada and N. Kawashima, Phys. Rev.
B 65 (2002) 052403.
[2] A. Andreev and I. Grishchuk, Sov. Phys.
JETP 60 (1984) 267.
[3] N. Shannon, T. Momoi, and P. Sindzingre, Phys. Rev. Lett. 96 (2006) 027213.

234

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical Diagonalization Study on Quantum Phase
Transitions of Frustrated Spin Systems
Tôru SAKAI1,2 , Hiroki NAKANO1 , Rito FURUCHI1 ,and Tokuro SHIMOKAWA3
1
Graduate School of Science, University of Hyogo,
Kouto, Kamigori, Hyogo 678-1297, Japan
2
National Institute for Quantum Science and Technology,
SPring-8, Kouto, Sayo, Hyogo 679-5148, Japan
3
Theory of Quantum Matter Unit,
Okinawa Institute of Science and Technology Graduate University,
Onna-son, Okinawa 904-0495, Japan

1

Magnetization plateau ofthe distorted diamond spin
chain with anisotropic ferromagnetic interaction

The S = 1/2 distorted diamond spin chain
with the anisotropic ferromagnetic interaction
is investigated using the numerical diagonalization and the level spectroscopy analysis. It
is known that the system exhibits a plateau of
the magnetization curve at the 1/3 of the saturation. The present study indicates that as theanisotropy is varied the quantum phase transition occurs between two diﬀerent mechanismsof the 1/3 magnetization plateau. The phase
diagram with respect to the anisotropy and theferromagnetic coupling is also presented[1].

2Magnetization process of
the S=1/2 Heisenberg antiferromagnet on the ﬂoret
pentagon lattice

We study the S = 1/2 Heisenberg antiferromagnet on the ﬂoret pentagonal lattice bynumericaldiagonalization method. We found

235

that magnetization plateaux appear at oneninth height of the saturation magnetization,
at one-third height, and at seven-ninth height.
The magnetization plateaux at one-third andseven-ninth heights come from interactions
linking the sixfold-coordinated spin sites. A
magnetization jump appears from the plateau
at one-ninth height to the plateau at one third
height. Another magnetization jump is observed between the heights corresponding tothe one third and seven-ninth plateaux; however the jump is away from the two plateaux,namely, the jump is not accompanied with any
magnetization plateaux[2].

References[1] T. Sakai, K. Okamoto, H. Nakano and R.
Furuchi, AIP Advances 12 (2022) 035030.
[2] R. Furuchi, H. Nakano, N. Todoroki and
T. Sakai, J. Phys. Commun. 5 (2021)
125008.

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical Diagonalization Study on Magnetization
Process of Quantum Spin Chain with the
Biquadratic Interaction
Tôru SAKAI1,2 , Hiroki NAKANO1 , Rito FURUCHI1 ,and Tokuro SHIMOKAWA3
1
Graduate School of Science, University of Hyogo,
Kouto, Kamigori, Hyogo 678-1297, Japan
2
National Institute for Quantum Science and Technology,
SPring-8, Kouto, Sayo, Hyogo 679-5148, Japan
3
Theory of Quantum Matter Unit,
Okinawa Institute of Science and Technology Graduate University,
Onna-son, Okinawa 904-0495, Japan

1

Quantum spin nematic liquid in the S=1 antiferromagnetic chain with the biquadratic interaction

The magnetization process of the S = 1 antiferromagnetic chain with the biquadratic interaction is invesitgated using the numerical
diagonalization. As a result, it is found thatthe quantum spin nematic liquid phase appears
below the saturation magnetization for suﬃciently large negative biquadratic interaction.
The ground state phase diagram is also presented. [1].

2Field-Induced Quantum
Spin Nematic Liquid Phasein the S=1 Antiferromagnetic Heisenberg Chainwith Additional Interactions

The S = 1/2 distorted diamond spin chain
with the anisotropic ferromagnetic interaction236

is investigated using the numerical diagonalization and the level spectroscopy analysis. It
is known that the system exhibits a plateau of
the magnetization curve at the 1/3 of the saturation. The present study indicates that as theanisotropy is varied the quantum phase transition occurs between two diﬀerent mechanismsof the 1/3 magnetization plateau. The phase
diagram with respect to the anisotropy and theferromagnetic coupling is also presented[2]References[1] T. Sakai, AIP Advances 11 (2021) 015306.
[2] T. Sakai, H. Nakano, R. Furuchi and K.
Okamoto, J. Phys.: Conf. Ser. 2164 (2022)
012030.

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

A proximate Tomonaga-Luttinger state in the S=1/2 Kitaev-
model on a Honeycomb Lattice
Takafumi SUZUKI
Graduate School of Engineering,
University of Hyogo, Shosha, Himeji, Hyogo 670-2280
We have investigated the ground-state phase
diagram and the dynamical properties of the
S=1/2 Kitaev- model [1] on a honeycomb
lattice by the numerical exact diagonalization(ED) method and the density-matrixrenormalization-group (DMRG) method. The
S=1/2 Kitaev-  model on a honeycomb lattice
was proposed as the effective model of thehoneycomb-lattice magnet, -RuCl3. The
ground-state phase diagram of this model with
the isotropic coupling strength has been muchstudied because of the simplicity of the model.
However, the anisotropy of the couplingstrength exists in -RuCl3, which originatesfrom the reduction of the lattice symmetry, andthe effect of the anisotropy has not been fully
understood yet.
In the previous study, we reported the partial
ground phase diagram of the S=1/2 Kitaev-
model on a honeycomb lattice shown in Fig. 1
and indicated that the dimerized phase, whichappears in the isolated dimer limit (d =∞), cansurvives up to the isotropically interacting
model (d=1), when the Kitaev interaction andthe  interaction are negative and positive
respectively [2]. In this study, we investigated
the ground-state phase diagram in 0≤d≤1 [3].
We find that a proximate Tomonaga-Luttinger
liquid (pTTL) is expected in the ground statewith the negative Kitaev interaction and thepositive  interaction (). This pTTL becomes
the Tomonaga-Luttinger liquid (TLL) in thespin chain limit (d=0), which was pointed out
in ref. [4]. When the condition, /|K|=1 (K<0),
is satisfied at d=0, the model is mapped on theantiferromagnetic Heisenberg chains andrecovers the hidden SU(2) symmetry [4]. Thus,
a gapless linear excitation derived from spinon
excitations appears in the low-energy excitation.
These characteristics is also observed in the
low-energy excitation of the pTTL phase. From
the ED calculations for the N=24 site clusterwith the C3 symmetry of the lattice, we findthat the pTTL phase can survive up to d=1.
Next, we calculated the temperaturedependence of the specific heat to investigate
the emergence of the Majorana fermions in thevicinity of d=1 and =0. At d=1 in 0 ≤ /|K|,the presence of the double-peak structure wasindicated in ref. [5]. We find that the highertemperature peak at d=1 corresponds to theprominent single peak in the spin chain limit
and the lower-temperature peak rapidly
develops in the vicinity of d=1. This means thatthe spinon-like excitation is continuously
converted into the Majorana excitation.

Fig. 1: Anisotropically interacting Kitaev-
model. The coupling strength on the X/Y bondis unity and d is the ratio of the couplingstrength on the Z bond against that on the X/Y
bond.

References[1] J. G. Rau, E. Lee, and H. -Y. Kee, Phys. Rev.
Lett. 112, 077204 (2014).
[2] T. Yamada, T. Suzuki, and S. Suga, Phys.
Rev. B 102, 024415 (2020).
[3] M. Gohlke, J. C. Pelayo, and T. Suzuki, in
preparation.
[4] W. Yang, et al., Phys. Rev. Lett. 124,
147205 (2020) and W. Yang, A. Nocera, and I.
Affleck, Phys. Rev. Research 2, 033268 (2020).
[5] A. Catuneanu, et al., npj Quant. Mater. 3, 23(2018).

237

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Hybrid Simulations on Fluid-Viscoelastic Membrane System
Using Multi-Scale Simulation Platform for Complex Fluids
Yohei MORII and Toshihiro KAWAKATSU
Department of Physics, Tohoku University,
Aza-Aoba, Aramaki, Aoba-ku, Sendai 980-8578
We develop general multiscale simulation

particles with smaller velocity gradient.

Amethods for inhomogeneous complex flows in

preliminary result using linear viscoelastic

viscoelastic fluids and elastoplastic solid. For

constitutive equation was developed during thesuch multiscale simulations, a general-purpose

previous project in 2020 [1]. In the present

platformproject, we extended this hybrid method to

namedMultis-Scale

Simulation

Platform for complex flows (MSSP) was

nonlineardeveloped by the present authors [1]. In our

Figure 1 shows the flow pattern around the

MSSP, the macroscopic flow is simulated byseparation point on a cylindrical obstacle,smoothed(SPH)

where the red SPH particles contains particle

method, to which the microscopic information

MD simulators while blue SPH particles

is introduced through a microscopic molecular

contain nonlinear constitutive equations. We

dynamics (MD) simulator embedded in each of

can confirm that the switching is successfully

the SPH particles.

implemented and 97% of 1,600,000 SPH

particlehydrodynamics

We simulate a viscoelastic flow of a diluteviscoelastic

constitutive

model.

particles are simulated with constitutive model.

polymer solution passing through an obstacle
and clarify the role of added polymers.

To

accurately simulate large scale dynamic flow
patterns behind the obstacle, such as Karmanvortex street, it is essential to use a large-scale
system, where the flow velocity and velocity
Fig.1 MSSP simulation of a polymer
flow around a cylindrical obstacle.
Bars attached to the particles show
the average elongation and its
direction of the polymer chains.

gradient are highly inhomogeneous. To avoid alarge computational cost as well as a large
unbalance in the computational load on thecomputer nodes, we proposed a hybrid method

Referenceswhere we switch the MD simulators with

[1] Y. Morii and T. Kawakatsu: Phys. Fluids 33

simpler constitutive equations for the SPH(2021) 093106.

238

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Thermal effects on quantum frustrated magnetisms
Tokuro Shimokawa
Theory of Quantum Matter Unit, Okinawa Institute of Science and Technology Graduate
University, Onna-son Okinawa 904-0412
Quantum frustrated magnets are well-known

them; we found that one of them is ansources of exotic states of matter, but

intriguing six sub-lattice (anti) skyrmion-

investigating their true nature, particularly at

lattice state with topological nature.

finite temperatures, is still a demanding and

2) High-field exact diagonalization code

challenging problem. This fiscal year, wedevelopment and the low-T physics in thehave focused on the following topics with the

S=1/2 J1-K square-lattice model

ISSP supercomputer.

We developed an exact diagonalization code,

1) S=1/2 breathing bilayer kagome (BBK)

quantum spin solver near saturation (QS3), as

magnet for Ca10Cr7O28

an open-source software [2]. Using this high-

Ca10Cr7O28 is a newly quantum spin liquidfield ED code, we investigated the low-T(QSL) material, and the effective

phase diagram of the S=1/2 square-lattice

Hamiltonian was proposed as an S=1/2 BBKHeisenberg model with a ring exchange

Heisenberg model. A recent semi-classicalinteraction (J1-K model).

study [1] supported the scenario of a QSLOur ED calculations revealed the existence

ground state in this material and suggestedof several ordered/disordered states in fields.

possible realizations of exotic low-

Especially in the high-field regime aroundtemperature multiple-q states in fields. But

K/J1~0.5, we clarified the realization of athe true nature of the multiple-q states wasn’t

bond-nematic state without any

uncovered yet because of the difficulty of

approximation to our Hamiltonian. We also

treating large systems.

computed the dynamical spin/quadrupole

We alternatively treated a classical J1-J2

structure factors for future neutron scattering

Heisenberg model on the honeycomb latticemeasurements on candidate materials.

model, which could also be considered aneffective model for Ca10Cr7O28 to investigate

References

the thermodynamic properties of the[1] R. Pohle, et al, PRB 104, 024426 (2021).

multiple-q states. Our large-scale Monte[2] H. Ueda, S. Yunoki, T. S., Comp. Phys.

Carlo simulations succeeded in identifying

Commun. 277, 108369 (2022).

239

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Steady states realized by a global thermodynamicbalance in nonequilibrium
Naoko NAKAGAWA
Department of Physics, Ibaraki University
2-1-1 Bunkyo, Mito, Ibaraki 310-8512

First-order phase transition and the separation of the phases have attracted scientific interests from various points of view, not only
from physics but also from the biological mechanism. The phase coexistence induces sometimes complicated and singular properties tothe system even though the bulks of respective
phases may behave rather ordinary.
In this project, we work on particle systems
interacting via a Lennard-Jones potential[( )12

V (r) = 4ϵσr−( )6 ]σr+ ϵ,with a diameter σ of each particle and a coupling strength ϵ, which have been a standard
model for numerical experiments. By choosing the total energy and the number density ofthe system appropriately, the system shows aliquid-gas transition. See Fig. 1 for the case of
N = 5 × 104 . We also used Weeks-ChandlerAndersen (WCA) potential when we want toavoid the liquid-gas transition.
Our most interest is the liquid-gas coexistence in heat conduction. Due to the steadyheat current, the coexistence pattern of the liquid and gas becomes much more stable compared with equilibrium systems. The local
states around the liquid-gas interface become
observable due to the induced stability. We
here notice that the rich behaviors related to
the first-order transition are often observed incomplex systems such as mixtures and dense
solutions. Their response to a nonequilibrium
driving will be of great interest. To initiate them, we start with the construction of amethod to know their thermodynamic properties in equilibrium. The details of the results
follow.
We derived a formula for determining themixing free energy for two-component fluids.
The formula is numerically verified with a good
accuracy by the molecular dynamics simulation using the LAMMPS package installed in
the supercomputers at ISSP. We have compared two kinds of protocols creating a mixtureof two pure substances. One is traditional protocol and the other is a protocol with ”alchemical change” of molecules, which may be valid
only in numerical experiments. We calculated
the free energy changes of the two protocols byadopting the Jarzynski equality and information thermodynamics. The comparison of thetwo results in a formula for the mixing Gibbs
free energy ∆mix G asN!
⟨e−β Ŵ(#) ⟩ ∆mix G = −kB T ln ,n!(N − n)!ρX (n) ⟨e−β Ŵ(ii) ⟩where n and N − n are the numbers of particles for the two components and ρX (n) is thenumber density of the first component in theregion x < X. Ŵ(#) is the work in each trajectory according to the alchemical process tocreate a mixture from the first pure substance,
whereas Ŵ(ii) is the work according to the alchemical process to create the second from thefirst pure substance.
By applying the above formula, we examined∆mix G for the mixture of argon and krypton.
By changing the mole fraction of the krypton,

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

the system shows liquid-gas transition for a
fixed temperature and pressure. The properties of the transition are well characterized in
the calculated ∆mix G as a double-well-shaped
function. The violation of convexity is likely
due to the finiteness of the system.
We have used the L4 CPU of System B with
4 nodes in 512 parallel computation using MPI
for the calculation of 104 particles, the L16
CPU of System B with 16 nodes in 2048 parallel computation using MPI for the calculationof 5 × 105 particles, the L72 CPU of System
B with 72 nodes in 9216 parallel computation
using MPI for the calculation of 8 × 106 particles.

References[1] A. Yoshida and N. Nakagawa: to appear
in Phys. Rev. Res. (2022)

Figure 1: Snapshot of the particles interactingwith Lennard-Jones potential in heat conduction. The system with N = 5 × 105 exhibits a
sharp liquid-gas interface.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Scrambling in quantum many-body systems
Masaki TEZUKA
Department of Physics,
Kyoto University, Kitashirakawa, Sakyo-ku, Kyoto 606-8502
Strongly correlated models realizable incondensed matter systems with possible
holographic correspondence to gravitational
systems including black holes have received
much attention in the recent years. Of
particular interest are scrambling and chaotic
dynamics. The scrambling phenomena inquantum systems is delocalization of quantum
information and has been discussed as theformation of quantum error correction (QEC)
code. Thus, we have been trying to study
scrambling and effect of dissipation inquantum many-body systems, toward
experimental demonstration in condensed
matter systems such as ultracold atoms.
The Sachdev-Ye-Kitaev (SYK) model is amodel of Majorana fermions with all-to-all
four-fermion interactions obeying theGaussian distribution. It has an analytic
solution in the limit of large number of
fermions and is maximally chaotic at low
temperatures. We have previously studied theeffect of a random hopping term, two-fermion
interactions, added to the model [1]. The
maximally chaotic behavior is lost and thespectral statistics turns to an uncorrelated one.
Furthermore, the localization transition is a
Fock-space localization, a type of many-body
localization, and quantities such as thelocation of the transition point, the momentsof the eigenstate wavefunctions, and bipartite
entanglement entropy have been obtained
analytically with numerical confirmation [2].
A “sparse” version of the SYK model, in
which the number of interaction terms is on
the order of the number of fermions, insteadof all the choices of four-fermion subsets,

have been proposed a few years ago.
To quantify the scrambling properties ofthese models, we have studied the QEC
capabilities of the unitary time evolution
according to their Hamiltonians according to
the Hayden-Preskill protocol [3]. In thisprotocol, the unknown quantum state throwninto a quantum many-body system is decoded
by a person who, knowing the initial state of
the remainder of the system and the time
evolution, obtains the quantum state of someof the qubits comprising the system, and theerror estimate for the time evolutions obeying
the circular unitary ensemble (CUE) is known.
Using the ISSP Supercomputer, weanalyzed the spectral statistics of a further
simplification of the sparse SYK model [4].
Also, we numerically observed that while forthe sparse SYK models, the QEC error
estimate approaches the CUE value as soon as
the spectral statistics becomes random-matrix
like, for the case of two-fermion interactions,the departure from the CUE value is observed
before the Fock space localization occurs [5].

References[1] A. M. Garcia-Garcia, B. Loureiro, A.
Romero-Bermudez, and M. Tezuka, Phys.
Rev. Lett. 120 (2018), 241603.
[2] F. Monteiro, T. Micklitz, M. Tezuka, and
A. Altland, Phys. Rev. Research 3 (2021),
013023; F. Monteiro, M. Tezuka, D. A. Huse,and T. Micklitz, Phys. Rev. Lett. 127 (2021),
030601.
[3] P. Hayden and J. Preskill, JHEP 0709
(2007), 120.
[4][5] M. Tezuka et al., in preparation.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Investigation of the molecular origins of the mechanical andthermal properties of realistic biopolymers using all-atomistic
molecular dynamics
Okazaki Susumu
Department of Advanced Materials Science,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
Mechanical and thermal properties ofpolymer chains forming network structures.

biopolymers, PBI and its three copolymers

We also investigated the microscopic origins

PBO-co-PBI, PBI-co-PBO-co-pPA, and PBI-of the stress causing the elastic deformation,

co-PBO-co-mPA, have been investigated based

yield point, strain softening, and strain

on all-atomistic molecular dynamics (MD)hardening observed in PC and OMMA, by

calculations to clarify molecular mechanism of

decomposing the stress into contributions fromfracture and glass transition of the polymers. We

various energetic energy terms. Our analysis

also investigated regular polymers, PC andshowed that the stress of the fracture process is

PMMA [1], as a reference system. The

mainly determined by the bond, angle, and vdW

calculations have been conducted on theterms, in addition to the system alignment in the

supercomputers at ISSP using a MD software

pulling direction. In the elastic region, almost

MODYLAS [2] developed by our group.

theModulus of elasticity, yielding stress, andentiresystemexperiences

affinedeformation

despite

the

local

existing

fracture stress were studied in detail. The

heterogeneous deformation in the later elastic

biopolymers showed the high modulus ofregion. As the deformation of the entanglement

elasticity at short strain followed by the highnetwork begins, the stress on the bonds andyielding stress and ductility showing strong

angles rapidly increases.

strain hardening at large strains after theReferences

yielding point.

[1] Z. Tang, K. Fujimoto, S. Okazaki, Polymer,

The biopolymers investigated here all
exhibited

very

high

glass

226(2021)123809.

transition

temperatures at 800 K – 900 K. The[2] Y. Andoh, S. Ichikawa, T. Sakashita, N.

temperatures are higher than their pyrolysis

Yoshii,temperatures. These high glass transition

42(2021)1073.

temperatures are from hydrogen bonds among

243

S.

Okazaki,

J.

Comp,

Chem.,

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Simulations of quantum-classical-hybrid algorithms forsensor materials with considering noise
Wataru Mizukami
Center for Quantum Information and Quantum Biology, Osaka University, Osaka 560-0043,
Japan
The development of quantum computers has

use charges high fees; error rates of today’s

made significant progress in recent years:

NISQs are still too high. Last year, we built aquantum computers with dozens or a hundred

framework to efficiently emulate quantum

qubits have been built. We now expect to see

circuits with (deplolarsing) noises using thequantum devices with hundreds or thousands ofsupercomputer of the ISSP.

qubits near future. Such quantum computers areThis year, we worked on improving theoften called noisy-intermediate scale quantum

efficiency of the quantum circuit optimization

devices (NISQs) since they do not have quantum

part in the VQE. We parallelized the gradienterror correction functionality. There have been

evaluations of the VQE’s cost function withintensive research efforts currently underway torespect to the quantum circuit parameters, using

exploit the computational potential of NISQs.

MPI. We tested our implementation by

One promising algorithm for NISQs is thecomputing the H2O molecule with the 6-31G

quantum-classical hybrid algorithm, which canbasis set. The benchmark calculation used aoperate even in the short coherence time of aminimum of 128 cores and a maximum of 9216

NISQ. Among them, the variational quantum

cores. The observed parallelization efficiency

eigensolver (VQE) can be applied to first-

was 75% with 4608 cores, relative to theprinciples calculations of materials or molecules.

execution time with 128 cores.

We are targeting applying the VQE to practical

Moreover, we developed a method toproblems in material science. In particular, weconsider solvation effects within the framework

aim to use the VQE for analyzing materials usedof the VQE. This was achieved by combining thein sensors. In this study, we use a quantum

VQE and 3D-RISM, an integral equation theory

circuit simulator rather than real quantumof molecular liquids. This method was used tocomputers to develop a new quantum-classicalinvestigate the impacts of solvents on the

hybrid algorithm and validate it. The reasons wecomputational cost of quantum computing. Our

employ such an emulator are the following: thecalculations indicate that solvation effects

number of NISQs is limited at this moment; theirvirtually have no impact on it.

244

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Molecular Dynamics Simulation of Stress Induced
Crystallization in Robust-Toughening Hydrogel
Koichi Mayumi, Kosuke Aomura, Takeyoshi Masumoto, Haru Shinohara

Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
In

this

project,

westudiedcrystallization of polymer chains inslide-ring gels under stretching by
means

of

coarse-grained

dynamics simulation.

molecular

In addition, we

performed a full-atomistic molecular
dynamics simulation of the melting
process of stretched polymer crystals inwater.
Fig. 1 Stress-extension ratio relation of
fixed crosslink gel and slide-ring gel.

Coarse-Grained Molecular Dynamics
Simulation of Strain-Induced Crystalli-

links.

zation of Slide-Ring Gel
In

this

study,

uniaxial

Further analysis was performed toelongation

simulations of slide-ring gels wereclarify

performed

coarse-grained

stretching. We calculated scattering

molecular dynamics simulation [1]. In

function of SR gel before and afterorder to investigate the strain-induced

stretching. At the extension ratio λ=12,

crystallization of slide-ring gel which isscattering function shows a circularobserved
introduced

using

in

experiments
attractive

[2],

we

aggregatedpeak on 𝑞

interaction

0σ

structureplane at

𝑞

under

𝑞

between polymer chains. Fig. 1 shows

6 σ . The peak suggests the formationstress-extension ratio curve of a fixedofcrosslink (FC) gel and slide-ring (SR) gel

polymer chains are aligned in thewith the same cross-linking density. SR

directionshows smaller stress than FC gelelongation.

because of the slidability of the cross-245

aggregate

structures

perpendicular

in
to

which
the

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analysis of Dissolution Process ofExtended Polyethylene Glycol Crystal
in Water
The reversibility of the strain-induced
Fig. 2 Snapshots of a scattering function

crystallization of PEG chains in waterof SR gel at (a) λ=1 (b) λ=12

allows the tough hydrogel to rapidly
recover from mechanical stress. To

A region of neatly aligned polymer

understand the dissolution process of

chains was extracted from the network,

extended PEG chain crystal in water,

and

was

all-atom MD simulation was carried out.

calculated for the region. As a result, we

GROMACS 2016.5 [3] was used as

observed spot peaks corresponding to asimulation software. We investigatedbody-centeredlatticethe dissolution process of helical PEG

crystal structure, as shown in Fig. 3.

chain crystal and zigzag PEG chain

This indicates that the slidability of thecrystal under stretching in water. For

cross-linking points equalizes the chain

helical chain crystal, the crystal partly

deformation and enhances the strain-remain after 200 ns even at no

induced crystallization.

elongation force. On the other hand,thescatteringfunctionorthorhombic

zigzag chain crystal dissolves fasterthan the helix chain crystal.

References[1] Kremer, K.; Grest, G. S.: J. Chem.

Phys. 92 (8), 5057–5086. (1990)[2] C. Liu, N. Morimoto, L. Jiang, S.
orthorhombic

Kawahara, T. Noritomi, H. Yokoyama, K.

lattice crystal structure observed in SR

Mayumi, K. Ito: Science 372 1078-1081.

gel at =12.

(2021)Fig.

3

Body-centered[3] Berendsen, H. J. C.; van der Spoel,D.; van Drunen, R. Comp. Phys. Comm.
91, 43–56. (1995)

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Molecular dynamics study of shear-induced
long-range correlations in simple ﬂuids
Hiroyoshi Nakano
Department of Applied Physics and Physico-Informatics, Keio University
Yokohama, Kanagawa 223-8522, Japan

We studied a nonequilibrium long-range correlation (LRC) in simple ﬂuids using a molecular dynamics (MD) simulation. The nonequilibrium LRC means that same-time spatial correlations of locally conserved quantities exhibit
power-law decays due to a lack of detailedbalance condition [1]. It is known to be oneof the general features of nonequilibrium systems with conserved quantities and anisotropy.
Because in equilibrium the LRCs are speciﬁcto the critical phenomena, the nonequilibrium
LRCs observed far from the critical points
have been extensively studied as the novel
phenomena induced by nonequilibrium conditions. However, the almost all of research
have been performed using phenomenologicalmodels such as ﬂuctuating hydrodynamics andstochastic lattice gases. Indeed, there are few
attempts to directly observe the nonequilibrium LRCs and examine their nature from underlying molecular systems.
In the present study, with the aim of direct observation of the nonequilibrium LRCs,
we focused on the simple ﬂuids under uniform shear ﬂow and performed the MD
simulation [2].
All the MD simulations
were performed by LAMMPS (Large-scale
Atomic/Molecular Massively Parallel Simulator) [3, 4]. The schematic illustration of oursystem is given in Fig. 1. The particles interact via the Weeks–Chandler–Andersen (WCA)
potential. The shear ﬂow is imposed by using
the Lees–Edwards boundary condition along
the z-axis. Along the x and y-axes, the stan-

Figure 1: Schematic illustration of shear ﬂow.
dard periodic boundary conditions are imposed. To maintain a constant temperature T
under shear ﬂow, the dissipative particle dynamics (DPD) thermostat is used. Thus, inthe steady state, the following averaged velocity proﬁle ⟨v(r)⟩ss = (γ̇z, 0, 0) is realized,
where ⟨·⟩ss denotes time average in the steadystate and the ensemble average over diﬀerent
noise realizations, and γ̇ is shear rate.
We observe the same-time correlations of
momentum ﬂuctuations in the steady state.
The momentum ﬂuctuations are given by
δg(r, t) =N∑pi (t)δ(r − ri (t)) − ⟨v(r)⟩ss , (1)i=1where ri (t) and pi (t) are, respectively, the position and momentum of ith particle at timet. Then, the same-time correlations of momentum ﬂuctuations are given by Cαβ (r, r ′ ) =⟨δg α (r, t)δg β (r ′ , t)⟩ss , where α, β = x, y, z.
We plot the Fourier transform of Czz (r, r ′ )in Fig. 2. Because our system has the spe-

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo
7

7

7

3
1

5
3
1

0.04

0.08

0.12

0.16

0.08

0.12

0.16

0.04

7

1

5
3
1

0.12

0.16

0.16

Lz = 1024σ
Czz (kx, 0, 0)

3

0.12

7

Lz = 512σ
Czz (kx, 0, 0)

5

0.08

kx

Lz = 256σ

0.08

3

kx

7

0.04

5

1
0.04

kx

Czz (kx, 0, 0)

Lz = 128σ
Czz (kx, 0, 0)

5

Lz = 64σ
Czz (kx, 0, 0)

Czz (kx, 0, 0)

Lz = 32σ

5
3
1

0.04

kx

0.08

0.12

0.16

kx

0.04

0.08

0.12

0.16

kx

Figure 2: Czz (kx , ky = kz = 0) for several system sizes Lz = 32σ, 64σ, 128σ, 256σ, 512σ, 1024σ.
The color circle points represent the MD simulation results, and the black square points theresults calculated from the ﬂuctuating hydrodynamics.
cial Galelian invariance, the Fourier transform of Czz (r, r ′ ) is given as Czz (k) =∫ 3
d rCzz (r, 0)e−ik·r . In Fig. 2, Czz (kx , ky =kz = 0) for diﬀerent Lz is presented. The otherparameters are set to Lx = 1024σ, Ly = 32σ,
−1and γ̇ = 0.02τunit, where σ and τunit are, respectively, the unit of length and time. The
black square points represent Czz (kx , ky =kz = 0) calculated from the phenomenological theory called the ﬂuctuating hydrodynamics [5]. The result obtained from the ﬂuctuating hydrodynamics is independent of Lz .

rium long-range correlations for the suﬃciently
large system that contains over 10 million particles.

From Fig. 2, we ﬁnd that the strong ﬁnitesize eﬀects exist for Czz (kx , ky = kz = 0). For
suﬃciently large Lz , the result calculated fromthe ﬂuctuating hydrodynamics is in quantitative agreement with the MD simulation results.
In contrast, for smaller Lz (e.g. 32σ or 64σ),
there is the clear deviation between their results. In other words, the quite large systemsize is required to observe the shear-induced
long-range correlations.

[3] S. Plimpton, Journal of Computational
Physics 117, 1 (1995).

In summary, we performed the MD simulations of the WCA ﬂuids under uniform shear
ﬂow. We successfully observed the nonequilib-

References[1] J. Dorfman, T. Kirkpatrick, and J. Sengers, Annual Review of Physical Chemistry 45, 213 (1994).
[2] H. Nakano, and Y. Minami, Physical Review Research (in press).

[4] A. P. Thompson, H. M. Aktulga, R.
Berger, D. S. Bolin-tineanu, W. M.
Brown, P. S. Crozier, P. J. in t Veld,A.
Kohlmeyer, S. G. Moore, T. D. Nguyen,
R. Shan, M. J.Stevens, J. Tranchida, C.
Trott, and S. J. Plimpton, Computer
Physics Communications 271, 108171(2022).
[5] J. Lutsko and J. W. Dufty, Phys. Rev. A
32, 3040 (1985).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical analysis of absorption and fluorescence
spectra for firefly bioluminescence related molecules
Miyabi HIYAMA
Graduate School of Science and Technology, Gunma University,
Tenjin-cho, Kiryu, Gunma 376-8515

Because firefly bioluminescence is widelyused such as in vivo imaging and reporter assay, many analogs of firefly bioluminescence
substrates (luciferin) are developed [1, 2]. AkaLumine is one of the analogs of luciferin andits bioluminescence with firefly luciferase produces the near-infrared emission, which canpenetrate through biological tissues [3]. For
studying the bioluminescence mechanism, basic knowledge about the chemical structures,electronic states, and absorption properties of
AkaLumine solution at various pH values ofsolution has to be acquired.
In this study, the absorption spectra for
Alakumine in aqueous solutions were studied
theoretically [4]. The optimization structureof ground state for AkaLumine and its conjugate acids and bases, which are expected to be
main component in the aqueous solutions, wereobtained from the density functional theory(DFT). The time dependent DFT (TDDFT)
calculations were carried out to estimate thetheoretical absorption spectra for these structures. The Gibbs free energies for the chemical
structures were obtained using the vibrational
analysis. Form these free energies, pKa values
for protonation/deprotonation of AkaLumine
in aqueous solutions were estimated and therelative concentrations of AkaLumine and its
conjugate acids and bases were obtained. All
calculations were performed using the GAUSSIAN09 program [5] on system B and C of Super Computer Center in ISSP.

for AkaLumine and its conjugate acids adbases appear at 369, 465, 314, 353, 352, 440,
322, and 317 nm and that all of these peaks
correspond to the excitation from S0 to thefirst excited state (S1 ) [4]. These S1 states
can be described dominantly by the one electron excitation configuration of which the coeﬃcients are large (∼0.5). From the theoretical results, the peaks at pH 7–10, pH 4, andpH 2 of AkaLumine experimental absorption
spectra are assigned to a carboxylate anion, acarboxylate anion with an N-protonated thiazoline ring, and a carboxylate anion with an Nprotonated thiazoline ring and N-protonateddimethylamino group, respectively.

References[1] Li et al. , Eur. J. Med. Chem., 211 (2020)
113111.
[2] Iwano et al. , Tetrahedron, 69 (2013)3847.
[3] Kuchimaru et al. , Nat. Comm., 7 (2016)
1.
[4] Ogawa et al. Photochem. Photobiol.
(2021) 97, 1016.
[5] Gaussian 09, Revision D.01, M. J. Frischet al.

It was found that the main absorption peaks

249

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Skyrmion crystal phase in the RKKY Heisenberg modelin two- and three- dimensions
Kota Mitsumoto and Hikaru Kawamura
Molecular Photoscience Research Center, Kobe University, Kobe 657-8501, Japan
Skyrmion, a swirling noncoplanar spin

three-dimensional stacked-triangular lattices by

texture whose constituent spin directions wrap a

extensive Monte Carlo simulations in order tosphere in spin space, has attracted much recent

get insights into the chiral-degenerate skyrmion

interest and been studied quite extensively. In

crystal of metallic magnets in the weak-coupling

magnets, skyrmion is usually stabilized in theregime [2].

form of the periodic array, i.e., the skyrmion

We find that the symmetric SkX is stabilized

crystal (SkX). While the SkX was first realized

under finite magnetic fields both in two andin chiral ferromagnets with the anti-symmetricthree dimensions, as shown in the temperature

Dzyaloshinskii-Moriya (DM) interaction, avs. magnetic-field phase diagram of the Figure

recent study has revealed that the SkX state canbelow, both the 2D (upper) and 3D (lower) ones.

also be realized in centrosymmetric magnets
without the DM interaction [1]. Such a“symmetric” SkX state is induced by frustration
among exchange interactions, and keeps thechiral degeneracy with respect to the right-left(R-L) symmetry, in sharp contrast to the DMinduced SkX.
Such a frustration-induced symmetric SkX
is possible both in insulating and metallic
magnets. In metallic magnets, the primaryinteraction is the long-range RKKY interaction
References

which oscillates in sign with the distance leading[1] T. Okubo, S. Chung and H. Kawamura, Phys.

to the frustration, in contrast to the insulating

Rev. Letters, 108, 017206-(1-5) (2012).

magnets possessing the short-range interactions.

[2] K. Mitsumoto and H. Kawamura, Phys. Rev.

In this year’s project, we study the ordering

B 104, 184432-(1-17) (2021); Phys. Rev. B 105,

properties of the isotropic RKKY Heisenberg

094427(2022).

model on the two-dimensional triangular and the250

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Topological phases and science of bulk-edgecorrespondence by numerical methods
Y. Hatsugai
Department of Physics, University of Tsukuba
1-1-1 Tennodai, Tsukuba 305-8571, Ibaraki, JapanThe bulk-edge correspondence[1] is widely used for the studies of topological phenomena
in various systems that include not only microscopic quantum systems but also macroscopic
classical ones such as photonic crystals and meta-materials. It is a scale-free concept. The
abstract mathematical concept of topology is reflected by the physics of boundaries throughgeneric edge states (zero to three-dimensional defects as well). We may further try to discussvarious kinds of localized states as a consequence of non-trivial bulk. A typical example is anequatorial wave on earth where the equator is a boundary for the Coriolis force. Collecting
such hidden reasons why the boundary states exist, we try to establish a universal view for the
localized states in nature and more. This is the science of bulk-edge correspondence. In thecurrent project, we try to apply the viewpoints for various systems using numerical techniques.
Topological pumps focusing on the role of edges are important systems where the bulk-edgecorrespondence governs the phenomena. We have numerically justified the bulk-edge correspondence of topological pumps for quantum spins and bosons with short-range interactions[2, 3]
where a plateau transition analogous to the quantum Hall effects is realized in dimerized high-S
quantum spins. Laughlin’s argument of the quantum Hall effects can be assumed as a variantof the topological pump where bulk-edge correspondence plays a fundamental role. It is numerically considered for a series of anyons with various statistical parameters associated with the
adiabatic heuristic argument[4]. Also, its spinful extension is discussed in details[5].
Fermion quantum Monte Carlo techniques are applied for three dimensional Hubbard model
on a pyrochlore lattice where the bulk-corner correspondence has been justified[6]. We further develop bulk-edge correspondence to non-quantum systems. One is heat conduction in 1dimension[7]. Surprising another example is a bulk-edge correspondence for the evolutional gametheory[8] where non-zero Chern number characterizes a boundary flow in the two-dimensional
game theory (Figure 1.).

References[1] Y. Hatsugai, ”Chern Number and Edge States in the Integer Quantum Hall effect”, Phys. Rev. Lett.
71, 3697 (1993).
[2] Y. Kuno and Y. Hatsugai, “Plateau transitions of a spin pump and bulk-edge correspondence”,
Phys. Rev. B 104, 045113 (2021).
[3] Y. Kuno and Y. Hatsugai, “Topological pump and bulk-edge-correspondence in an extended BoseHubbard model”, Phys. Rev. B 104, 125146 (2021).
[4] K. Kudo, Y. Kuno, and Y. Hatsugai, “Bulk-edge correspondence in the adiabatic heuristic principle”,
Phys. Rev. B 104, L241113(2021)[5] K. Kudo and Y. Hatsugai, “Adiabatic Continuity of the Spinful Quantum Hall States”,
arXiv:2201.07893

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 1: RPS-game on a Kagome lattice (left) and its bundary flow governed by non zero Chern
number of the evolutionary game theory (right). (See ref.[8].)[6] Y. Otsuka, T. Yoshida, K. Kudo, S. Yunoki and Y. Hatsugai , “Higher-order topological Mott
insulator on the pyrochlore lattice”, Scientific Reports 11, 20270 (2021)[7] S. Makino, T. Fukui, T. Yoshida and Y. Hatsugai, “Edge states of a diffusion equation in one
dimension: Rapid heat conduction to the heat bath”, Phys. Rev. E 105, 024137 (2022).
[8] T. Yoshida, T. Mizoguchi, and Y. Hatsugai, “Chiral edge modes in evolutionary game theory: A
kagome network of rock-paper-scissors cycles”, Phys. Rev. E 104, 025003 (2021).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Molecular dynamics simulation of BaTiO3 nanostructure
T. Hashimoto
National Institute of Advanced Industrial Science and Technology (AIST),
Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan

Dielectrics clusters have fascinating newproperties. It is shown that large oﬀ-center displacements of atoms exists even for very small
clusters as small as 5 nm, and vortex structuresof local polarization vectors could be used as
memory devices[1, 2]. However, despite theeﬀorts of preceding studies, the surface termination dependence of the vortex structures
and the toroidal moments are not well understood. In this project, we studied these issues
by molecular dynamics (MD) simulations using a shell model.
The calculations were performed with thecode developed by us. We used a shell model
potential developed by Tinte et al.[3, 4]. The
calculations were performed under constant(N, V, T) conditions. To simulate isolated
clusters, the open circuit boundary condition
was used; i.e., we calculated interactions for
all the atom pairs in the cluster. The temperature was ﬁxed to 10 K to monitor the structures near the ground state while preventing
the system from converging to false structures.
We controlled the temperature by the massive
Nose-Hoover chain method[5]. For each clustermodel, the system was equilibrated for morethan 20000 time steps, and data collection runs
for more than 100000 time steps followed. One
time step was 0.1 fs.
We studied BaO-terminated,
TiO2 terminated,and stoichiometric models.
The former model was rounded apex cubicmodels with eight Ba atoms missing, while thelatter two were cubic models. The number ofthe unit cells on one edge, n, were varied from
3 to 12. The TiO2 terminated surfaces were
unstable, and the TiO2 terminated clusters
were unstable for n ≤ 5. In all terminations,the toroidal moments become non-zero forclusters larger than n = 6. We also studied thetoroidal moment direction dependent energy
for the BaO-terminated clusters, because they
were stable for all n. In these clusters, thestructures with the toroidal moments parallelto [111] which are naturally formed in otherstudies were stable, and structures in which
the toroidal moments were parallel to [110]or [001] were metastable. We also analyzed
the domain structures inside these clusters.
They were found to have domain walls thatare known to be stable in the rhombohedralphase.
[1] H. Fu and L. Bellaiche: Phys. Rev. Lett.
91 (2003) 257601.
[2] I. I. Naumov, L. Bellaiche, and H. Fu: Nature 432 (2004) 737.
[3] S. Tinte, M. Stachiotti, S. Phillpot,
M. Sepliarsky, D. Wolf, and R. Migoni: J.
Phys.: Condens. Matter 16 (2004) 3495.
[4] M. Sepliarsky, A. Asthagiri, S. R.
Phillpot, M. G. Stachiotti, and R. L.
Migoni: Curr. Opin. Solid. St. M. 9 (2005)
107.
[5] G. Martyna, M. Tuckerman, D. Tobias,
and M. Klein: Mol. Phys. 87 (1996) 1117.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

DPD simulations of cross-linked networks to study
topological effect using MP-SRP method
Katsumi HAGITA,1 Takahiro MURASHIMA,2 and Hayato SHIBA3
1

Department of Applied Physics, National Defense Academy, Yokosuka 239-8686
2
3

Department of Physics, Tohoku University, Sendai 980-8578

Information Technology Center, University of Tokyo, Kashiwa 277-0882

Ring-linear blends have garnered increasing

dynamics (DPD) simulations [6]. Multipointinterest among researchers in recent years forsegmental repulsive potential (MP-SRP) [7]both basic science and industrial applications.

was used to ensure thermodynamic consistency

In ring–linear blends, a deeper understanding ofwhile comparing between the systems thatpenetration behaviors among rings and linear

permitted and prohibited chain crossing in DPD

chainsthepolymer simulations. To extract the topologicalmechanical properties of the blends and theireffect of ring polymers, we observed theapplications. Hagita and Murashima [1–4]distribution of penetration in ring–linear blends

investigated the dependence between ring size

and the radius of gyration of rings.

isimportantforcontrolling

and the penetration of linear chains into the ring

Based on a prototype code as an in-housethrough coarse-grained molecular dynamics

user package of MP-SRP [7] for LAMMPS [8],(CGMD) simulations of the Kremer–Grest

we remade a public open version of the user

(KG) model [5]. They estimated the distribution

packageof the number of chains penetrating a ring bycomputational cost, we improved several

estimating the Gauss linking number (GLN) for

implementations as shown in Figure 1. We also

all pairs of linear chains and rings. The number

confirmed the high scalability in the MPI-basednP of linear chains penetrating a ring wasparallel computing.

of

MP-SRP[7,9].

To

reducepresented as a function of the size of the ring(the number of KG particles in a ring, Nring).
These penetration behaviors are governed by
the spread and concentration of the ring
polymers.
In this study, we investigated the topologicalFig. 1: Schematic of the applied improvement

effect caused by chain crossing prohibition in

to reduce omissible computations by changing

ring-linear blends through dissipative particle

sweep of the SRP points along a bond.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

uncatenated rings repel each other because of

In this study, DPD simulations (MP-SRP

the topological constraints.

and sDPD) of ring–linear blends with a ringfraction of approximately 0.1. Here, sDPD

We performed systematic investigations formeans the standard DPD polymer simulation

other values of (Nring, Nlinear) as shown in thewith the Groot–Warren model [6].

published paper [9]. We concluded that the

Figure 2 shows the results of (Nring, Nlinear)

topological effect prohibits ring–ring crossing,= (80, 80), where Nring and Nlinear denote theresulting in a small radius of gyration of thenumber of DPD particles in a ring and in arings. In the DPD polymer system with MP-

linear chain, respectively. Compared to the

SRP, the minimum size of a ring withsDPD model, the number of penetrations in thepenetration was found to be 30, which is less

MP-SRP model decreased owing to thethan half of the value of 80 observed inprohibition of ring–ring crossing. It should be

previous work using the Kremer–Grest bead-

noted that the penetration state of the initialspring model.

configuration

generatedbythepush-off

procedure was far from equilibrium in both

Referencesmodels.

[1] K. Hagita and T. Murashima: Polymer 218(2021) 123493.
[2] K. Hagita and T. Murashima: Polymer 223(2021) 123705.
[3] K. Hagita and T. Murashima: Macromolecules
54 (2021) 8043-8051.
[4] T. Murashima, K. Hagita, and T. Kawakatsu:
Macromolecules 54 (2021) 7210-7225.
[5] K. Kremer and G. S. Grest: J. Chem. Phys. 92(1990) 5057.
[6] R. D. Groot and P. B. Warren: J. Chem. Phys.

Fig. 2: Probability distributions of linear chains

107 (1997) 4423.

penetrating into a single ring with (Nlinear, Nring)[7] N. Iwaoka, K. Hagita and H. Takano: J. Chem.

= (80,80).

Phys. 149 (2018)114901.
[8] S. Plimpton: J. Comp. Phys. 117 (1995) 117.

We also confirmed the decrease of the[9] K. Hagita, T. Murashima, H. Shiba, N. Iwaoka,squared radius of gyration in comparison to theand T. Kawakatsu: Comput. Mater. Sci., 203

phantom chain of the sDPD model. The(2022) 111104.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Kinetics of phase transition and polyamorphism
Kazuhiro Fuchizaki, Hiroki Naruta, and Katsumi Nakamura
Department of Physics, Ehime University, Matsuyama 790-8577

The problem of what drives a liquid-liquidtransition motivated us to study entropy estimation for liquids. We first report the results
attained in FY2021. The latter part of the report consists of the outcomes obtained froma study of memory hysteresis using machinelearning (ML).
The two-phase model’s justifiability for entropy
estimation [1]The two-phase model [2] extends the onephase model for describing the thermodynamics of crystalline phases, regarding them as anaggregate of harmonic oscillators with 3N degrees of freedom (DF). Then, the logarithm of
the partition function Z is given by ln Z =∑j ln zj , where zj is the partition function of
the jth oscillator. If the microscopic states
are densely distributed to allow a continuum
description, we may rewrite this relation as∫
ln Z = dϵD(ϵ) ln z(ϵ), where D(ϵ) defines thedensity of states (DOS) in the energy range between ϵ and ϵ + dϵ. Berens et al. [3] prescribedobtaining the DOS from Fourier transforming
the velocity autocorrelation function. Thus,
the entropy for a solid state may be approxi∫∞mated as S = kB 0 dωD(ω)WSHO (ω), where
kB is Boltzmann’s constant. The analytic expression for the entropy spectrum WSHO is easily obtainable.
The one-phase model is not applicable to estimating thermodynamic properties of liquidand amorphous states with non-negligible lowfrequency modes of D(ω). Goddard et al. [2]have constructed the two-phase model basedon their intuitive observation that the DOS ofsuch non-crystalline systems looks like a superposition of DOSs of solid and gas states. They

introduced the notion “fluidicity” f , in termsof which the DOS of non-crystalline systems
could be divided into 3N f DFs of gas component Dg and remaining crystalline component
Ds . Thus, the two-phase model modifies theabove expression for the entropy as∫ ∞S/kB =dω Dg (ω|f )WSg (ω)
0∫ ∞+dω Ds (ω|1 − f )WSHO (ω). (1)0Goddard et al. [2] assumed a hard-sphere gas
to evaluate Dg and WSg . For WSg , they employed the entropy per DF for a HS system
WSHS obtainable from the Carnahan–Starling(CS) equation of state (EOS), whereas they
invoked the Chapman–Enskog (CE) theory tosettle the expression for Dg . The CE theory
also allowed them to determine f . Thus, if theactual DOS D(ω) is available from experiments
or simulations, Eq. (1) gives us an entropy estimate by putting Ds = D − Dg .
We employed a simple liquid whose thermodynamic properties are well studied to test
the two-phase model’s prediction. Thus, wechose the modified Lennard-Jones system [4]with 2048 particles, to which we conducted
isothermal–isochore molecular dynamics simulation at slightly above the critical temperature. We adopted three densities; one was thecritical density ρc , and the other two are below and above ρc . We used the λ- and thermodynamic integrations to estimate the entropies
precisely. We calculated the entropy also fromthe modified Benedict–Webb–Rubin EOS [5].
The entropies resulting from the former
three approaches coincided within the error margin. However, the two-phase model256

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

gave systematically lower entropies than those
three. The deviation increases with density.
However, the most significant deviation was
limited to 6% at the highest density examined. Because both the CS EOS and the CE
theory would not be appropriate to capturesuch a high-density liquid (even though simple), many factors employed in the two-phasemodel would cancel to attain such an accuracy. Unfortunately, because the two-phasemodel was constructed in an ad-hoc way, we
cannot give any suggestions to improve it at
this moment.
Judging the (dis)continuity of phase transition
using ML [7]
Based on the valuable discovery that thesum of weights Wsum in a convolutional neural network (CNN) behaves like an order parameter when it learns spin configurations ofa 2-dimensional Ising system as a functionof (inverse) temperature, we have proposed amethod to detect the phase-transition point at
an early stage of learning processes. The latterwork prompted us to consider whether a CNN
can judge the order of phase transition fromthe viewpoint of memory hysteresis.
When we see a series of continuously changing pictures from, say, A to B, we notice asalient change at C on its way. However, when
we view the same series in reverse order from
B to A, the noticeable point of change does
not necessarily coincide with C. This hysteresis may be related to the mechanism of ourshort-term memory equipped with our brain.
A CNN could already implement such a mechanism. Thus, it will exhibit a hysteretic behavior depending on an impetus applied througha learning process.
Here we only outline what we examined.
We used the same CNN as employed in [6].
However, the crucial diﬀerence was the wayof learning. In [6], learning data has been input randomly, as usually employed in ML. Thistime, the data was input in order of increasing(decreasing) magnitude of external parameterssuch as magnetic field and temperature. Undervarious magnetic fields, we prepared equilibrium spin configurations of the 2-dimensional
64 × 64 Ising system below and above the critical temperature. We also made equilibrium
patterns of 256 q-state Potts model for q = 3
through 7 at various temperatures below andabove the critical temperature. System B tookcare of generating these data sets.
In all of the cases examined, for a discontinuous phase transition, a sharp peak showed up
precisely at the transition point when Wsum
was plotted as a function of the externalparameter, regardless of the direction of itschange. In contrast, Wsum oﬀered a roundedpeak for a continuous transition with the peak
position shifted as if the CNN missed the exacttransition point, leaving a clear-cut hysteresis
against a cyclic change of the external parameter. We thus conclude that our approach will
be applicable to judge the order of a generalphase transition if the learning data are available.

References[1] H. Naruta and K. Fuchizaki: to be presented at The 18th International Conference on Liquid and Amorphous Metals.
[2] S-T. Lin, M. Blanco, and W. A. Goddard:
J. Chem. Phys. 119 (2003) 11792.
[3] P. H. Berens, D. H. J. Mackay, G. M.
White, and K. R. Wilson: J. Chem. 79(1983) 2375.
[4] Y. Asano and K. Fuchizaki: J. Chem.
Phys. 137 (2012) 174502.
[5] Y. Asano and K. Fuchizaki: J. Phys. Soc.
Jpn. 86 (2014) 034601.
[6] K. Fuchizaki, K. Nakamura, and D. Hiroi:
J. Phys. Soc. Jpn. 90 (2021) 055001.
[7] K. Nakamura and K. Fuchizaki: in preparation.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Three-Dimensional Finite Element Analysis of Friction
between solids
Michio OTSUKI
Graduate School of Engineering Science, Osaka University,
Osaka University, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
According to Amontons’ law, the maximum
static friction force of a solid object is
proportional to the applied loading force andindependent of the apparent contact area, which
Rigid rodindicates that the static friction coefficient does
not depend on the applied pressure and the

Sliding
direction
Viscoelastic
block
Rigid substrate
Friction force

Fig. 1: Schematic of the 3D FEM calculation.

shape of the solid. Previous studies haveclarified that Amontons’ law systematically

The object exhibits macroscopic stick-slip

breaks down for macroscopic objects due tomotions, which are characterized by the

precursor slip before the onset of bulk sliding

macroscopic static friction coefficient 𝜇& . 𝜇&[1], which is consistent with experiments [2].

decreases with the external pressure 𝑃!"# andHowever, the analysis in the previous works is

the width 𝑊 , as shown in Fig. 2, which

restricted to 2D systems. Therefore, it is notcontradicts Amontons' law. We also find thatclear whether the result is applicable to morequasi-static precursor slip occurs in the 2D

realistic 3D systems.

interface between the object and the substrateThis year, we numerically investigate thebefore bulk sliding, which is related to thesliding motion of a 3D viscoelastic object withdecrease of 𝜇& .

length 𝐿 , width 𝑊 , height 𝐻 , and Young’s
modulus 𝐸 on a solid substrate using the finite
element method (FEM) with 500,000 nodes by
MPI of 1000 processors, as shown in Fig. 1. A
Fig. 2: Static friction coefficient 𝜇! against

rigid rod slowly pushes the object with aconstant velocity. A uniform pressure 𝑃!"# isReferences

applied to the top of the object. The friction[1] M. Otsuki and H. Matsukawa: Sci. Rep. 3

force at the bottom locally satisfies Amontons’(2013) 1586.

law with the local static and kinetic friction[2] Y. Katano. et al.: Sci. Rep. 4 (2014) 6324

coefficients 𝜇$ and 𝜇% , respectively.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Constructing a Dataset of Dielectric and Thermal Properties
of Polymeric Materials
Yuta YOSHIMOTO
Department of Mechanical Engineering,
The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656
We have constructed a dataset of dielectric and[3] and MD simulations are performed using

thermal properties of polymeric materials using

the LAMMPS software package [4]. All

quantum chemical (QC) calculations andcalculations are automated using RadonPy [5]molecular

and performed on System B (ohtaka).

dynamics(MD)

simulations.

Seventy-seven polymer systems are constructed
from

the

repeating

units

of

Figure 1(a) compares calculated andpreviously

experimental values of coefficients of linear

synthesized polymers [1,2], where atomic

thermal expansion, exhibiting a weakly linear

charges are derived from QC calculations using

relation

the Gaussian 16 electronic structure package

experimental values have large uncertainties.

betweenthem,

althoughtheCalculated static dielectric constants also show
reasonable agreements with the experimental
values except for several polymers, as shown in
Fig. 1(b). These results validate our simulation
methodology,

althoughmorethoroughinvestigation is required to further improve thepredictive performance.

References[1] L. Chen et al.: npj Comput. Mater. 6 (2020)
61.
[2] S. Otsuka et al.: Int. Conf. on Emerging
Intelligent Data and Web Technologies(2011) 22.
[3] M. J. Frisch et al.: Gaussian 16, Revision

Fig. 1: Comparison of calculated andC.01 (2019).

experimental values for coefficients of[4] A. P. Thompson et al.: Comput. Phys.

–4linear thermal expansion [10 /K] (a) andCommun. 271 (2022) 108171.

static dielectric constants (b).

[5] Y. Hayashi et al.: arXiv:2203.14090 (2022).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Nanoscale phonon transport across ceramics
interfaces
Susumu FUJIIDivision of Materials and Manufacturing Science, Osaka University
Yamadaoka, Suita, Osaka, 565-0871
Nanostructures Research Laboratory, Japan Fine Ceramics Center
Mutsuno, Atsuta, Nagoya 456-8587

Lattice thermal conductivity is a fundamental property of materials, which is important
for a wide spectrum of applications, e.g., thermoelectrics, thermal barrier coatings, and electronic devices. Interfaces embedded in materials, such as grain boundaries and heterogeneous interfaces, are known to signiﬁcantly
suppress lattice thermal conduction becauseof their distinguished atomic/electronic structures from the corresponding crystal, which induce the scattering of group motion of atoms,
i.e., phonons. Recently, miniaturization ofelectronic devices and development of nanostructuring techniques have led to an increaseof number of cases in which the interfaces are
the rate-limiting factor for the thermal conduction in materials. For more precise control ofthermal conductivity, it is necessary to reveal
the mechanisms of thermal transport across interfaces from the microscopic point of view.
However, there are few studies that quantitatively reveal the correlations between interfacial atomic structures and thermal conduction,and that investigate the scattering mechanismsof phonons at interfaces. The main obstacles
are follows: (1) the lack of method to quantitatively connect the structure and thermal
conduction; and (2) the lack of method to evaluate thermal conductivity of local structure at
atomic-scale.
In this project, we have attempted to elucidate the microscopic mechanisms of inter-

facial thermal transport by using two kindsof molecular dynamics simulations. One is
the perturbed molecular dynamics simulations,in which atomic contributions to overall lattice thermal conduction (atomic thermal conductivity) can be estimated. The other isthe phonon wave packet simulations, in whichtransmission coeﬃcient of individual phonons
can be estimated. Combinations of these two
methods can provide the insights of interfacialphonon scattering from the phenomenologicaland theoretical perspectives. The necessary
codes were developed by the author and implemented to the Large-scale Atomic/Molecular
Massively Parallel Simulator (LAMMPS) [1].
We chose grain boundaries of crystalline silicons and interfaces between (1) crystalline silicon and amorphous silica (SiO2 ) and (2) crystalline and amorphous silicons as model systems, because it has many technologically important applications.
For silicon grain boundaries, we used
a machine learning potential for Si distributed in MACHINE LEARNING POTENTIAL REPOSITORY [2], which accurately reproduce the results of ab initio calculations but
are less computationally demanding. Thermal conductivity calculations using perturbed
molecular dynamics require a large computational cells with at least a few thousands ofatoms, with the time steps of more than one
million. Such large-scale calculations were per-260

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

For heterogenious interfaces between crystalline and amorphous silica, we have performed a large number of perturbed molecular dynamics and phonon wave packet simulations, by using an empirical Tersoﬀ potential,
which is less computationally demanding thanthe machine learning potential. The computational cells typically contains about a million of atoms for phonon wave packet simulations. It was found that the transmission coeﬃcients of acoustic phonons dramatically decrease as a function of the thickness of amorphous SiO2 layer, resulting in very low thermal
conductivity. The signiﬁcant amount of reﬂected phonons at the interface make the spatial depdendence of thermal conductivity evenin the crystalline silicon. Comparisons with
the interfaces between crystalline and amorphous silicons indicates that compositional dif-ferences between two materials enhance thescattering and reﬂection of phonons at the interfaces, because of the mismatch of phonon
frequencies between the two adjoined materials.
All the molecular dynamics calculations
were performed in a single node rather thanmultiple nodes. This is because it is necessary
to perform many calculations with diﬀerent
structures and diﬀerent conditions, and performing calculations on a single node is more
eﬃcient than parallel.

GB thermal resistance (10-9mK-1W-1)

formed with ﬁve diﬀerent magnitudes of perturbations for each grain boundary, to obtain the thermal conductivity with high statistical accuracy. The results indicates that
thermal conductivity of Si grain boundaries
highly depends on their microscopic atomic
structures as well as their crystal misorientations, as shown in Fig. 1 [3]. On the other
hand, phonon wave packet simulations showsthat acoustic phonons mainly conduct heat
across interfaces and the transmission coeﬃcients are not signiﬁcantly diﬀerent between
the grain boundaries with diﬀerent crystal orientation and/or atomic structures. This indicates that anharmonic nature of atomic vibrations at grain boundaries, which is naturally
included in the perturbed molecular dynamics but is intentionally excluded in the phonon
wave packet simulations, determines the interfacial thermal conduction. Additional calculations for 18 silicon grain boundaries suggestthat bond strains induced by the open-core
structures of silicon grain boundaries highly
correlate with the reduction of atomic thermal
conductivities, which should be related withthe magnitude of anhamonicity.

MLP

Tersoff

Σ5(310)/[001]Σ3(112)/[110]

1.5

_

1.0

0.5

0.0

Figure 1: Interfacial thermal resistances ofΣ5(310) and Σ3(112) grain boundaries estimated by perturbed molecular dynamics simulations, with the machine learning potentinal(MLP) and an empirical atomic potential (Tersoﬀ) [3]. The results of two diﬀerent atomic
sturctures are shown for each grain orientation.

References[1] S. Plimpton, J. Comput. Phys. 117 (1995)
1.
[2] A. Seko, arXiv:2007.14206.
[3] S. Fujii, A. Seko, Comput. Mater. Sci. 204(2022) 111137.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical Study of Spin Systems on the
Honeycomb Lattice
Chitoshi YASUDA
Department of Physics and Earth Sciences, Faculty of Science,
University of the Ryukyus, Okinawa 903-0213, JapanThe quasi-two-dimensional (quasi-2D) antiferromagnetic Heisenberg (AFH) model ona cubic lattice consisting of the nearestneighbor intra-layer (J = 1) and inter-layer(J ′ ) interactions has a ﬁnite-temperaturephase transition at which the critical behavior belongs to the universality class sameas the three-dimensional classical Heisenberg
system. In the previous work [1] on the quasi2D square-lattice AFH model using the quantum Monte Carlo method, it was numericallyfound that the Néel temperature TN obeys anuniversal relation between J ′ and the staggered susceptibility χs (TN ) of the 2D systemon the square lattice, i.e., besides an eﬀective coordination number deﬁned by ζ(J ′ ) ≡1/(J ′ χs (TN (J ′ ))) does not depend on J ′ forJ ′ ≤ 0.02, the value becomes ζ(J ′ ) ≈ 0.65z(z = 2) all for S = 1/2, 1 and ∞. The
universal relation has also been predicted byan analysis of the quantum nonlinear sigma
model [2].

at the Néel temperature. Our results suggestthat ζ/z ≈ 0.65 in the small J ′ region. The
consistent value of ζ/z in the square and honeycomb lattices indicates that ζ is a universal quantity independent of the lattice. However, the accuracy of the result for the smallest J ′ , J ′ = 0.001, is not yet suﬃcient, andfurther calculations for larger sizes might beneeded in the future. Hastings et al. haveproposed that there exists a universal function even in the region of J ′ larger than J ′where ζ is constant [2]. Our results suggestthat there is one lattice-independent function
ζ(J ′ ) at J ′ = 0.05 and 0.1.
In this project, we also research zinc phthalocyanine (ZnC32 N8 H16 (ZnPc)) and theﬂuorinated ZnPc (ZnC32 N8 F16 (F16 ZnPc))
consisting of hexagon as with the honeycomb
lattice as testing calculations for the density functional method using the program
package VASP. The compound ZnPc is anaromatic compound composed of four isoindoline units (C8 H4 N) consisting of a sixmembered ring of benzene bonded to hydrogen and a ﬁve-membered ring containing nitrogen. We conﬁrmed that the energy
levels of F16 ZnPc are deeper than those of
ZnPc. The numerical result corresponds tothe electron-accepting property of F16 ZnPc
and the electron-releasing property of ZnPc.

In this project, we research the renormalized coordination number in the quasi2D honeycomb lattice AFH model with spin
S = 1/2 using the quantum Monte Carlo
method with the continuous imaginary-timeloop algorithm, and compare the results withthose of the square lattice to investigate theuniversality. The Néel temperatures were
evaluated by ﬁnite-size scaling analysis using data up to the system size 80 × 40 × 40,
and it was conﬁrmed that there is a relation
TN ∝ 1/(b − ln(J ′ )). Here, b is a constant.
We have also estimated the renormalized coordination numbers by evaluating the staggered susceptibility on the honeycomb lattice

References[1] C. Yasuda et al, Phys. Rev. Lett. 94(2005) 217201.
[2] M. B. Hastings and C. Mudry, Phys.
Rev. Lett. 96 (2006) 027215.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Data analysis method using a tensor network
representation
KENJI HARADA
Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan

We study data analysis methods based on
tensor network representations in this study
project.
The first topic is quantum machine learning. Using tensor network schemes, we numerically study the relationship between the performance of a quantum circuit and the entanglement properties. In particular, the quantum circuits on a tree tensor network structure can be efficiently estimated about theentanglement capability[1]. We found that aquantum circuit with a high entanglement capability shows good performance in a classification problem until some hundred qubit
cases. Therefore, the entanglement capability is an important property for estimating
performance[2]. In this study, we use the system B for calculation of a tensor contraction toestimate the entanglement capability throughtensor network representations.
The second topic is tensorized neuralnetworks[3]. A tensor network as MPO represents the weight matrix in a neural network.
We numerically evaluate the profile of an entanglement property in MPO in the learning
process. It much depends on the initial tensors
in MPO[4]. We derive a stable initialization
method for MPO in the tensorized neural network. The deeper tensorized neural network
can also be stably converged by the initialization. In this study, we use the system B for
the systematic calculation of the profile of entanglement in MPO in the learning process.

gling capability of parameterized quantum circuits for hybrid quantum-classicalalgorithms. Advanced Quantum Technologies 2, 1900070 (2019).
[2] H. Manabe and K. Harada, Quantum circuit learning with tensor network structure, 23pA1-1, JPS Autumn meeting(2021).
[3] A. Novikov, D. Podoprikhin, A. Osokin,
D. Vetrov, Tensorizing Neural Networks,
NIPS 2015.
[4] Y. Asoshina and K. Harada, Entanglement Analysis of Neural Networks,
22pL4-9, JPS Autumn meeting (2021).

[1] S. Sim, Peter D. Johnson, and Alán
Aspuru-Guzik, Expressibility and entan-

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical Analysis for Stability and Dynamics
of Magnetic Structures such as SkyrmionsKenji KONDO
Research Institute for Electronic Science, Hokkaido University,
Sapporo, Hokkaido, 001-0020.

Magnetic skyrmions are expected to be promising candidates for representing and transferring one
bit of information. This is because they are topologically protected from external perturbations, which
ensures the stability of information. Moreover,they are very small in size and they are able to be
driven using the current. In this study, we utilize
the spin dynamics code “Spirit” [1] which can incorporate the demagnetization ﬁelds or can calculate three-dimensional magnetic structures in orderto perform the numerical calculations of the dynamics of topological magnetic structures such asskyrmions. In our previous work, we investigatedthe dynamics of skyrmions driven by the spin polarized current [2,3] using a handmade ﬁnite-elementmethod (FEM) program. At that time, we did nottake the demagnetization ﬁelds into consideration
since we considered the inﬂuence to be negligible.
Also, there was an aspect that we avoided considering the demagnetization ﬁelds since it takes
much time to calculate them. Thus, in this study,
we investigate the inﬂuence on the velocities of theskyrmions with the demagnetization ﬁelds or without them using Spirit. Figure 1 shows the current
density dependences of the average velocities of theskyrmions in the ferromagnets (FMs) driven by the
spin-transfer torque (STT) with the demagnetization ﬁelds or without them. In this calculation, we
assume Co thin ﬁlm as the FM and use the material
parameters of the FM from the references [4–6].
The blue and the red lines represent the averagevelocities of the skyrmions in the FMs with andwithout the demagnetization ﬁelds, respectively. It

is found that the existence or the non-existence ofthe demagnetization ﬁelds have only 3.729% inﬂuences on the velocities of the skyrmions, whichis almost negligible. Our previous estimation of
the inﬂuences on the velocities of the skyrmions isfound to be right. On the other hand, we investigate the dynamics of three-dimensional topological magnetic structures, so-called skyrmion strings,
using Spirit. The skyrmions can form string structures by spreading in the out-of-plane direction.
Especially, we investigate the diﬀerences of theskyrmion string structures under the positive andnegative Dzyaloshinskii-Moriya interaction (DMI)
constants. The signs of DMI constants are deﬁned
in Fig. 2. When the DMI vectors point outwards,
we deﬁne the DMI constant as positive. When
the DMI vectors point inwards, we deﬁne the DMI
constant as negative. Figures 2(𝑎) and 2(𝑏) show
the skyrmion string structures in the FMs in thecases of the positive and negative DMI constants,
respectively. It is found that the directions of themagnetization vectors of the skyrmion strings arecounterclockwise and clockwise when seeing fromthe top view in the cases of the positive and negative DMI constants, respectively. Figures 3(𝑎)-3(𝑐)show the contour plots of the 𝑥, 𝑦, and 𝑧 componentsof the eﬀective magnetic ﬁelds 𝐻eﬀ in the case of
the positive DMI constant, respectively. Moreover,ﬁgures 3(𝑑)-3( 𝑓 ) show the contour plots of the 𝑥,𝑦, and 𝑧 components of 𝐻eﬀ in the case of the negative DMI constant, respectively. Comparing theseresults, it is found that the eﬀective magnetic ﬁelds
𝐻eﬀ point to the opposite directions in the 𝑥𝑦-plane.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Therefore, the positive and negative DMI constantscause the magnetization vectors of the skyrmion
strings to point to the opposite directions in the 𝑥𝑦plane. As a result, there manifest themselves thecounterclockwise skyrmion strings and the clockwise skyrmion strings depending on the signs of
DMI constants. It took approximately one monthto perform all of these calculations as the computer
run time using the ISSP supercomputer system B(Ohtaka). Also, we have calculated the dynamics
of the logic gates consisting of the skyrmions in
the antiferromagnets, which we will not state here
in detail. We are preparing the paper concerning
the logic gates consisting of the skyrmions in theantiferromagnets.
45
Without demagnetization field

40

With demagnetization field

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 3: The contour plots of the 𝑥, 𝑦, and 𝑧 components of 𝐻eﬀ of skyrmion strings are shown inﬁgures (𝑎)-(𝑐) in the case of the positive DMI constant, respectively. The contour plots of the 𝑥, 𝑦,
and 𝑧 components of 𝐻eﬀ of skyrmion strings areshown in ﬁgures (𝑑)-( 𝑓 ) in the case of the negative
DMI constant, respectively.

v (m/s)35

References30
25[1] G. P. Müller, M. Hoﬀmann, C. Dißelkamp,
D. Schürhoﬀ, S. Mavros, M. Sallermann, N.
S. Kiselev. H. Jónsson, and S. Blügel, Phys.
Rev. B. 99, 224414 (2019).

20
15
10
5
0.00

0.25

0.50

0.75

1.00

1.25

2

[2] Y. Ishida and K. Kondo, J. Magn. Magn.
Mater. 493, 165687 (2020).

Currentdensity (TA/m )Fig. 1: The current density dependences of theaverage velocities of the skyrmions in the FMs withthe demagnetization ﬁelds or without them.

(a) Positive DMI constantD(b) Negative DMI constantD[3] Y. Ishida and K. Kondo, Jpn. J. Appl. Phys.
59, SGGI04 (2020).
[4] J. Sampaio, V. Cros, S. Rohart, A. Thiaville,and A. Fert, Nat. Nanotechnology. 8, 839-844(2013).
[5] L. S. E. Alvarez, K.-Y. Wang, S. Lepadatu,
S. Landi, S. J. Bending, and C. H. Marrows,
Phys. Rev. Lett. 104, 137205 (2010).
[6] D. J. Monsma and S. S. P. Parkin, Appl. Phys.
Lett. 77, 883 (2000).

Fig. 2: The 3D vector plots of the skyrmion string
structures in the FMs in the cases of (𝑎) the positiveand (𝑏) the negative DMI constants.

265

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical study on low-energy states of quantum
spin systems
Hiroki NAKANO
Graduate School of Science, University of Hyogo
Kouto, Kamigori, Hyogo 678-1297, Japan

Many-body problems have to been tackled
in the field of the condensed matter physics;
therefore, it is diﬃcult to estimate physicalquantities precisely in many cases. Quantum
spin systems are such a typical one. To investigate these systems, numerical approaches
have widely and eﬀectively been used. A lot ofcomputational studies have been carried out;
useful information of the target systems has
been provided.
Generally speaking, three methods are eﬀectively used within the Field of quantum spin
systems. The first and traditional one is thenumerical diagonalization method; the second
is the quantum Monte Carlo (QMC) method.
The third method is the density matrix renormalization group (DMRG) method. Each ofthem has some advantages; on the other hand,
it has disadvantages, too. The QMC simulations can treat significantly large systems
irrespective of the spatial dimensions of thesystems; however, the negative sign problem
in this approach prevent us with a diﬃculty
in precise evaluation of physical quantities infrustrated systems. The DMRG method is
a very useful method for a one-dimensional
system irrespective of whether the target system includes frustration or not. However,this method is still under development for thecases when the spatial dimension is larger thanone. The numerical diagonalization method
can be applicable irrespective of the presenceof frustrations and the spatial dimension. Thismethod, on the other hand, has a severe weak

point that it can treat only very small system sizes. To overcome this disadvantageof the numerical diagonalization, we developed a hybrid-type parallelized code of Lanczos diagonalization[1]. This code enables us
to treat various large systems that have notbeen previously treated yet within this method
and to evaluate physical quantities precisely.
Therefore, we examine various quantum spin
systems by this method as a primary approachin this project.

Figure 1: Floret-pentagonal lattice.
In the project in 2021, we tackled the S =1/2 Heisenberg antiferromagnet on the floretpentagonal lattice[5]. Among pentagonal lattices, studies concerning the Cairo-pentagonallattice antiferromagnet has been known[2, 3,
4]. However, the floret-pentagonal-lattice an-266

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

tiferromagnet has not been investigated to thebest of our knowledge; this system is the second example as pentagonal lattices that include equivalent two directions in the system.
(See Fig.1.) We have observed the magnetization process of this system and find magnetization plateaux at one-ninth height of the saturation magnetization, at one-third height, andat seven-ninth height. We have also discovered a magnetization jump between the onethird-height and seven-ninth-height plateaux.
The jump is a peculiar phenomenon because
this jump is away from the two plateaux. Our
study contributes much to our deeper understandings of the frustrated quantum antiferromagnets. Further investigations would clarify
nontrivial quantum eﬀects due to frustration.

References[1] H.
NakanoandA.
Terai:
J. Phys. Soc. Jpn. 78, 014003 (2009).
[2] I. Rousochatzakis, A. M. Läuchli and
R. Moessner: Phys. Rev. B 85, 104415(2012).
[3] H. Nakano, M. Isoda, and T. Sakai:
J. Phys. Soc. Jpn. 83, 053702 (2014).
[4] M. Isoda, H. Nakano, and T. Sakai:
J. Phys. Soc. Jpn. 83, 084710 (2014).
[5] R. Furuchi, H. Nakano, N. Todoroki, and
T. Sakai: J. Phys. Commun. 5, 125008(2021).

267

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of the Low-Temperature Oxidation Modelfor Alternative Fuels Using Machine Learning
Minhyeok LEE, Tomotaka MIZUNO, and Yuji SUZUKI
Department of Mechanical Engineering, School of Engineering,
The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656
To improve thermal efficiencies and reduce10

pollutant emissions of Internal Combustion
simultaneously,itiscrucial4

Number of reactions

engines5

tounderstand the detailed reaction mechanism offuels. Recently, various reaction kinetic models
have been proposed to precisely explain the

10

n-C7-12 (LLNL)
n-C8-16 (LLNL)
n-C7-12 (KUCRS)

4

n-C7 (NUI)
n-C7 (LLNL)
2 AramcoMech 2.0
3 AramcoMech 1.3
4

10

4
2

reaction process of the target fuel. However, as
10

shown in Fig. 1, as increasing the size of the fuelmolecule, the number of reactions involved isn-C1-16 (CRECK)

2n-Ci (KUCRS)USC-Mech II
GRI-Mech 3.0

2

0

2

4

6 8 10 12 14 16
Carbon number

Fig. 1: Reaction size of various kinetic models

increased exponentially. It makes hard to solve

for normal-alkane fuels.

the entire model numerically without reducing
the reaction size due to high computational costs.
1.5 x 10

particularly in the low-temperature region [1].
Therefore, we conducted numerical simulations
with full mechanisms by means of thesupercomputer system at ISSP to evaluate thenC103decrease in accuracy of the numerical estimation,

1.0[kmol/m ]HCHO molar concentration

Note that such model reduction causes a

-4

0.5
nC10

One-dimensional axisymmetric stagnation

KUCRS

nC7
0.0
600

ignition process of cool flames.

nC7

CRECK

650
700
750
800
Wall temperature, Tw [K]850

Fig. 2: Cool flame ignition of n-C7 and n-C10.

flows formed by impinging a mixture of fuel andair on a heated wall were assumed. The nozzle-

K to 850 K under the quasi-steady state. Normal-

to-wall distance was 15 mm. The outlet velocity,

heptane (n-C7H16) and -decane (n-C10H22) weretemperature, and equivalence ratio of the fuel/air

used as the fuel. Two reaction models including

mixture were 50 cm/s, 300 K, and 1, respectively.

both fuels were used, which respectively

The wall temperature was ramped up from 600

proposed by the CRECK modeling group [2]268

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

using

the

KUCRS

estimating not only the low- and intermediate-utilities

forcomplextemperature reactivity of each fuel, but also

reaction systems) [3]. The Cantera code [4] washierarchical difference with respect to theemployed to conduct numerical simulation

molecule (chain) size.

andgeneratedby(Knowledge-basing

Further improvements in the reaction model

under the above condition.

should be made through the experimental

As increasing the wall temperature, coolvalidation.

flames are ignited on the wall due to initiation of
the low-temperature oxidation. Figure 2 showsincreases of the calculated HCHO molar

References

concentration on the wall as a function of the[1] C.B. Reuter, M. Lee, S.H. Won, Y. Ju:

wall

Combust. Flame 179 (2017) 23.

temperature.

While

the

HCHO

concentration estimated by the CRECK model is[2] A. Miyoshi: KUCRS software library,higher, the onset temperature calculated by the

http://akrmys.com/KUCRS/KUCRS model is slightly lower for both fuels.

[3]

Furthermore,

http://creckmodeling.chem.polimi.itadifference

in

the

onset

The

CRECK

Modeling

Group:

temperature between two fuel is negligible for[4] D.G. Goodwin, R.L. Speth, H.K. Moffat,

the KUCRS model, but n-decane’s onset

B.W. Weber: Cantera: An object-oriented

temperature is approximately 12 K lower thansoftwaretoolkitforchemicalkinetics,

that of n-heptane in the CRECK model. It means

thermodynamics,

andtransport

processes,that two models show the discrepancy inhttps://www.cantera.org

269

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Formation of Lipid Rafts Studied by Molecular Dynamics
Simulation
Satoru G. ITOH
Institute for Molecular Science, Okazaki, Aichi 444-8787
Exploratory Research Center on Life and Living Systems, Okazaki, Aichi 444-8787
The Graduate University for Advanced Studies, Okazaki, Aichi 444-8787

In cell membranes, lipid rafts are formed by

perform MD simulations with various force

aggregation of sphingolipids and cholesterolfields for the all-atom model. We have also

molecules [1]. It has been clarified that lipid

made it possible to perform MD simulations onrafts play important roles in functions such as

molecules other than proteins. In addition, thesignal transduction and protein transport in vivo

program has been modified to allow the[2,3]. Lipid rafts are also related to virus

Coulomb replica-permutation method to scale

infection and protein aggregation [4,5]. It is

onlyessential to elucidate their structures andinteractions

formation

molecules.

processes

tounderstand

their

the

intermolecularelectrostatic

betweenganglioside

GM1

functions. Therefore, we aim to elucidate theseby using molecular dynamics (MD) simulation.

References

In particular, we are interested in lipid rafts[1] K. Simons and E. Ikonen: Nature 387

containing GM1 gangliosides, which are(1997) 569.

abundant[2] K. Simons and D. Toomre: Nat. Rev. Mol.

in

nerve

cell

membranes.

To

investigate the structure of GM1 ganglioside

Cell Biol. 1, (2000) 31.

clusters, we employed the Coulomb replica-[3] D. Lingwood and K. Simons: Sience

permutation molecular dynamics simulation [6].

327 (2010) 46.

The Coulomb replica-permutation method is[4] N. Chazal and D. Gerlier: Microbiol. Mol.

one of the Hamiltonian replica-permutation

Biol. Rev. 67 (2003) 226.

methods, and it is possible to efficiently[5] J. M. Cordy, N. M. Hooper and A. J. Turner:

investigate

Mol. Membr. Biol. 23 (2006) 111.

thecomplexstructureofbiomolecules by using this method.

[6] S. G. Itoh and H. Okumura: J. Comput.

In the last year, we have made significant

Chem. 34 (2013) 2493.

improvements to our own program to be able to270

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical calculation of spin Hall magnetoresistanceby the quantum Monte Carlo method
Takeo KATO
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

Spin Hall magnetoresistance (SMR), thatis a magnetoresistance caused by the absorption of spin current generated by the spin
Hall eﬀect in a bilayer system composed ofa metal and a magnetic insulator [1], isbeing actively studied for potential applications in spintronics devices such as memory applications. Although SMR is well described quantitatively by a phenomenologicaltheory [2], its temperature dependence for a
metal/antiferromagnetic-insulator bilayer system [3] are diﬃcult to be described by it.
In this numerical study, we evaluate the spin
conductance at the interface by expanding thetheory of Ref. [4]. The spin current is expressed in terms of the spin susceptibility of
the antiferromagnetic insulator and is calculated by the quantum Monte Carlo method. Inorder to obtain dynamic properites, we need toperform the numerical analytic continuation.
However, this is usually an ill-deﬁned probpem
and is diﬃcult to be applied for obtaining thespin conductance. We improved the method
to stably obtain the spin conductance using
only the component of Matsubara frequency ofGreen’s function and succeeded in its accurate
calculation.
As a result of examining the temperaturedependence and the thickness dependence of
the SMR, the sign was reversed as the risingtemperature rose in the negative sign from thelow temperature region, and the result agreed
with the experimental result with the peak of
the positive sign. In addition, it was conﬁrmedthat the behavior of SMR diﬀered dependingon the size of the spin of the antiferromagnetic
insulator, and that SMR at S = 1 was larger
than S = 1/2. We also showed that SMR
vanishes above the magnetic transition temperature unlike the experiment. We are now
preparing for a paper on these results [5].

Figure 1: SMR Measurement Setup.

References[1] H. Nakayama, et al., Phys. Rev. Lett.
110, 206601 (2013).
[2] Y. T. Chen, et al., Phys. Rev. B 87,
144411(2013).
[3] D. Hou, et al., Phys. Rev. Lett. 118,
147202 (2017).
[4] T. Kato, Y. Ohnuma, and M. Matsuo,
Phys. Rev. B 102, 094437(2020).
[5] T. Ishikawa, M. Matsuo, and T. Kato in
preparation.

271

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Dynamical property of a resistively shunted
Josephson junction
Tsuyoshi Yamamoto
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

Physical properties of quantum systems are
drastically changed by interaction with anenvironment, because thousand of modes inthe environment are complexly entangled withquantum states of systems. A typical example is the Kondo problem, in which a spin ofa magnetic impurity is screened by surrounding conduction electrons in a normal metal [1].
Such kind of a dissipative system has been acentral topic of condensed matter physics for along time.
One of the most notable problems in dissipative systems is a dissipation-driven quantum phase transition. In 1983, Schmid predicted that a single Josephson junction connected to a resistance, which is called the resistively shunted Josephson junction (RSJJ),
undergoes a superconductor-insulator transition at zero temperature [2]. When the resistance is larger than a resistance quantum(R > RQ = h/4e2 ), the Josephson junction
becomes insulating, while when R < RQ , it becomes superconducting (see Fig. 1). However,there is no clear experimental evidence to haveobserved the transition, and it is still controversial [3]. The recent development of superconducting circuits allows us to access the dynamical property of the RSJJ using microwave
spectroscopy while it has been discussed in thedc limit. This development motivates us to approach the RSJJ from the dynamical response,and it provides a new perspective to solve thecontroversial problem, the Schmid transition.
To this end, we calculated frequency depen-

Figure 1: (left) A Josephson junction with
the Josephson energy EJ and the charging energy EC connected to a resistance R. (right)
Schmid transition diagram. In the phase I (S),the Josephson junction becomes an insulator(a superconductor) at zero temperature.

dence of an impedance of the RSJJ circuit andexamined dynamic properties in the microwave
reﬂection via the RSJJ circuit. We ﬁrst calculated the phase-phase correlation function
deﬁned on the imaginary-time axis using thepath-integral Monte Carlo simulation [4] andthen performed the analytical continuation to
the phase-phase correlation function numerically to obtain the dynamic impedance of the
RSJJ. We checked that our numerical results
agree well with analytical results at some solvable points such as the Toulouse point and thefree-fermion point. This work is expected toprovide a deep understanding of the Josephson junction on environments, which pushes
further development for the superconducting
circuit using Josephson junctions.

272

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[1] J. Kondo, Prog. Theor. Phys. 32, 37(1964).
[2] A. Schmid, Phys. Rev. Lett. 51, 1506
(1983).
[3] A. Murani et al., Phys. Rev. X 10, 021003(2020).
[4] P. Werner and M. Troyer, Phys. Rev. Lett.
95, 060201 (2005).

273

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Elucidation of Pathways for the Crystallization of Ionic
Liquids by Large-Scale Metadynamics Simulation
Hiroki NADA
Environmental Management Research Institute,
National Institute of Advanced Industrial Science and Technology (AIST), Onogawa 16-1,
Tsukuba 305-8569

A classical molecular dynamics (MD)predicted with the FES, did not show any

simulation combined with the metadynamics

energetic barrier.

(MTD) method (hereafter, MTD simulation)

In addition, a crystal-like structure, which

was performed for an ionic liquid, 1-alkyl-3-

was different from the ordered structures for the

methylimidazolium

shallow local minima, also appeared at a highhexafluorophosphates([Cnmin]PF6, n=1 [1]), at 298 K in the NVT

freeensemble. A force field proposed by Canongia

arrangement of ions in this crystal-like structure

Lopes et al. was used for estimation of thewas different from those for the crystalline

interionic interaction [2]. The simulation

forms, which were reported in literature [1].

systemrectangular-parallelepiped

This crystal-like structure might correspond to

consisting of 108 ion pairs. The MTD

a high-pressure phase, which has not yet been

simulation was carried out using DL_POLY

found experimentally.

wasaenergyregion

on

the

FES.

The

2.20 [3], in which PLUMED 1.3 [4] wasimplemented to permit combination with theReferences

MTD method.

[1] T. Endo, H. Masu, K. Fujii, T. Morita, H.

A free energy surface (FES) obtained using

seki, S. Sen and K. Nishikawa: Cryst. Growth

discrete C-C and P-F radial distribution& Des. 13 (2013) 5383.

functions quantified by Gaussian window[2] J. N. Canongia Lopez, J. Deschamps and A.

functions as collective variables indicated a few

A. H. Pádua: J. Phys. Chem. B 108 (2004) 2038.

shallow local minima. The structure of the[3] W. Smith and T. R. Forester: J. Mol. Graph.

system at each shallow local minimum

14 (1996) 136.

represented an ordered arrangement of ions.

[4] M. Bonomi et al.: Comput. Phys. Commun.

The pathway for the formation of this ordered

180 (2009) 1961.

structure from the bulk ionic liquid, which was274

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Creation of a Method for Design of Scale Formation Control
Molecules by a Metadynamics Method
Hiroki NADA
Environmental Management Research Institute,
National Institute of Advanced Industrial Science and Technology (AIST), Onogawa 16-1,
Tsukuba 305-8569

Classical

molecular

dynamics

more pronounced effect than Na+

(MD)

ions.

simulations combined with the metadynamics

Furthermore, the simulation results suggested(MTD) method [1] (hereafter, MTD simulation)that the binding stability at the calcite surface

were conducted to elucidate the stable binding

was higher for the PMA additive than for theconformations of a deprotonated polymaleic

PAA additives, and the PAA additive with aacid (PMA) additive and two deprotonatedpolymerization degree of 10 displayed apolyacrylic acid (PAA) additives with different

binding stability that was similar to or lower

polymerization degrees in the presence ofthan that of the PAA additive with avarious countercations at a hydrated CaCO3

polymerization degree of 5.

calcite (104) surface. The MTD simulations

The present simulation method provides awere performed using DL_POLY 2.20 [2] innewstrategy for

analyzingthebinding

which PLUMED 1.3 [3] was implemented.

conformations of complex additives at material

The simulated free-energy surfaces (FES)

surfaces, developing additives that stably bindsuggested the existence of several slightly

to these surfaces, and designing additives todifferent stable binding conformations for eachcontrol crystal growth.

additive. The appearance of these distinct
binding

conformationsis

speculated

Referencestooriginate from different balances of the[1] A. Laio and M. Parrinello: Proc. Natl. Acad.

interactions between the additive, calcite

Sci. USA 99 (2002) 12562.

surface, and countercations. The binding[2] W. Smith and T. R. Forester: J. Mol. Graph.

conformations and binding stabilities at the

14 (1996) 136.

calcite[3] M. Bonomi et al.: Comput. Phys. Commun.

surfacewereaffectedbythecountercations, with Ca2+ ions displaying a

180 (2009) 1961.

275

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Stability of the hedgehog-lattice topological spin
texture in breathing-pyrochlore antiferromagnets
Kazushi AOYAMA
Department of Earth and Space Science, Graduate School of Science, Osaka University
Machikaneyama-cho, Toyonaka-shi, Osaka 560-0043

The quest for topological spin textures insolids is one of the central issues in condensed
matter physics because of their possible applications to spin-electronic devices. A magnetic skyrmion in two dimensions and a magnetic hedgehog in three dimensions are typical examples of such topological objects. In
magnetic materials, they often appear in theform of crystal orders, so-called skyrmion crystal (SkX) and hedgehog lattice (HL), where
the Dzaloshinskii-Moriya (DM) interaction is
known to be essential for their stabilities. Concerning the SkX, it has been shown that magnetic frustration serves as another stabilization
mechanism [1], but as for the HL, a counter
ordering mechanism has not been reported sofar. In view of such a situation, we havesearched for a new mechanism other than the
DM interaction for the HL. Previously, we theoretically demonstrated that the HL is realized in breathing-pyrochlore antiferromagnets
in the absence of the DM interaction, where
the nearest-neighbor (NN) exchange interactions for small and large tetrahedra, J1 andJ1′ , are assumed to be antiferromagnetic [2].
In this work, we extend our previous theoretical work, examining the stability of the HL ina wider parameter space.
We consider the J1 -J3 classical Heisenberg
model on the breathing pyrochlore latticewhich is given by

H = J1∑⟨i,j⟩S

Si · Sj + J1′∑⟨i,j⟩LSi · Sj+J3∑

Si · Sj(1)⟨⟨i,j⟩⟩

where J1 and J1′ take diﬀerent positive or
negative values due to the breathing bondalternation and J3 is the third NN antiferromagnetic interaction along the bond direction.
In the model, the breathing bond-alternationof the lattice is characterized by J1′ /J1 , andJ3 is essential for the occurrence of the HL
which in the present case, is a quadruple-Q
state characterized by the ordering vectors of(± 21 , ± 12 , ± 12 ). By performing Monte Carlosimulations, we investigate the ordering properties of the Hamiltonian (1). In our simulations, 2×105 MC sweeps are carried out under the periodic boundary condition and theﬁrst half is discarded for thermalization. Our
1 MC sweep consists of 1 heatbath sweep andsuccessive 10 overrelaxation sweeps, and observations are done at every MC sweep. The
statistical average is taken over 4 independentruns starting from diﬀerent random initial conﬁgurations.
It is found that the quadruple-Q ( 12 , 12 , 12 ) HL
is stable irrespective of the signs of J1 and J1′
and that in an applied magnetic ﬁeld, there appear six quadruple-Q states depending on thevalues of J1 and J1′ , among which three phases
including the in-ﬁeld hedgehog-lattice state exhibit nonzero total chirality [3]. We have also
checked that the HL is robust against relatively
weak single-ion magnetic anisotropies.
In addition to the three-dimensional system,
we investigate an associated two-dimensional

276

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyosystem. We have demonstrated that the J1 J3 Heisenberg model on the breathing kagome
lattice exhibits a chiral transition and that the
low-temperature chiral state can be viewed as aminiature SkX [4]. In contrast to conventional
SkX appearing in an applied magnetic ﬁeld,
the miniature SkX is realized at zero ﬁeld, suggesting that a zero-ﬁeld topological Hall eﬀect
is possible in a metallic system.

References[1] T. Okubo, S. Chung, and H. Kawamura,Phys. Rev. Lett. 108, (2012) 017206.
[2] K. Aoyama and H. Kawamura, Phys. Rev.
B 103 (2021) 014406.
[3] K. Aoyama and H. kawamura, in preparation.
[4] K. Aoyama and H. Kawamura, Phys. Rev.
B 105, (2022) L100407.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Dimensional reduction eﬀect in the two-dimensional maple-leaf lattice
Heisenberg antiferromagnet
Chisa HOTTA
Department of Basic Science, University of Tokyo
3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan

We aim to clarify the features of uniform
magnetic susceptibilities of a series of frustrated magnets in two dimensions. This year,
we focused on the maple-leaf lattice spin1/2 Heisenberg model, whose lattice structure is regarded as a 1/7-site-depleted triangular lattice. There is recently experimental
evidence that the material called bluebellite
Cu6 I6 O3 (OH)10 Cl shows a particular magnetic
susceptibility that almost perfectly matches
the Bonner-Fisher curve, namely the susceptibility curve of the one-dimensional (1D) spin1/2 antiferromagnetic Heisenberg model[1].
Motivated by this experiment, we analyzed
the ground state and the ﬁnite temperature
properties of the maple leaf lattice Heisenberg
model. By combining the analysis of the several energy eigen states of the model on aﬁnite cluster using the exact diagonalization(ED), we found that the constituent of thelow energy eigenstates have the UUD/DDU
conﬁgurations, i.e. the spins on all the triangular units of the lattice are two-up-onedown or two-down-one-up. This situation issimilar to the antiferromagnetic triangular lattice Ising model, where the UUD/DDU state
contributes macroscopically to the residual entropy. However, in our model, not all the interactions are antiferromagnetic, but the interactions on bonds forming a hexagon aroundthe depleted sites are staggard in their sign.
Even in such a case, there is a substantial
frustration eﬀect, and UUD/DDU are favored.
Due to the quantum ﬂuctuation eﬀect, these
UUD/DDU manifold mixes, and a stripe-typeground state appears. The temperature dependence of the susceptibility turned out not tomatch the Bonner-Fisher curve even though wevary the sign and amplitudes of ﬁve diﬀerent
Heisenberg interaction parameters. Instead,
we found that the susceptibility shows an almost perfect coincidence with that of the 1D
XXZ model having a ﬁnite spin gap. The reason for this dimensional reduction behavior isthat the magnetic excitation from the orderedground state resembles the spinon excitationof the 1D XXZ model above the spin gap. Indeed, ﬂipping one of the spins of the stripge
ground state, the two plaquettes(two+two triangles) with UUUD spins are formed, each carrying spin-1/2. The Heisenberg exchange interactions separate these two plaquettes into
opposite directions, while such spinon propagation takes place only in a particular spatial
direction. A series of calculations on the susceptibility of both the maple leaf lattice andthe 1D XXZ model was done using a TPQ
method combined with SSD[2] The variation ofparameters we needed to search for was large
and the 2D susceptibility is maximally given
for N = 24, 30 sites[3].

References[1] Y. Haraguchi, et.al.: Phys. Rev. B 104,
174439 (2021).
[2] C Hotta and K Asano: Phys. Rev. B 98,
140405 (2018).
[3] R. Makuta and C. Hotta: Phys. Rev. B
104, 224415 (2021).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

The eﬀect of a quantum phase transition on quantum
approximate optimization algorithm
Tatsuhiko Shirai
Department of Computer Science and Communications Engineering, Waseda University
Ookubo, Shinjuku-ku, Tokyo 169-8555−iβp H −iγp X⃗ ⃗γ ⟩ := e|β,−iβ1 H −iγ1 X

|+⟩ ,
(1)
⃗
where β = (β1 , . . . , βp ) and ⃗γ = (γ1 , . . . , γp ).
p denotes a circuit depth. X is called a∑N xmixer and adopted as X =i=1 σi whereyxz⃗σi = (σi , σi , σi ) is the Pauli operator acting
on site i. |+⟩ is deﬁned as σix |+⟩ = |+⟩ for all⃗ ⃗γ ) toi. The classical computer optimizes (β,⃗⃗minimize the value of ⟨β, ⃗γ | H |β, ⃗γ ⟩. Here, we
adopt the transverse ﬁeld Ising model given by
H = −g

e

N
∑
i=1

···e

z
σiz σi+1
−

e

N
∑

σix ,

(2)

10-1

10

6E/N

We have studied the eﬀect of a quantum phase transition on the performance ofquantum approximate optimization algorithm(QAOA) in the transverse-ﬁeld Ising model.
QAOA is a hybrid quantum-classical algorithm
designed to approximate the ground state ofa Hamiltonian H with N spins [1]. It has
a wide application in chemistry, physics, andcomputer science.
QAOA consists of calculations in a quantum
computer and classical computer. The quantum computer calculates the expectation valueof H over a variational state, which is given by

-2

10-3

10-4

10-5 0
10

g=0.8
g=0.9
g=1
g=1.1
g=1.2
slope -1
slope -2101Depth pFigure 1: p-dependences of the residual energies ∆E⃗ ⃗γ ) and the ground state)
timum values of (β,in the ferromagnetic phase, critical point, andparamagnetic phase in the thermodynamic
limit. The numerics is based on the Jordan–
Wigner transformation and time-dependent
Bogoliubov transformation. Figure 1 showsthat the asymptotic behavior discontinuously
changes at the critical point. It indicates theintimate relation between the quantum phasetransition and the performance of QAOA.

i=1

where the periodic boundary condition is imposed (i.e., ⃗σi+N = ⃗σi ). This model shows aquantum phase transition at g = gc = 1. The
ground state is ferromagnetic for g > gc , while
it is paramagnetic for 0 ≤ g < gc .
We numerically study p-dependences of theresidual energies ∆E (i.e., the energy diﬀerence between the variational state at the op-

References[1] E. Fahri, et al., arXiv:1411.4028 (2014).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Calculation of ordered structures, dynamics and opticalproperties of soft materials
Jun-ichi FUKUDA
Department of Physics, Kyushu University, Motooka 744, Nishi-ku, Fukuoka 819-0395
Our numerical study is based on the

Motivated by a recent experimental study[1] demonstrating the structural transformation

Landau-de

Gennescontinuum

theoryof a cholesteric blue phase liquid crystal

describing the orientational order by a second-(BPLC) by an electric field, we carried out arank tensor. We use the program developed insimulation study on the behavior of BPLC

Ref. [2] where we were particularly interested

under an electric field. Ref. [1] showed that ain the surface behavior, and dealt withstructure with tetragonal (I4122) symmetry,

relatively thin systems. In the present study, towhich had been known to be stable under ansimulate a system whose thickness is close to aelectric field, can be stable even after therealistic experimental value (≃12μm in Ref.

cessation of the electric field when the temporal[1]), 1,351 grid points are taken in the thickness

variation of the applied electric field isdirection. Our numerical system is on a regularappropriately controlled. Possibility of stable

grid and allows a use of OpenMP for efficient(or metastable) tetragonal structures of BPLC

calculations.
Our calculations demonstrate that theunder no electric field has never been discussed

presence of confining boundaries discretize thetheoretically.
Previous numerical studies on BPLCs under

number of periodic structures along thean electric field focused on the bulk behavior

thickness direction, and that the tetragonal(to be precise, in an infinite system withstructure is indeed metastable under no electric

periodic boundaries). We are interested in how

field. We are carrying out systematic studies on

the planar boundaries confining the BPLC will

the free energy versus the number of periodic

affect its structural stability. Elucidation of thestructures, and on the optical properties of the

dynamical behavior under a temporally varying

BPLC structures we find numerically.

electric field turns out to be a daunting task

Referenceseven with the aid of the ISSP supercomputer,[1] D.-Y. Guo et al., Nature Mater. 19 (2020) 94.

and therefore we restrict ourselves to static[2] J. Fukuda and S. Žumer, Phys. Rev.

behavior.

Research 2 (2020) 033407.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Non-equilibrium response and phase transition in thedense hard sphere systems
Masaharu ISOBE
Nagoya Institute of Technology
Gokiso-cho, Showa-ku, Nagoya, 466-8555

As the simplest models, the hard
disk/sphere systems have been investigated
via molecular simulation in both equilibriumand non-equilibrium phenomena [1]. In thisproject, we focus on the equilibration and thenon-equilibrium response interfered with thephase transition in the hard disk/sphere model
system with modern algorithms, i.e., EventChain Monte Carlo (ECMC) [2, 3], Newtonian
ECMC (NEC) [4] and Event-Driven Molecular
Dynamics(EDMD) [5].
Equilibration and relaxation times in dense
molecular systems
The equilibration and relaxation times of thephysical properties have historically been fundamental issues in molecular simulation. As
practical tasks in the molecular simulation,‘equilibration’ (relaxation toward equilibrium
states) from initial non-equilibrium states isjust preprocessing step before a production
run. Such a step needs to obtain the physicalproperties in the equilibrium state in the specific system. However, the computational costoften becomes high, especially for high-density
and larger scale particle systems, and may
sometimes exceed the human lifetime. In general, the equilibration of particle positions indense systems is much more diﬃcult due to the
excluded volume eﬀect being dominant, which
is why the crystallization and glass/jamming
transition problems remain one of the critical issues and have been actively studied recently. The two standard molecular simulation methods for many-body systems are of-ten used; one is molecular dynamics (MD)using Newton’s equations of motion, and theother is Markov chain Monte Carlo (MC) using a pseudo-random number generator. Various novel algorithms focusing on equilibration
based on MD and MC have been implemented
in the history of molecular simulation, whichenables to reduce the relaxing time. An eﬃcient algorithm for the acceleration of equilibration, termed the ‘event-chain Monte Carlo(ECMC)’ [2] was the breakthrough on this
topic. The ECMC has become one of the milestones, and its variants have been investigatedactively over the past decade [3]. To obtainthe ‘true’ equilibrium states, it is a reasonablechoice to use ECMC for positional relaxation
at first, which is the idea of a hybrid scheme [1].
Recently, an ECMC variant termed the Newtonian ECMC (NEC) was proposed [4]. In NEC,the velocity collision rule was added to dictate
the direction of particle movement. This isoften used in EDMD of hard-sphere systems.
The NEC clearly improves the eﬃciencies ofthe diﬀusion coeﬃcient, nucleation rate, andmelting process. Recently, this eﬃcient algorithm has been extended to anisotropic hard
polygons without any approximations [6].
In these ECMC and its variants (includingNEC), the systems are driven by the sequential
collisions composed of a dozen of particles thatseem to behave like a chain. The eﬃciency depends on chain length, physical properties, andsystem size. However, the microscopic mechanism of equilibration for each parameter re-281

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

mains elusive. To identify key factors aﬀecting equilibration in the hard disk system, we
focus on the event-based algorithms [2, 4, 5]
described above and investigate the comparison between them in cases of (i) the diﬀusional
characteristics per event (collision) and (ii) the
relaxing process toward the liquid states as a
non-equilibrium response after disturbance ofthe homogeneous expansion.
(i) Diﬀusional characteristics of the eventbased algorithms in hard disk systems
To survey the key factors explaining why
the eﬃciency of equilibration diﬀered between
the event-based algorithms, we focus on thediﬀusional characteristics per event (collision)
between event-based algorithms in the liquidstates of the hard disk systems. We defined
the self- and pair-diﬀusion coeﬃcient based on
the displacement number of disks and compared the dependence in terms of the chain
length and the system size systematically. In
ECMC and NEC, as the chain length increases,
the diﬀusion coeﬃcient grows and reaches thehighest values at a specific chain length. We
visualized the spatial distribution of the accumulated number of displacements per particle
and calculated its probability density distribution. We found that NEC has an advantage
over ECMC in the diﬀusion coeﬃcient in thissystem since NEC samples homogeneously inthe system due to the Maxwell Boltzmann distribution of disk velocities for each displacement during the event chain, which can sample
disks uniformly in the liquid state [7].
(ii) Non-equilibrium response and equilibrationin hard disk melting
We then focus on the non-equilibrium response during the equilibration process induced by a disturbance of the homogeneous
expansion. In the case of EDMD, we observed
the anomalous slow equilibration in the harddisk systems around the co-existence phases
toward the liquid states in large-scale simulation via a couple of physical properties. As
the physical mechanism of this anomalous slow

equilibration, we assumed that the spatial inhomogeneity of the initial equilibrated phases
would contribute to the relaxation time significantly. The assumption was confirmed by theprobability distribution of local density andorientational order parameter [8]. We also observed anomalous slow equilibration both in
ECMC and NEC; however, the distinct diﬀerences between methods in the eﬃciency andfunctional forms of relaxation of physical properties are detected. We found that NEC and
NEC are more eﬃcient than EDMD.
As a typical non-equilibrium response, we
also investigated the thermodynamic cycles bymodeling the Stirling engine (SE) at the nanoscale molecular level [9]. We established a numerical model of a β-type SE with a displacer
piston and figured out the minimal necessary
conditions for stable rotation, as well as thelower limits of both the diﬀerence in temperature and the particle number.

References[1] M. Isobe: Mol. Sim. 42 (2016) 1317.
[2] E. P. Bernard, W. Krauth, and D. B. Wilson: Phys. Rev. E 80 (2009) 056704.
[3] W. Krauth: Front. Phys. 9 (2021) 229.
[4] M. Klement and M. Engel, J. Chem. Phys.
150 (2019) 174108.
[5] M. Isobe: Int. J. Mod. Phys. C 10 (1999)
1281.
[6] M. Klement, S. Lee, J. A. Anderson and
M. Engel, J. Chem. Theor. and Comp. 17(2021) 4686.
[7] H. Banno, D. Mugita, and M. Isobe: J. of
Phys.: Conf. Ser. 2207 012011 (2022).
[8] D. Mugita and M. Isobe: EPJ Web Conferences, 249 14004 (2021).
[9] K. Kitaya and M. Isobe: J. of Phys.:Conf. Ser. 2207 012006 (2022).

282

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Structural Formation of Patchy Particles
Takamichi TERAO
Department of Electrical, Electronic and Computer Engineering,
Gifu University, Yanagido 1-1, Gifu, 501-1132
Patchy particles are spheres in which theeffective

interaction

betweenparticlesisanisotropic. Among the patched particles, there
is interest in those that have anisotropy ininterparticle interactions due to inhomogeneous
surface charges [1]. Charged patchy particles
are expected to have a new structure, different
from previous patchy particle systems, because
Fig. 1: Modeling of a charged patchy particle

the interaction between particles can be both
attractive and repulsive.
In this study, we focused on the structuralformation of charged patchy particles, in which
the particle surface is charged and the sign ofthe surface charge is reversed between the
bipolar part and the other parts. Cluster
formation in these systems was studied bymolecular dynamics simulations. Modeling of
charged Patchy particles is shown in Figure 1.
Figure 2 shows an example of the structure

Fig. 2: Snapshot of charged patchy particles

formation of the system when the motion of thecharged patchy particles was constrained
between a pair of two-dimensional planes. In

References

thermalpatchy[1] P. D. J. van Oostrum, M. Hejazifar, C.

particles exhibit a variety of configurations,

Niedermayer, and E. Reimhult: J. Phys.:including triangular, square, pentagonal, andCondens. Matter 27 (2015) 234105.

equilibrium,thechargedhexagonal lattices.

283

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Tensor-network study of real-time dynamics in
two-dimensional quantum many-body systems
Ryui KANEKO
Department of Physics, Kindai University
Higashi-Osaka, Osaka 577-8502, JapanThe nonequilibrium physics of quantum
many-body systems have attracted much interest in recent years. Among others, real-time
dynamics of isolated quantum systems has
been investigated intensively in experiments
very recently. Such examples include analog
quantum simulators using ultracold atoms in
optical lattices [1–3] and those using Rydberg
atom arrays [4, 5]. The former is suitable forstudying the Bose-Hubbard models in 1D, 2D,
and 3D, and the latter is often used for studying the quantum Ising systems. The number ofcontrollable Rydberg atoms has now exceeded
200 [6–8], which would be more qubits thanclassical computers can handle. These recent
developments of analog quantum simulators
demand cross-validating the accuracy of experiments and numerical simulations. Althoughnumerical methods based on matrix productstates are powerful in 1D [1, 3, 9], no decisive
methods exist for simulating dynamics in 2D
systems.
In the present study, we examine the applicability of the 2D tensor-network method
based on the infinite projected entangled pairstate (iPEPS) [10, 11] for simulating the realtime dynamics. We first focus on the 2D BoseHubbard model, whose time-dependent singleparticle correlation functions have been measured in the recent experiment [3], and investigate sudden and short-time quench dynamics starting from the Mott insulator [12]. We
calculate the real-time evolved states by thesimple update algorithm. The tensor-network

Figure 1: Comparison of the time-dependent
single-particle correlation functions between
the experiment (red squares) and the iPEPS
simulations (blue line with symbols). We consider a finite-time quench and optimize thewave functions up to the bond dimensions
D = 8.
library TeNeS [13] is adopted.
We show the calculated single-particle correlation functions for the short-time quench to
the Mott insulating region in Fig. 1. They
are in good agreement with the recent experiment. We also predict how group and phasevelocities behave for the sudden quench to theweaker interaction region, which has not been
explored in experiments. Our findings would
serve as a quantitative benchmark for future
experiments.
After checking the applicability of the
iPEPS method to the 2D Bose-Hubbard
model, we apply the method to the 2D
transverse-field Ising model. We focus on asudden quench starting from the fully disordered state (Γ/J → ∞) to the disordered region (Γ > Γc ). Calculated longitudinal spin-

284

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

spin correlation functions agree very well withthe results obtained by the small-size exact diagonalization method and by the spin-wave approximation. We extract the group velocity
from the correlation functions in the stronger
field region. The group velocity is known
to be bounded above by the Lieb-Robinson
bound [14, 15]. The estimated group velocity in the present iPEPS study is much slower
than the recently updated bound [16], suggesting that there is room for improving the analytical bound.

[10] T. Nishino et al., Prog. Theor. Phys. 105,409 (2001).

References[11] F. Verstraete and J. I. Cirac, arXiv:condmat/0407066.

[1] M. Cheneau et al., Nature 481, 484(2012).

[6] S. Ebadi et al., Nature 595, 227 (2021).
[7] P. Scholl et al., Nature 595, 233 (2021).
[8] D. Bluvstein et al., Science 371, 1355
(2021).
[9] P. Barmettler et al., Phys. Rev. A 85,
053625 (2012).

[12] R. Kaneko and I. Danshita, Commun.
Phys. 5, 65 (2022).

[2] P. Jurcevic et al., Nature 511, 202 (2014).
[3] Y. Takasu et al., Sci. Adv. 6, eaba9255(2020).

[13] Y. Motoyama et al., arXiv:2112.13184.
[14] E. H. Lieb and D. W. Robinson, Commun.
Math. Phys. 28, 251 (1972)[4] E. Guardado-Sanche et al., Phys. Rev. X
8, 021069 (2018).

[15] M. B. Hastings, arXiv:1008.5137.

[5] V. Lienhard et al., Phys. Rev. X 8, 021070(2018).

[16] Z. Wang and K. R. Hazzard, PRX Quantum 1, 010303 (2020).

285

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Tensor-network study of the SU(4) Heisenberg model
on a tetramerized square lattice
Ryui KANEKO
Department of Physics, Kindai University
Higashi-Osaka, Osaka 577-8502, JapanThe SU(N ) Hubbard and Heisenberg models
have attracted much attention recently [1–4].
They can be realized in the ultracold atoms
in optical lattices and in specific antiferromagnets. Since these models possess many internal degrees of freedom and would realize novel
quantum states that are absent in the wellknown SU(2) model, it is desirable to explore
ground states of the models on various lattices.
In the present study, we focus on how multimerization affects the ground states of the
SU(N ) Heisenberg model. To this end, we consider the SU(4) antiferromagnetic Heisenberg
model [5]X

H0 = J

Pij + J 0

hijiintra

X

Pij

X X

+J

X X

Sαβ (i)Sβα (j)Sαβ (i)Sβα (j).

Figure 1: Tetramerized square lattice. WhenJ  J 0 or J  J 0 , the system decouples into
isolated four-site chains. When J = J 0 , thesystem becomes the conventional square lattice, whose ground state is believed to exhibit
simultaneous dimerization and SU(4) symmetry breaking [5].
vors 0 and 1:

hijiinterhijiintra αβ
0

J0

(1)

on a tetramerized square lattice [6] (see Fig. 1),
where Pij is a transposition operator which
exchanges flavors at site i and j, namely,
Pij |αi βj i = |βi αj i (αi , βi ∈ {0, 1, 2, 3}). It canbe written by using the flavor-changing operator Sαβ (i) = |αi ihβj | as
H0 = JJ(2)

hijiinter αβ

We specifically investigate the ground state of
the model in the presence of the population
imbalance (effective field), which favors the fla-

H = H0 + Himb
(3)
X
Himb = Dz[−S00 (i) − S11 (i) + S22 (i) + S33 (i)].
i(4)
In the limit of J 0 /J = 0 or J/J 0 = 0, thesystem decouples into four-site chains. The
ground state is an SU(4) singlet for lower fields,
while it is a resonating-valence-bond (RVB)
state consisting of the 0 and 1 flavors forhigher fields. In the presence of weak couplings
among four-site chains (0 < J 0 /J  1), a
previous cluster-mean-field study with a small
2×1 sublattice structure [6] suggests the emergence of the crystal, which is a mixture of thesinglet and RVB states, in the intermediate
field region.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

0.8
energy density

0.9 J 0/J = 0.2
1.0
1.1
1.2
1.3
1.40.0

RVB
singlet-RVB crystal
SU(4) singlet
Ground state
0.2
0.4
0.6
Dz

0.8

1.0

Figure 2: Energy comparison of selected
ground-state candidate states at J 0 /J = 0.2.
The states are obtained for the bond dimensions D = 7. In the intermediate field region(0.5 . Dz /J . 0.6), we have confirmed thatthe ground state is the singlet-RVB crystal.
To investigate the stability of such a crystal state beyond the mean-field study, weapply the 2D tensor-network method basedon the infinite projected entangled pair state(iPEPS) [7,8]. The ground-state candidate singlet and RVB states can be represented by the
iPEPS with the bond dimensions D = 7 and
D = 3, respectively. The singlet-RVB crystal can also be represented by the iPEPS with
D = 7. We consider a variety of crystal statesthat can be realized within a 2 × 2 sublattice.
We take these states as initial states and optimize these wave functions. We adopt the
TeNeS library [9] and calculate the groundstate candidates at D = 7 using the simple
update algorithm [10].
Figure 2 shows the energy comparison of
selected ground-state candidate states in thepresence of weak couplings J 0 /J = 0.2. The
iPEPS energy is slightly lower than the result obtained by the previous cluster-meanfield study [6]. On the other hand, the phaseboundaries are found to be nearly consistent
with the previous study; the singlet-RVB crystal (0.5 . Dz /J . 0.6) emerges between
the lower-field SU(4) singlet and the higherfield RVB states. The ground-state singletRVB crystal is found to be a mixture of theSU(4) singlet and RVB states in equal proportions, and mixing in different ratios result inhigher energy. As for the ground-state candidate states we have studied, the intermediate
singlet-RVB crystal is stable in the presence of
weak couplings among four-site chains.

References[1] C. Wu et al., Phys. Rev. Lett. 91, 186402(2003).
[2] C. Honerkamp and W. Hofstetter, Phys.
Rev. Lett. 92, 170403 (2004).
[3] M. A. Cazalilla et al., New J. Phys. 11,103033 (2009).
[4] A. V. Gorshkov, Nat. Phys. 6, 289 (2010).
[5] P. Corboz et al., Phys. Rev. Lett. 107,215301 (2011).
[6] Y. Miyazaki et al., AIP Advances 11,025202 (2021).
[7] T. Nishino et al., Prog. Theor. Phys. 105,409 (2001).
[8] F. Verstraete and J. I. Cirac, arXiv:condmat/0407066.
[9] Y. Motoyama et al., arXiv:2112.13184.
[10] H. C. Jiang et al., Phys. Rev. Lett. 101,
090603 (2008).

287

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Simulated scanning tunneling microscopy images ofgraphene nanoribbons with armchair edges
Junhuan LI, Kenta ARIMA
Graduate School of Engineering, Osaka University, Yamada-oka, Suita, Osaka 565-0871
We are aiming at elucidating local electronic
structures of finite-size graphene sheets and theirribbons. Besides, the bandgaps of ribbons were
investigated based on their band structures. It

impacts on scanning tunneling microscopy

helps to check the validity of our simulations and(STM) images [1]. For this purpose, we

discuss more details in simulated images.

simulated STM images of armchair-edged
graphene nanoribbons (AGNRs), using a(a) W=3a-2

simulation package named STATE (Simulation
Tool for Atom TEchnology).

W=22

W=25

W=28

W=26

W=29

W=27

W=30

We simulated STM images at a 𝑉! of −0.05
V for AGNRs with the width ranging from 𝑊 =22 to 𝑊 = 30 (in terms of ribbon width, 𝑊 is(b) W=3a-1

defined as the number of dimer lines across the

W=23

ribbon width). STM images change periodicallyas the ribbon width increases. Figures 1(a)−1(c)summarize the results for AGNRs with 𝑊 =3𝑎 − 2 , 3𝑎 − 1 , 3𝑎 , respectively. For Figure1(a) and 1(b), the electron density is slightly(c) W=3a
W=24

3.7 Å

high at the armchair edges. The dot patterns forma -√3 × √30𝑅30° superstructure in the interiorof the ribbons. In contrast, for the case of 𝑊 =0.0 Å

3𝑎 in Figure 1(c), electrons are not localized at

10 Å

edges and bright dots in the images appear toform a rectangular lattice, which resembles

Fig. 1: Simulated STM images. A unit structure
is superimposed in each image.

superstructures observed experimentally. This
periodic change of simulated images was also
confirmed to continue until reaching a width ofat least 8 nm, in which the value of 𝑊 was 65.

References

Simulated STM images at higher sample
biases, or larger absolute values than that in[1] J. Li, S. Li, T. Higashi, K. Kawai, K.
Inagaki, K. Yamamura, and K. Arima: Phys.
Rev. B 103 (2021) 245433.

Figure 1， were also calculated in the same288

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Towards a unified understanding of thermodynamic
properties in S=1/2 spherical kagome systems{W72V30} and {Mo72V30}
Yoshiyuki Fukumoto
Department of Physics, Faculty of Science and Technology, Tokyo University of Science
2641 Yamazaki, Noda, Chiba 278-8510

The spherical kagome systems, or quantumspin icosidodecahedrons, are frustrated magnetic clusters with 30 spins. It has beenargued that {W72 V30 } can be described asa regular, non-distorted, icosidodecahedron,and {Mo72 V30 } contains structural distortion[1]. The experimental magnetization curves for
those increase linearly with magnetic field [2],although a cluster Heisenberg antiferromagnet
should show stepwise behavior. In a theoretical study on {W72 V30 }, Schnack et al. has reported that the discrepancies are attributed tothe distribution of nearest-neighbor exchange
couplings, which is called bond-randomness,where the width of the variance in exchangeinteractions was estimated to be 30% of the average value J = 115K [2]. On the other hand,
our group has reported that the incorporationof about 10% of Dzyaloshinskii-Moriya (DM)interactions also leads to the collapse of thestaircase structure [3].
Subsequently, Kihara et al. experimentallymeasured specific heats of both materials at
temperatures T < 11K under magnetic fields
up to 15T [4], and revealed that magnitudesof the specific heats are comparable to calculated results of the non-distorted and distorted
Heisenberg models [1]. For {Mo72 V30 }, temperature dependence of the specific heats has
a shoulder around 2 ∼ 3K and depends onmagnetic field, which is consistent with calculated results with the distorted Heisenberg
model [1]. However, for {W72 V30 }, the calculated specific heats with the non-distorted

289

Heisenberg model shows a peak around 2K andsignificant magnetic field dependence, but theexperimental result has no peak and does notshow magnetic field dependence. As for thedisappearance of the 2K peak, a possible origin
is blurring of the density of states due to thebond randomness. Because the 2K peak comesfrom low-energy singlet excitations, we expectthat the 2K peak is readily dispersed by about
10% bond randomness, which is much smaller
than Schnack’s value [2]. We actually calculate
the density of state and specific heat to confirm
this expectation [5]. However, quantitative reproduction of experiment is not achieved.
It is interesting to study whether larger bondrandomness leads to quantitative reproductionof experimental specific heat or not. We also
calculate the case of 30% bond randomness
and find that the magnetic field dependence
becomes smaller and the shape of the curve
approaches to the experiment, which suggests
an adequate choice of bond randomness, which
would be 40-50%, gives quantitative reproduction. On the other hand, because the specificheat of {Mo72 V30 } has magnetic field dependence and a shoulder in it’s temperature dependence, we naively expect {Mo72 V30 } has
no bond randomness. The investigation of theorigin of presence or absence of the bond randomness will be an issue in the future.
[1] N. Kunisada et al., PTEP 2014, 41I01 (2014).
[2] J. Schnack et al., arXiv:1304.2603v1.
[3] Y. Fukumoto et al., JPSJ 87, 124710, 2018.
[4] T. Kihara et al., PRB 99, 064430 (2019).
[5] M. Motohashi et al., arXiv:2112.07923v1.

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical studies on excitation spectra of
Heisenberg antiferromagnets on the triangular andkagome lattices
Yoshiyuki Fukumoto
Department of Physics, Faculty of Science and Technology, Tokyo University of Science
2641 Yamazaki, Noda, Chiba 278-8510

This project consists of two research topics, (i) virational study of the triangular-latticesystem with the fermionic representation and(ii) series expansion study of the kagomelattice system in Cs2 Cu3 SnF12 .
As for (i), a neutron scattering experiment on Ba3 CoSb2 O9 revealed the existenceof spinon continuum in the dynamical structure factor, in addition to magnon excitations[1]. Zhang et al. used the fermionic spinon operators to study the spinon continuum within
random-phase approximation (RPA) [2]. This
RPA treatment, however, does not exclude unphysical states exactly. This year, we havedeveloped a program code using Monte-Carlo
method to obtain the energy of the variational
wave function proposed by Zhang et al. [1],completely considering the constraints. We
also developed a program code to calculate thevariational energy for a 36-site system exactly,
without using Monte-Carlo sampling. The
variational parameter is the strength of thestaggered magnetic field conjugate to the 120
degree structure. We use wavenumbers thatsatisfy periodic or anti-periodic conditions in
two directions of the triangular lattice. There
are four combinations of wave numbers, andwe make four states from each. The optimal
combination of the four states is found by solving the generalized eigenvalue problem. In thenext fiscal year, we will start developing a program code for the particle-hole excitations to
obtain the dynamic structure factor.
As for (ii), Cs2 Cu3 SnF12 has the q=0 order,
and a theoretical analysis, based on the lin-290

ear spin wave theory, of the observed magnon
dispersion resulted in the exchange parameter
which is 40% less than the result by an analysis
of susceptibility. This fact indicates diﬃcultyin the linear spin wave theory for frustrated
systems.
In this study, we calculate the dispersion relation by series expansion from the Ising limit.
We include Dzyaloshinskii-Moriya (DM) interactions into our model, where we set the DM
vector to be perpendicular to the plane on
which ordered moment lies. The direction of
the DM vector is chosen to stabilize the q=0
state. The linked cluster expansion algorithm
is used to make expansion coeﬃcients. We developed a calculation program using the previous research that applied the cluster expansion method to the triangular-lattice system
as a benchmark test [3], and extended it to the
kagome-lattice system. As a result, it is clarified that the bandwidth of the magnon spectrum in the series expansion is about 1/4 ofthe linear spin wave theory, and its shape isalso changed significantly. We also find thatthe correction for the linear spin wave theory
is larger in the kagome lattice than in the caseof the triangular lattice. Also, the shape ofthe magnon spectrum obtained by series expansion is comparable to the experimental results of Cs2 Cu3 SnF12 . It is speculated that theagreement can be improved by making the DM
interaction more realistic in the future.
[1] S. Ito et al., Nat. commn. 8, 235, 2017.
[2] C. Zhang et al., PRB 102, 075108, 2020.
[3] W. Zheng et al., PRB 74, 224420, 2006.

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Gapless symmetry-protected topological phase ofquantum spin system
Yuichiro HIDAKA1 , Shunsuke C. FURUYA2,3 , Atsushi UEDA1 , and Yasuhiro TADA4
1
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581
2
Department of Physics, Ibaraki University
Mito, Ibaraki 310-8512
3Department of Basic Science, University of Tokyo
Meguro, Tokyo 153-8902
4
Quantum Matter Program, Graduate School of Advanced Science and Engineering,
Hiroshima University, Higashihiroshima, Hiroshima 739-8530

Classifying phases of matter is one of theparamount issues in condensed matter physics.
One of the important classes of the quantum
phase of matter is symmetry-protected topological (SPT) phases. A SPT phase is a gapped
phase which preserves some given symmetries
but not adiabatically connected to a trivial
phase without breaking the symmetries [1].
Recently many researchers attempt to extend
the concept of SPT phase into gapless system[2, 3].
In the present study, we proposed a quantum
spin model that has the properties of gaplessness and nontrivial SPT phase simultaneously.
The model we proposed is the anisotropic triangular strip (ATS) XXZ model, shown in
Fig.1, which consists of three-leg antiferromagnetic ladder with frustrated interchain couplings. We used the density matrix renormalization group (DMRG) method to calculate
the ground state of the ATS XXZ model at
the specific parameters, J = 1.0, ∆ = 0.8, and
J× = 0.5. We used the ITensor and TeNPy
libraries [4, 5].

that the central charge of the ATS XXZ model
is one. The calculation result of central charge
is shown in Fig.2, and the central charge become close to one, which is derived from the extrapolation of the entanglement entropy about
the system size. In addition, Fig.3 shows thecalculation result of entanglement spectrum
and we can see double degeneracy, which is an
important feature of Haldane state in quantum spin system. From these two results, theground state of ATS XXZ model is TomonagaLuttinger liquid which has the property of nontrivial SPT phase. Therefore we can conclude
that the ground state of ATS XXZ model with
J = 1.0, ∆ = 0.8, and J× = 0.5, is in gapless SPT phase. We presented these results atthe 2022 Annual (77th) Meeting of the Physical Society of Japan [6].

We found that the entanglement entropy of
the ATS XXZ model fits with Calabrese-Cardy
formula of open boundary condition. According to the conformal field theory, it is expected

Figure 1: ATS XXZ model

291

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 2: Entanglement entropy of the ATS
XXZ model. The purple line is the fitting
line of entanglement entropy by the CalabreseCardy formula.

Figure 3: Entanglement spectrum of ATS XXZ
model.

References[1] X. Chen, Z.-C. Gu, and X.-G. Wen, Phys.
Rev. B 83, 035107 (2011).
[2] T. Scaﬃdi, D. E. Parker, and R. Vasseur,
Phys. Rev. X 7, 041048 (2017).
[3] S. C. Furuya and M. Oshikawa, Phys.
Rev. Lett. 118, 021601(2017).
[4] M. Fishman, S. R. White, and E. M.
Stoudenmire, arXiv:2007.14 (2020).
[5] J. Hauschild and F. Pollmann, SciPost
Phys. Lect. Notes , 5 (2018).
[6] Y. Hidaka, S. C. Furuya, A. Ueda, and Y.
Tada: in preparation.

292

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of multiscale simulation techniquefor liquids and solids
Takahiro MURASHIMA
Department of Physics, Tohoku University,
6-3, Aramaki-Aza-Aoba, Aoba-Ward, Sendai, Miyagi 980-8578
Predicting the flow and deformation of soft

elongational flow.)matter and composite materials is still a very
difficult problem. Aside from the problem ofsolving macroscale continuum equations, there
are difficulties in determining constitutive lawsthat characterize materials. An approach todetermine the constitutive law (rheology) of amaterial using molecular simulations has been
popular in recent years. Multiscale simulations
that connect these molecular simulations tocontinuum simulations as constitutive laws do

Fig.1: Polymers under uniaxial elongation 𝜅𝜅 =𝜖𝜖̇00
�0 𝜖𝜖̇/2 0 �.
0 0 𝜖𝜖̇/2

not explicitly require constitutive laws, thus
avoiding the difficulty of deriving constitutive
laws [1]. However, there is a problem ofboundary conditions for treating general flow

For general deformations in the molecularfields in molecular dynamics simulations.

dynamics simulation, we proposed a method

Therefore, in this research project, wethat uses QR decomposition to exclude theattempted to extend the boundary conditions torotational component of the deformation tensor

solve this problem.

and impose only pure deformations on the

Recently, we have developed the UEFEX

molecular simulation system [3]. Here, we

method [2], which enables large-elongationconsidered problems in which large

flow simulations. Here, the elongation axis anddeformations and rotations do not occur. This

the unit cell are not parallel to each other totime, we extended this method to include

avoid collapsing the unit cell under

vortex flow in fluids. (Figure 2 shows aelongational deformation. （Figure 1 shows thepolymer chain in a rotating flow.) Before

steady state of polymer chains under uniaxial

293Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

conducting multiscale simulations using thismethod, we are currently conducting an

References

analysis assuming a corner vortex phenomenon[1] T. Murashima, T. Taniguchi, EPL 96 (2011)that appears in polymer melts. We intend to18002.

summarize the results in a future paper.

[2] T. Murashima, K. Hagita, T. Kawakatsu,
Nihon Reoroji Gakkaishi 46 (2018) 207.
[3] T. Murashima, S. Urata, S. Li, Euro. Phys. J.
B 92 (2019) 211.

Fig. 2: Polymers under rotational flow 𝜅𝜅 =0 𝑎𝑎̇ 0�−𝑏𝑏̇ 0 0�, where 𝑎𝑎̇ > 𝑏𝑏̇.
0 0 0

294

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ashkin-Teller-like phase transition in thetwo-dimensional classical dimer-monomer model
Satoshi MORITA
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

An attractive interaction between dimersaligning on a square induces finite-temperaturephase transitions [1, 2]. The phase transition between the liquid and columnar phases
is known as the Kosterlitz-Thouless transition.
When monomers are introduced, the criticalexponents smoothly change and its universality class is the same as the Ashkin-Teller(AT) model. On the other hand, another ordered phase appears between the two phases
when the nearest-neighbor attractive interaction along the dimer direction is sufficiently
large [3]. This phase called the nematic phasebreaks only the lattice rotational symmetry.
Although preceding studies reported these interesting features, an intermediate parameterregion, where two attractive interactions arecomparable, were not investigated. It is notknown yet how the phase transition between
the columnar and disordered phases splits into
two transitions involving the nematic phase.
To address this problem, we investigate aclassical dimer-monomer model on the squarelattice by using the Monte Carlo (MC) method
and the tensor network (TN) method. For the
MC method, we generalize the worm algorithm
to the grand-canonical ensemble of this dimer
model. The TN method for infinite systems iscomplementary to the MC method. From the
TN representation of the partition function,
the row-to-row transfer matrix is constructed
as the matrix product operator (MPO). Itseigenvector with the maximum eigenvalue isapproximated by the uniform matrix prod-

uct state (uMPS). We determine the phasestructure and find the existence of the multicritical point. The universality classes of thephase transitions are discussed by estimating
the scaling dimension and the central charge.
We find that the columnar and nematic orders
correspond to the magnetization and polarization in the Ashkin-Teller model, respectively.
The estimated scaling dimensions clearly indicate the Ashkin-Teller universality class. We
also confirm the 4-state Potts universality at
the multi-critical point.

Figure 1: A typical configuration of the nematic and disordered phases generated by theMC simulations.

References[1] F. Alet, et al., Phys. Rev. Lett. 94, 235702(2005).
[2] F. Alet, et al., Phys. Rev. E 74, 041124 (2006).
[3] S. Papanikolaou, D. Charrier, and E. Fradkin,
Phys. Rev. B 89, 035128 (2014).
[4] S. Morita, H. Lee, K. Damle, N. Kawashima,in preparation

295

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

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 3  ,          ? =0    # ! "! 9 @" # ! 9 @" 
# ! "  ! '"   ! '"    //                       ,      3  ,      ,      '           '          3  ,          # ! "# ! " 
# ! "  !  "   ! '" /      3  ,              +      //           ! "  ! '"&          //                     -   3   .          7  $.  7   >  
A 4.      8 .  7 $.  4 6
+     4.  B ?  4 B  '@''
!':" C / 5,  .  4 ?  BD?  E'!FG"1 B H 7  ,  ; B    B?  6  : !FG)") 7 >   2 7 , B ?  2 G)@ !FF:"@ H ? >    ?  2  *E !FGE"


−0.4

−0.2

0.0 ΔAF 0.2+  < =           ' % ' :                ! "                   (           
3  ,        :      -   ,          3   
  ! "   +      ! '"      &          3  ,                                           
-    3  ,      +           4;      //      5,  . 7  ,     &        
     >  
7 , )
      
 3  ,             ! '"  !  " 4 



297

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First Principle Calculation and Charge Order Structure in
Organic Charge Order Materials
Masatoshi SAKAI, Ryoma ISHII
Department of Electrical and Electronic Engineering,
Chiba University, 1-33 Yayoi-cho Inage, Chiba 263-8522

We tried to calculate the electronic structure

that, Wannier calculation was carried out byof -(BEDT-TTF)2PF6 from the first principle

RESPACK to calculate Wannier orbitals so that

calculation

Espresso,

the band dispersion curve around HOMORESPACK, and mVMC. Starting from theorbitals in scf calculation is reproduced byloading cif file into Quantum Espresso, we

using the Wannier function. Fig. 1 (a) shows

obtained the results of the scf calculation. Afterone of the selected Wannier functions used inusing

Quantum

this calculation, and Fig. 1(b) shows the band(a)dispersion curves of the Wannier function
superimposed into the result of the scf
calculation. Wannier function represents themolecular orbital of the BEDT-TTF, and band
dispersion curves are also well reproduced.
Therefore, we obtained reasonable results in(b)

RESPACK calculation in the 3x3x3 K-meshcondition. Then we carried out the cRPA
calculation

toobtaindielectric

function,

Coulomb integrals, and exchange integrals. We(c)spent a long time converging these calculations;however,weobtainedtheinteraction

parameters in -(BEDT-TTF)2PF6. Now we aretrying to execute mVMC calculation both in Fig. 1 (a) One of the calculated Wannierorbital around the Fermi level of (BEDT-TTF)2PF6. (b) Band dispersion curvesof Wannier function superimposed in the scf
calculation. (c) Coulomb interaction as afunction of inter center distance.

(BEDT-TTF)2PF6

and

-(BEDT-TTF)2I3

organic charge order system to elucidate ourexperiment.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Structural analysis of surface superstructures and atomic layermaterials using by 2DMAT on supercomputer system at ISSP
Akari TAKAYAMA
Department of Physics,
Waseda University, Ohkubo, Shinjuku-ku, Tokyo 169-8555
In our research, we use supercomputers forsupercomputer is very useful for structure

structural analysis in terms of determining theanalysis of large periodic structure and surface

structure of materials. Since structure andsuperstructure

physical properties are closely related, it isbecause they require many variables for analysis.

essential to know the exact structure in order toFigure 1 shows the rocking curve under thewithlatticereconstruction

correctly understand the physical properties.

one-beam

Generally, surface and interface structures areexperiment (circles) and from calculation (solid

complicated than bulk crystal due to structuralline) for 0-BL graphene (buffer layer) of

relaxation and structural reconstruction at

SiC(0001). From the fitting calculation for thissurface and interface. For instance, structure ofrocking curve, we determined the buckling

epitaxial graphene growth on SiC is still

structure of buffer layer and found that ourcontroversial due to the underlying-buffer layer

determined structure corresponds well with thewith a long-period (6√3×6√3-R30°). Also thestructural model proposed by Lima et al. [2].

√3×√3-Pb/Si(111) surface superstructure, which

Moreover, the ratio of bounding and free-

is known to undergo a structural phase transition

standing regions with/from substrate wereat T = 86 K, forms a “mosaic” structure, thus its

determined to be 22 % and 78 %, respectively,

detailed structure is fully understood. In thisin this sample. The ratio is consistent withstudy, we investigated the structure of graphene

previous studies [3, 4].

condition

obtained

from

the

on SiC including a buffer layer and Pb/Si(111)
surface superstructure by using total reflection
high-energy positron diffraction (TRHEPD)
method. For structure analysis, we used
“2DMAT” [1], an open source framework for 2D
material structure analysis, which is included as

Fig. 1: Structure analysis results of buffer

standard software in ISSP’s supercomputer.

layer on SiC.

Using massive parallel computer simulations on

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References

Figure 2 shows the rocking curve under the
one-beam

condition

obtainedfrom[1] Y. Motoyama, et al., arXiv:2204.04484

theexperiment (circles) and from calculation (solid[2] L. H. de Lima, et al, Chem. Commun., 50line) for mosaic phase of √3×√3-Pb/Si(111). We(2014) 13571.

have succeeded in determining the structure of[3] M. Conrad, et al., Phys. Rev. B 96 (2017)

the mosaic phase by analyzing the Pb occupancy

195304.

as a variable. In addition, no noticeable changes[4] J. D. Emery, et al., Phys. Rev. Lett. 111

in the rocking curves were observed at low (T =(2013) 215501.

13 K) and room temperatures. This suggests that[5] I. Brihuega et al., Phys. Rev. Lett. 94 (2005)

the phase transition in this structure is caused by

046101.

soft phonons [5].

Fig. 2: Structure analysis results of mosaic
phase of Pb/Si(111).

300

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Minority Driving Transition in Collective Movement
Katsuyoshi Matsushita
Department of Biological Science, Osaka University
Machikaneyama, Toyonaka 560-0043

In biological organisms, cells aggregate andform tissues to function. Cell aggregation
exhibits various dynamics, including rotationand translational movements. The transition
from the rotation to the translational movements is well known in the developmental process in Dictyostelium Discoideum (dicty) [1].
The physical mechanism of this transition has
been theoretically investigated on the basis of
the behavior of cells [2, 3]. In particular, theworks consider the response of cells to chemical gradients, which is observed in a earlier
stage of development. These works successfully explained the transition and apperently
unified the cell movements throughout the developmental process of dicty combined withthe works for later stages [4].
These works assume homogeneous cell systems. However, as well known, the transition istightly associated with cell differentiation. Cell
differentiation means the change in the material properties of the cells. Therefore, the response property to the chemical gradient may
not be conserved in the transition. Recent
advances in the investigations of this transition showed the lack of the response of dicty
cells [5]. Furthermore, both the rotational andtranslational movements do not depend on the
response [6, 7]. These results imply the existence of another physical mechanism associated with cell differentiation.
A possible mechanism is the material parameter change in the cells. In particular, therate of differentiation in population graduallychanges during the transition process with several hours [1]. Therefore, we can expect thefollowing situation: The collective movement
is rotational when the differentiated cells are aminority in the cell population. Otherwise, thecollective movement is a transnational movement. Namely, the minority change in cell population in the differentiation process drives thetransition in collective movements.
To examine this scenario of the transition,
we theoretically considered the process of cell
population change [8]. We use the cellular
Potts model [9, 10]. The cell population is assumed to consist of leader and follower cells[11]. The leader cells correspond to the differentiated cells and can lead the following cells
using the cell-cell adhesion [12]. We also consider cell polarities by memorizing the cell trajectories [13, 14]. These polarities correlatewith the adhesion [15] and stabilize the ordering of the cell movements [16, 17].
From the simulation results based on theabove model, we examine the population dependence of the collective cell movements. We
showed that the minority change in cell population in the differentiation process drives thetransition of collective movements. A motilityinducing phase separation (MIPS) inner thecell aggregation appears for intermediate populations. The MIPS divides the cell aggregation into two aggregations: a homogeneous
un-differentiated population and a highly differentiated population. Therefore, this minority change cannot explain the transition fromrotation to translational movements for stable
cell aggregations. The improvement of the scenario based on the minority change remains in
the future.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

The clarification of the origin of this aggregation division is expected to give us hints toimprove the scenario. In our recent work, weinvestigate a homogeneous cell system to identify the parameters of collective movements[18]. We find that the occurrence of the collective movement, including the rotation andtransnational movements, depends on the interface tension of the cell aggregations. This
result implies the transition due to minoritychange originates from a change in the interface tension of the aggregation. The minority change is speculated to reduce the interface
tension, and aggregation division is associatedwith the transition. This speculation implies
the fine-tuning of the interface tension in the
differentiation. However, it is not realizable ina realistic system and the necessity for anotheridea.

References[1] J. T. Bonner, The Social Amoebae: The
Biology of Cellular Slime Molds (Princeton University Press, Princeton, 2009).
[2] T. Umeda and K. Inouye, J. theor. Biol.
219, 301 (2002).
[3] B. Vasiev C. J. Weijer. J. Theor. Biol.
223, 347 (2003)

Fujimoto, Proc. Sympo. Traffic Flow
Self-Driven Particles 26 39-42 (2020).
[9] F. Graner and J. A. Glazier, Phys. Rev.
Lett. 69, 2013 (1992).
[10] F. Graner, J. Theor. Biol. 164, 455(1993).
[11] A. J. Kabla, J. R. Soc. Interface 9, 3268
(2012).
[12] K. Matsushita, Phys. Rev. E 97, 042413(2018).
[13] P. Szabó, M. Nagy, and T. Vicsek, Phys.
Rev. E 79,021908 (2007).
[14] K. Matsushita, Phys. Rev. E 97, 042413(2018).
[15] J. C. Coates and A. J. Wood. J. Cell Sci.
114, 4349 (2001)[16] K. Matsushita, K. Horibe, N. Kamamoto,and K. Fujimoto, J. Phys. Soc. Jpn. 88,
103801 (2019).
[17] K. Matsushita, S. Yabunaka, and K. Fujimoto, J. Phys. Soc. Jpn. 90, 054801(2021).
[18] K. Matsushita, N. Kamamoto, M. Sudo,
and K. Fujimoto, Proc. Sympo. Traffic
Flow and Self-Driven Part. 27, 23 (2021).

[4] A. Maree et al. J Their. Biol. 199, 297(1997); Proc. Natl. Acad. Sci. USA 98,
3879 (2001) (2000).
[5] H. Hashimura, Y. V. Morimoto, M. Yasui,
and M. Ueda, Communications Biology 2,
34 (2019).
[6] W.-J. Rappel, A. Nicol, A. Sarkissian, H.
Levine, and W. F. Loomis, Phys. Rev.
Lett. 83, 1247 (1999)[7] Y. Kida, K. Pan, and H. Kuwayama, Differentiation 105, 71 (2019).
[8] K. Matsushita, S. Yabunaka, H.
Hashimura, H. Kuwayama, and K.

302

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Non-uniform thermal transport properties in proteins
Takahisa YAMATO
Graduate School of Science,
Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602

Protein molecules are thermally fluctuating andautocorrelation function is shown in blue. Its

tightly packed amino acid residues strongly

short time behavior is shown in the inset. Theinteract with each other. Such interactions arevalue of λ is shown in orange as a function ofcharacterized in terms of heat current at the

integration time, τ, for τ > 3.0 ps. The red line

atomic level. We calculated the thermal

indicates the running mean of λ with a window

conductivity of a small globular protein, villin

size of 100 fs.

headpiece subdomain, based on the linear
response theory using equilibrium molecular
dynamics simulation. The value of its thermal
conductivity was 0.3 ± 0.01 [W m –1 K–1],
which is in good agreement with experimental
and computational studies on the other proteinsin the literature (Figure 1). Heat current along
the main chain was dominated by local
vibrations in the polypeptide bonds, with amide

Figure 2: Fourier transform of the backbone

I, II, III, and A bands on the Fourier transformheat current autocorrelation function. Theof the heat current autocorrelation function [1]Fourier transform of the average heat current(Figure 2).

autocorrelation function is shown for the
backbone heat current.

References[1] T. Yamato, T. Wang, W. Sugiura, O.
Laprévote, T. Katagiri: J. Phys. Chem. B (2022)
https://doi.org/10.1021/acs.jpcb.2c00958

Figure 1: Thermal conductivity. The time
evolution of the average heat current

303

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Majorana Kramers Qubits and Yang-Lee Anyons in
Topological Superconductors
Takeshi MIZUSHIMA
Department of Materials Engineering Science, Osaka University
Toyonaka, Osaka 560-8531

We have investigated non-Abelian statisticsof Majorana Kramers pairs (MKPs) in timereversal invariant topological superconductors(TRITSCs) [1]. We have also demonstrated
that a Yang-Lee anyon system is constructedfrom Majorana bound states in topological superconductors [2].
In Ref. [1], we numerically simulated braiding dynamics of MKPs in a network of onedimensional TRITSCs, and examined the tolerance against various perturbations which
may cause decoherence of MKPs. We first considered eﬀects of a magnetic field which breaks
time-reversal symmetry. In contrast to a naive
expectation, we find the non-Abelian braidingof MKPs is robust against applied magnetic
fields provided that the initial and final statesof a braiding process are invariant under the
combination of a time reversal and a mirror reflection, even when intermediate states breakthe combined symmetry. In addition, we investigated the tolerance of non-Abelian braidings against gate-induced inhomogeneous potentials at junctions between superconducting
nanowires. The potential generally generates
a non-Majorana nearly zero-energy Andreeev
bound state at the junctions. We demonstrated that the non-Majorana states interferewith MKPs, resulting in the failure of nonAbelian braidings.
Yang-Lee anyons, described by the nonunitary conformal field theory with the central
charge c = −22/5, are non-unitary counterparts of Fibonacci anyons, obeying the sameron bath)

Metal (electFigure 1: Schematics of Yang-Lee anyon system with Majorana quasiparticles.
fusion rule. Therefore, the Yang-Lee anyon
system is expected to be a platform for realizing universal topological quantum computation. In Ref. [2], we considered a topologicalsuperconductor junction system coupled with
dissipative electron baths (see Fig. 1), which
realizes a non-Hermitian interacting Majorana
system. Numerically estimating the central
charge, we examined the condition that the
non-Hermitian Majorana system can simulate
the Ising spin model of the Yang-Lee edge singularity, and confirmed that, by controllingmodel parameters in a feasible way, the YangLee edge criticality is realized. We also discuss
the scheme for the measurement and the braiding of Yang-Lee anyons, aiming at the application to the universal quantum computation.

References[1] Y. Tanaka, T. Sanno, T. Mizushima, andS. Fujimoto: submitted.
[2] T. Sanno, M. G. Yamada, T. Mizushima,and S. Fujimoto: submitted.

304

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Extension of susceptibilities, screened exchange andspin-fluctuation integrals into ultrasoft
pseudopotentials
Mitsuaki KAWAMURA
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

In the Eliashberg theory or density
functional
theoryforsuperconductors(SCDFT) [1], where the electron-phonon,
screened Coulomb, spin-fluctuation mediatedinteractions are included non-empilically, weneed to compute the folowing product of two
Kohn-Sham orbitals
ρnkn0 k0 (r) = ϕ∗nk (r)ϕn0 k0 (r),

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

15

20

25

30

(b) Nb : Spin fluctuation

0.2
Averaged interaction

Bloch wavenumber, respectively. To perform
this product together with the ultrasoft pseudopotentials (USPP) or projector augumented
waves (PAW) that are widely used because of
the good accuracy and reasonable numericalcosts [2], we need a correction term for the
norm-conservation. Such a correction is originally proposed for the calculation of the susceptibility [3] asX∆ρnkn0 k0 (r) =hϕnk |βτ i0 ihβτ i |ϕn0 k0 iQτ ii0 (r),

NC :
US :
US wo Q :0.10q-point index
0.8(c) V : Screened exchange

0.6
0.4
0.2
0
0
1.4
1.2
1
0.8
0.6
0.4
0.2
0

τ ii0

(2)

To utilise this correction to the calculationof the spin-fluctuation mediated interaction,

10

0.3

where n (n0 ) and k (k0 ) are the band index and

P S∗
PS
AE
Qτ ii0 (r) ≡ ψτAE∗i (r)ψτ i0 (r) − ψτ i (r)ψτ i0 (r).
(3)

5

0.4

(1)

where βτ i is the projector dual to the atomic
pseudo orbital ψτPiS at atom τ and orbital i,and the augumentation charge Qτ ii0 (r) is computed from the pseudo (PS) and all-electron(AE) atomic orbitals as follows:(a) Nb : Screened exchange

5

10

15

20

25

30

35

(d) V : Spin fluctuation

Figure 1: Spin-fluctuation mediated- (a, c) andscreened exchange- (b, d) interactions averaged over the Fermi surface of Nb (a, b) and V(c, d). “+”, “×”, and “◦” idicate results with
norm-conserving (NC) ultrasoft (US) with andwithout augumentation charge Q(r), respectivelly.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[1] M. Lüders, M. A. L. Marques, N. N. Lathiotakis, A. Floris, G. Profeta, L. Fast, A.
Continenza, S. Massidda, and E. K. U.
Gross Phys. Rev. B 72, 024545 (2005).
[2] G. Prandini, A. Marrazzo, I. E. Castelli,
N. Mounet and N. Marzari:npjComputational Materials 4, 72 (2018).
https://materialscloud.org/sssp[3] M. Gajdoš, K. Hummer, G. Kresse, J.
Furthmüller and F. Bechstedt: Phys. Rev.
B 73, 045112 (2006).

100
Computed Tc [K]we implemented this formalism into our firstprinciples program package SuperconductingToolkit [4] which is based on SCDFT.
Figure 1 shows the screened exchange andspin-fluctuation interactions averaged over the
Fermi surface of Nb and V. In Nb, the effect of the augmentation charges Q is small
because the USPP for this atom is almost
norm-conserving. At the same time, V has
a significant contribution from Q due to thenodeless 3d orbitals. In Fig. 1(d), we cansee a deviation between the result by NC and
US pseudopotential even if we include thecorrection. This deviation may be because
the exchange-correlation kernel included in the
spin-fluctuation is sensitive to the charge density in the vicinity of atoms.
We also performed the benchmark of the calculation of Tc for 15 materials, namely Al, V,
Ta, In, Zn, Cd, Sn, ZrN, TaC, MgB2 , H3 S
(at a pressure of 200 GPa), CaC6 , YNi2 B2 C,
and V3 Si. Figure 2 shows the experimental,
and calculated Tc ; we performed four kindof calculations by changing superconducting
density functional, namely the conventional
plasmon-assisted [5], Sanna’s Eliashbergmimic (Sanna) [6], Sanna+Coulomb renormalization (ZC ) [7], and Sanna + ZC + Spinfluctuation [9, 8] functional.

10
Conventional :Sanna :
Sanna/ZC :Sanna/ZC/SF :

1
1

10

100

Experimental Tc [K]Figure 2:
Computed- and experimental
Tc . “+”, “×”, “4”, and “5” indicate result with conventional plasmon-assisted [5],Sanna’s Eliashberg-mimic (Sanna) [6],Sanna+Coulomb renormalization (ZC ) [7],and Sanna + ZC + Spin-fluctuation [9, 8]
functional, respectively.
[4] M. Kawamura, Y. Hizume, and T.
Ozaki: Phys. Rev. B 101, 134511 (2020).
https://sctk.osdn.jp/index.html[5] R. Akashi and R. Arita Phys. Rev. Lett.
111, 057006 (2013).
[6] A. Sanna, C. Pellegrini, and E. K. U.
Gross Phys. Rev. Lett. 125, 057001(2020).
[7] A. Davydov, A. Sanna, C. Pellegrini, J. K.
Dewhurst, S. Sharma, and E. K. U. Gross
Phys. Rev. B 102, 214508 (2020).
[8] K. Tsutsumi, Y. Hizume, M. Kawamura,
R. Akashi, and S. Tsuneyuki Phys. Rev.
B 102, 214515 (2020).
[9] F. Essenberger, A. Sanna, A. Linscheid,
F. Tandetzky, G. Profeta, P. Cudazzo,
and E. K. U. Gross Phys. Rev. B 90,
214504 (2014).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of Algorithms for Ising Machines Basedon Statistical Mechanics
Shu TANAKA
Department of Applied Physics and Physico-Informatics, Keio University
Hiyoshi, Yokohama, Kanagawa, 223-8522

Ising machines are a promising computational technique for highly eﬃcient combinatorial optimization problems. Simulated annealing and quantum annealing are known as
the internal algorithms of Ising machines, anda thorough investigation of the statistical dynamic properties of the Ising model is expected
to improve the performance of Ising machines.
In addition, investigating new ways of utilizing Ising machines is also an essential topic in
the ﬁeld of Ising machines. In this research
project, we concentrated on the following two
points.
(I) Dynamical properties of onedimensional random Ising model withrandom transverse ﬁeld [1]Quantum annealing is a method of introducing an Ising Hamiltonian and Hamiltonian
expressing noncommutative quantum ﬂuctuations. We wish to search the ground state, andby varying the coeﬃcients of each Hamiltonian with time, we eventually ﬁnd the groundstate of the Ising Hamiltonian. One of the factors that deteriorate the computational performance of quantum annealing is the reduction of the energy gap. The study of quantum phase transitions, where the energy gap
systematically decreases with system size, is acommon strategy for understanding the performance of quantum annealing from the perspective of statistical mechanics.
We considered an Ising model with random interactions deﬁned as a one-dimensional
chain. We investigate the system size depen-

dence of the energy gap and the behavior ofthe dynamical critical exponent when a transverse magnetic ﬁeld with randomness uncorrelated with the randomness of the interaction isapplied and when a transverse magnetic ﬁeld
with randomness correlated with the randomness of the interaction is applied. As a result,it was found that there is a diﬀerence between
the two cases.
(II) Black-box continuous optimization
using Ising machines [2]
An Ising machine is a hardware that takes
an Ising model or equivalent QUBO representation as input format and operates to search
its ground state. Ising machines have been applied in various situations to combinatorial optimization problems that Ising models or QUBOs can represent. On the other hand, amethod for utilizing Ising machines for blackbox discrete optimization, i.e., discrete optimization problems for which the objectivefunction is not explicitly given, was proposedby us in 2020 [3]. We extended it and proposeda method to perform black-box continuous optimization with Ising machines.

References[1] T. Shirai and S. Tanaka: Ann. Phys. 435(2021) 168483[2] S. Izawa, K. Kitai, S. Tanaka, R. Tamura,and K. Tsuda: Phys. Rev. Res. 4 (2022)
023062.

307

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo[3] K. Kitai, J. Guo, S. Ju, S. Tanaka, K.
Tsuda, J. Shiomi, and R. Tamura: Phys.
Rev. Res. 2 (2020) 013319.

308

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical Study of One Dimensional Frustrated
Quantum Spin Systems
Kazuo HIDA
Professor Emeritus, Division of Material Science,
Graduate School of Science and Engineering,
Saitama University, Saitama, Saitama 338-8570

We investigate the ground-state phases of
mixed diamond chains with bond alternation
described by the following Hamiltonian : [1]
H=

L [
∑

(1)

(1 + δ)S l (τ l
(1)

(2)

(2)

(1) (2)+ τ l )S l+1 + λτ l τ l

(1)

]
, (1)

(2)

where S l , τ l and τ l are spin operators with(1)
(2)
magnitudes Sl = τl = 1/2 and τl = 1. The
number of unit cells is denoted by L, and thetotal number of sites is 3L. Here, the parameters λ and δ control the frustration and bondalternation, respectively, as depicted in Fig. 1.
(1)

τl
1+δ
Sl
1+δ

δ=0
δ=0.004
δ=0.01
δ=0.02
δ=0.03
δ=0.04
δ=0.05+ τl )

l=1+ (1 − δ)(τ lmsp (a)1~0.807λc0(0)−
0
0.65

0.7

(b)

1−δ
λ

0.5

1−δ
(2)

τl

Figure 1: Structure of the diamond chain investigated in this work.
Deﬁning the composite spin operators T l as
(1)
(2)
T l ≡ τ l + τ l , it is evident that ∀l [T 2l , H] =0. Thus, we have L good quantum numbers
T 2l ≡ (Tl + 1)Tl where Tl = 1/2 and 3/2. The
total Hilbert space of the Hamiltonian (1) consists of separated subspaces, each of which is
speciﬁed by a deﬁnite set {Tl }.
For large λ, ∀l Tl = 1/2. Hence, for δ ̸= 0,
the ground state is equivalent to that of thespin 1/2 chain with bond alternation δ. Therefore, the ground state is a gapped spin liquid.

309

λ

0.8

δ=0
δ=0.004
δ=0.006
δ=0.008δ=0.01

msp
0.15

Sl+1

0.75

~0.807λc0(0)−

0.1

0.05

0

0.79

0.8

λ

0.81

Figure 2: (a) λ-dependence of msp calculatedby the inﬁnite-size DMRG method. (b) Magniﬁed ﬁgure around λ ∼ λc0 (0).

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo0.81
λc0(δ)

This energy gap vanishes for δ = 0. For small
λ, ∀l Tl = 3/2. Hence, the ground state isequivalent to that of the spin 1/2-3/2 alternating chain. Therefore, the ground state is aferrimagnetic phase with a spontaneous magnetization msp = 1 per unit cell. Between
these two phases, we carry out the inﬁnite-size
DMRG calculations for various conﬁgurationsof {Tl } to obtain the ground-state energy perunit cell. As a result, we ﬁnd that the groundstate undergoes a transition at λ = λc0 (δ) to aseries of ferrimagnetic phases with msp = 1/p
where p takes positive integer values. Thistransition is a ﬁrst-order transition for δ ̸= 0
with a discontinuous change mcsp in msp , while
no discontinuity is found for δ = 0.[2]The critical behaviors of mcsp and λc0 (δ)
around the critical point (δ, λ) = (0, λc0 (0))
turned out to be

(a)

0.8

0.79

0.78
0

0.15
c
msp

0.05

0.1

2/3

δ

(b)

mcsp ∝ δ 2/3 ,(2)λc0 (δ) − λc0 (0) ∝ δ 2/3 .

(3)

These
relationsanalytically.[1]

are

also

explained

0.1

References[1] K. Hida, J. Phys. Soc. Jpn. 91, 024706(2022).
[2] K. Hida, J. Phys. Soc. Jpn. 90, 054701(2021).

0.05

0
0

0.05

2/3

δ

0.1

Figure 3: δ-dependence of (a) λc0 (δ) and (b)mcsp .plotted against δ 2/3 .

310

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Quantum simulation using Ising models
Yuya SEKI
Graduate School of Science and Technology, Keio University, Kanagawa 223-8522
consider the problem of finding the groundWe have studied properties of factorization
machine with annealing (FMA) [1] for quantum

state

simulations. The FMA method approximates

Hamiltonian consists of fermions. In thisthe Hamiltonian of the target system with Ising

project, we used three encoding methods:

model through a machine learning model calledbinaryfactorization machine (FM) [2]. Instead of

domain-wallfinding the low-energy states of the target

performance for each encoding method, we

system that is hard to analysis, we investigate

calculate the distribution of the accuracy of

low-energy states of the approximated Ising

solution of the developed method by runningspin system. In FMA procedure, we use Montethe developed method repeatedly. As a result,

Carlo methods to generate low-energy samples

we obtained the optimal region of parametersfrom the trained FM. In addition, the training

where the developed method provides aprocess of FM includes the backpropagation

solution that is close to the true ground statemethod for updating the model parameters inwith a high probability for each encoding

FM, which requires a linear algebra library formethod. Adjusting the parameters, we obtaincalculation. These calculations were performed

the ground-state of the hydrogen moleculeusing multithreading to reduce the execution

where relative energy error is less than 10!" .

time. FMA includes various hyperparameters

Also, we determined the proper encodingthat should be optimized to achieve highmethod from the obtained data. Among theaccuracy solutions. To search for optimal

encoding methods, one-hot encoding shows

hyperparameters efficiently, we performed thebetter performance than the others. This result

calculation

indicates that the sparsity of data expression

inparallelbychangingtheparameters.

of

the

hydrogenencoding,

one-hot

encoding.

molecule,

whose

encoding,Toandinvestigate

determines the performance of FMA.

References

This year we developed a new method thatcombines FMA with integer-encoding methods.

[1] K. Kitai et al.: Phys. Rev. Research 2

The developed method enables us to calculate(2020) 013319.

the[2] S. Rendle: 2010 IEEE Int. Conf. Data Min.

groundstateofquantum

systems

approximately. As a benchmark problem, we(2010) 995.

311

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Large-scale molecular-dynamics simulation of silica melt and glass
under high pressure with ANN potentials by active learning
Daisuke WAKABAYASHI
Photon Factory, Institute of Materials Structure Science,High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801
Silica is well known as an archetypal oxide

obtaining required training data through active

and the compression behavior of silica glass andlearning.

melt has attracted considerable attention in

An active-learning method can be roughly

various research fields of physical sciences. Due

divided into three stages. First, multiple ANN

to the strong covalent bonding, the melting point

potentials are decided for the same set of training

is extremely high.

data and MD simulations are made with each

It is difficult to perform

experiments on silica melt under high pressure,potential.

and theoretical calculations are a powerful

made for the atomic arrangement corresponding

research tool.

to the steps for which the calculation results in

In contrast to crystalline materials, non-

Second, ab-initio calculations are

the first stage differ significantly among the

crystalline materials do not have long-range

potentials.

order, and therefore, in order to obtain reliable

added as new training data for the next potential

information,

fitting.

itisnecessary

toperform

Finally, the ab-initio results aretheoretical calculations on a system as large as

The test calculations were performed for the

possible. There is a limit to the size of thesolidification process of silica melt under highsystem which can be calculated by ab-initio

pressure. The ANN potential was determined bymethods.

In this study, we have fitted thethe machine-learning method with the potential,

potential with a machine-learning techniqueforce, and stress data obtained by ab-initio(ANN potential) on the basis of the results of ab-

calculations for a temperature range of 300-

initio calculations, and have applied it for the

5,000 K at 60 GPa with 144 atoms. Active

calculations with an extended system. However,learning was performed three times to search forin our previous projects, it has been observed

the conditions under which calculations on silica

that the large-scale calculations of melt weremelt do not diverge at 60 GPa and 4,000 K for adifficult to stabilize and quickly diverged,

system expanded to about 30,000 atoms.

making them impossible to continue. In thisThe number of data was originally 15,000

project, we tested a new method of efficiently

and about 2,000 were added for each active

312Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

learning. Although there was improvement inlearning. This may be due to the fact that thethe differences in calculation results between

active learning process increases the likelihood

ANN potentials and in the number of steps atof mixing training data of unrealistic atomic

which divergence occurred in the expanded

arrangements. It was found that active learning

system up to the second active learning, there

enables us to delay, if not completely prevent,

was almost no improvement after the third

divergence.

313

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical study of thermoelectric properties
in doped Fe2VAl: A weak-coupling approach
Kazutaka NISHIGUCHI
Graduate School of System Informatics, Kobe University
Rokkodai-cho, Nada-ku, Kobe 657-8501

1 Heusler compound Fe2 VAl

Fe (d)
V (d)

4.0

2.0

Energy (eV)

Heusler compound Fe2 VAl is one of the promising thermoelectric materials, which exhibits large
power factor P = σS 2 with σ and S being theelectrical conductivity and Seebeck coeﬃcient, respectively, although the thermal the dimensionlessfigure of merit ZT = σS 2 T/κ is not so large yetreflecting its large thermal conductivity κ.
Recently, it is experimentally observed in
doped Fe2 VAl (i.e., Fe2 V0.9 Cr0.1 Al0.9 Si0.1 andFe2.2 V0.8 Al1−y Siy ) as a weekly ferromagnetic material that ferromagnetic fluctuations enhance thethermoelectric properties such as S and P aroundthe Curie temperature (T c = 285 K). [1] It is not
only a desirable property for practical use in realistic (room) temperatures, but also a fundamental
and intriguing quantum phenomena where quantum fluctuations and thermoelectric eﬀects are entangled by electron correlations.
Motivated above, we have studied electronic
properties of Fe2 VAl using first-principles calculations based on the density functional theory (DFT) within the generalized gradient approximation (GGA). We performed DFT calculations with the Perdew–Burke–Ernzerhof (PBE)
exchange-correlation functional and the projector
augmented wave (PAW) method using The Vienna Ab Initio Simulation Package (VASP) [2] andQUANTUM ESPRESSO package. [3] One could
observe from the band structure and density ofstates (DOS) are shown in Figure 1 that the Fe andV d-orbitals around the Fermi level mainly contribute to the low-energy electronic structures.
We have also considered the dopant eﬀects on

6.0

0.0

−2.0

−4.0

−6.0

−8.0

W

L

Γ

X

W

K

Γ

a.u.

Figure 1: (Left) Band structure and (Right) DOS
of Fe2 VAl. The energy is measured from the Fermi
level. The components of Fe and V d-orbitals areprojected (by red and blue), respectively.

the doped Fe2 VAl to investigate its magnetic properties: the Cr and Fe substitution for V and the Si
substitution for Si were taken into account by the(2 × 2 × 2) supercell calculations. We could observe that the Cr and Fe substitution for V induce
the spin-polarized states and the magnetic momentarises at the Cr and Fe, respectively, while the electronic structure for the Si substitution for Si is stillparamagnetic state.
Furthermore, we have constructed the firstprinciples eﬀective model for Fe2 VAl using the
maximally localized Wannier functions with Wannier90. [4] We here found that the eﬀective modelhas to involve not only Fe and V d-orbitals mentioned above but also Al s- and p-orbitals in or-314

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

der to reproduce the original band structure aroundthe Fermi level since these orbitals highly entangle with each other and have large hybridization.
Therefore, we adopted a 19-orbital eﬀective model
for Fe2 VAl: 5(Fe − d) × 2 + 5(V − d) + 4(Al − sp).

+1/0

0/-1

Sc
+2/+1

+1/0 0/-1
Y+2/+1+1/0 0/-1La

2 122 Zintl Phase Compound
CaZn2 X2 (X = As, P)
In order to search for high-performance thermoelectric materials, the possibility of n-type dopingof CaAl2 Si2 -type Zintl phase compound CaZn2 X2(X = As, P) is explored using first-principles calculations based on DFT. [5] We consider n-type(electron carrier) doping of CaZn2 X2 with the following two situations: interstitial-site doping of alkaline earth metals AE (= Mg, Ca, Sr, Ba) andgroup 3 elements G3 (= Sc, Y, La), and G3 substitutional doping for the Ca site.
To see this, the defect formation energy of thesecharged states is evaluated within GGA using thesupercell approach. Among the considered possibilities, the interstitial-site doping of AE = Ca,
Mg or G3 = Sc, Y, and the G3 = La, Y substitutional doping for the Ca have been found to haverelatively small formation energies. In particular,
the formation energy of the La substitutional doping is found to be negative for both CaZn2 As2 and
CaZn2 P2 (Figure 2). This suggests that La can substitute the Ca site spontaneously and hence provide electron carriers, as far as these calculation
results are concerned. We have also found thatthe formation energies of the defects are smaller
for CaZn2 As2 than for CaZn2 P2 , which suggeststhat n-type doping is relatively easier for the former than for the latter.

+2/+1

Figure 2: The formation energy of the G3 substitutional doping for the Ca site Eform against the
Fermi energy ∆EF = EF − EV for CaZn2 As2 . The
group 3 elements G3 (= Sc, Y, La) are chosen as
dopant D. The dotted line denotes the position of
the conduction band minimum (EF = 0.408 eV).
tational Materials Science 6 (1996) 15; Phys.
Rev. B 54 (1996) 11169.
[3] P. Giannozzi et. al.: J. Phys.: Condens. Matter 21 (2009) 395502; J. Phys.: Condens.
Matter 29 (2017) 465901; J. Chem. Phys. 152(2020) 154105.
[4] I. Souza, N. Marzari, and D. Vanderbilt:
Phys. Rev. B 65 (2001) 035109; A. A.
Mostofi et. al.: Comput. Phys. Commun. 178(2008) 685; A. A. Mostofi et. al.: Comput.
Phys. Commun. 185 (2014) 2309; G. Pizzi
et. al.: J. Phys.: Condens. Matter 32 (2020)
165902.
[5] K. Nishiguchi, M. Ochi, C. H. Lee, and K.
Kuroki: J. Phys. Soc. Jpn. (to be published).

References[1] N. Tsujii, A. Nishide, J. Hayakawa, and T.
Mori: Sci. Adv. 5 (2019) eaat5935.
[2] G. Kresse et. al.: Phys. Rev. B 47 (1993)
558; Phys. Rev. B 49 (1994) 14251; Compu-

315

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Spontaneous formation of multiple-Q orders ininversion-symmetric Hubbard Models
Takashi UCHIDA
Hokkaido University of Science
4-1, 7-15, Maeda, Teine-ku, Sapporo 006-8585

In the last decade, multiple-Q orders inmagnetic systems have attracted attention because they sometimes reveal topologically protected magnetic structures such as magnetic
skyrmions. Typically, these structures are realized in the Dzyaloshinskii-Moriya (DM) interaction driven systems under magnetic ﬁeld.
The multiple-Q orders can also be realized
in inversion-symmetric systems where the DM
interaction is absent [1, 2]. In the present
work, we have attempted to explore theoretically the possibility of multiple-Q orders in
the inversion-symmetric systems in the absence of external magnetic ﬁeld. For this purpose, we have applied the molecular spin dynamics (MSD) method [3] to the triangularlattice single-band Hubbard model.
The MSD method is based on the functional
integral method for the spin ﬂuctuation theories and the isothermal molecular dynamics
method. The method allows us to ﬁnd automatically the magnetic structure of a large system with thousands of atoms in a unit cell at
ﬁnite temperatures. Starting from the Hamiltonian expressed in terms of the locally rotated coordinates and by adopting the static
approximation to the functional integral technique, the MSD method reduces to the generalized Hartree-Fock approximation at the
ground state.
In the numerical calculations the most timeconsuming process is the magnetic force calculation at each time step, where the local electronic structures are calculated in real

space by means of the recursion method. We
have adopted the automatic parallel calculation scheme and found it eﬀective in saving
both computing time and CPU resources.
We have performed magnetic structure calculations on a hexagonal supercell with 972
lattice points, which is embedded in a large
cluster consisting of 6 such supercells, each ofwhich are connected by the periodic boundary
condition. Under zero magnetic ﬁeld and theﬁxed value of the temperature T /t = 0.0005,
we have explored the magnetic structureschanging the Coulomb interaction strength
U/t (U/t = 3.0 ∼ 8.0) and the electron number n (n = 1.10 ∼ 1.60) along
the antiferromagnetic-ferromagnetic boundary. We have found that for U/t ∼ 3.5 andn = 1.48 ∼ 1.53 the dominant state is 3Qstructure with Q1 = (0.3889, −0.2245)2π/a,Q2 = (0.3889, 0.2245)2π/a, and Q3 =(0.0, 0.4491)2π/a (with a being the lattice constant), which is superimposed with satellite 3Q
structures with the Q vectors pointing in thesame direction ( in the direction of three axesof the triangular lattice).

References[1] T. Okubo, S. Chung, and H. Kawamura:Phys. Rev. Lett. 108 (2012) 017206[2] Y. Kakehashi: J. Phys. Soc. Jpn. 89 (2020)
094710.
[3] Y. Kakehashi, S. Akbar, and N. Kimura:Phys. Rev. B57 (1998) 8354.

316

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Molecular Dynamics Simulations of Reversibly Cross-linked Rubbers
Yusuke Yasuda
Research Center for Computational Design of Advanced Functional Materials.

National Institute for Advanced Industrial Science and Technology, Ibaraki 305-8568.
that

Reversibly cross-linked rubbers, whose

dissociationsynchronizes

tostresscross-links are made of reversible bonds, suchretardation. Self-healing test was conducted via

as hydrogen bonds, ionic bonds, and dynamic

equilibrium calculation at high temperaturecovalent bonds, have self-healing property andafter loading and unloading. In the elongation

toughness. Though many researchers haveafter equilibrium, stress recovered completely,

studiedmolecular

and our model can reproduce the feature ofmechanisms of these properties are still unclear

self-healing. (Fig.(b)) From these results, we

due to the difficulty of the observations ofhave succeeded in constructing coarse-grained

molecular dynamics. To understand thosemodel of reversibly cross-linked rubbers.

thosematerials,

thematerials, it is needed to study the relationshipbetween structure, dynamics, and properties ofthese rubbers from several research methods.
In this work, we constructed coarse-grainedmodel for reversibly cross-linked rubbers basedon Kremer-Grest model [1], by introducing
associating and dissociating condition (Fig.(a))
changing bond dissociation energy and bondpotential shape. Calculation was conductedusing molecular dynamics simulation software
packages OCTA and LAMMPS on ISSP
Supercomputer

System.

Fromequilibrium

simulation, we found that association constants
and bond lifetime are controlled by bondFig. (a) The schematic illustration of coarse-

dissociation energy and bond potential shape.

grained dynamic bonds, (b) loading-unloading

Mechanical simulation was conducted via

curves of the model.

loading-unloading test conducted in the rangeof elongation ratio λ= 1 – 4. From loading-

References [1] K, Kremer, G. S. Grest; J. Chem.

unloading simulation, stress-extension rate

Phys., 92, (1990) 5057.

curve shows stress retardation and specifichysteresis (Mullins effect, Fig.(b)) which is

Acknowledgement

observed experimentally in reversibly cross-

This

work

is

partially

supported by a project JPNP18016, commissioned

linked elastomer. We also found that theby the New Energy and Industrial Technology

dynamic bonds dissociate by elongation, andDevelopment

317

Organization(NEDO).

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of integrated interface of eigensolvers
Rokko and application to quantum spin systems
Tatsuya Sakashita
Center for Quantum Information and Quantum Biology, Osaka University
1-2 Machikaneyamachō, Toyonaka, Osaka 560-0043

To establish universal exact diagonalization
package for quantum lattice models including the Heisenberg-Kitaev model, we focusedon developing integrated interfaces for eigensolvers, “Rokko”[1].
In Rokko, we implemented the integrated interfaces for the following types:• Serial solvers for dense matrices (Eigen3,
LAPACK)• MPI parallelized solvers for dense matrices (EigenExa[2], ELPA[3], Elemental[4],ScaLAPACK)• MPI parallelized solvers for sparse matrices (Anasazi in Trilinos[5], SLEPc[6]) tocover matrix representations below:– CRS (Compressed Row Storage)– Matrix-free method (the method togive matrix-vector product routines
to solvers)• Unit and integrated test programs by
GoogleTest• Install scripts of eigensolvers for various
architectures
We prepare a paper to report design policy, software structure, and usage examples ofRokko.

References[1] T. Sakashita, R. Igarashi, Y. Motoyama,
T. Okubo, and S. Todo.
Repository of Rokko.
https://github.com/
t-sakashita/rokko.git, 2012.
[2] T.
Imamura,T.
Hirota,andT. Fukaya.
EigenExa web page.
https://www.r-ccs.riken.jp/labs/
lpnctrt/projects/eigenexa/, 2021.

Rokko has the following features:[3] ELPA Consortium. ELPA (Eigenvalue
soLvers for Petaflop Applications webpage). http://elpa.rzg.mpg.de, 2013.

• Integrated interfaces for eigensolvers andmatrices, independent of individual eigensolver libraries[4] J. Poulson. Distributed-memory dense linear algebra Elemental web page. https://github.com/elemental/Elemental, 2013.

• Rokko’s interfaces are implemented byutilizing factory. It enables the user todynamically select a solver.

[5] M. A. Heroux, R. A. Bartlett, and V. E.
Howle. Trilinos Project web page. https://trilinos.github.io, 2003.

• C, Fortran, and Python bindings of Rokko[6] V. Hernandez, J. E. Roman, and V. Vidal.
SLEPc web page. http://slepc.upv.es,
2002.

• Automatically detecting libraries by using
CMake in building Rokko

318

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Molecular dynamics analyses of ion migration at grainboundaries in solid state electrolyte
Ryo KOBAYASHI
Department of Applied Physics, Nagoya Institute of Technology,
Gokiso-cho, Showa-ku, Nagoya, Aichi 466-8555
All-solid-state battery (ASSB) is considered

GBs. From the simulation and local ion-flux

as a candidate of next generation Li-ion

analyses[1], we showed that, in poly-crystalline

batteries because it uses a solid-state electrolytematerials, the ions migrate towards the lower

instead of liquid-state electrolytes that are usedreaches of grain and go through spots at GBs,

in conventional Li-ion batteries. The key toand the high-flux spots contain migration paths

achieve high-performance in ASSB is toas low energy as the bulk ones.

reduce/control the resistivities at interfaces

In this study, we have developed a newsuch as electrode/electrolyte interface and graintechnique to obtain local ion-flux information

boundary (GB) inside electrolyte. For thisfrom non-equilibrium MD implemented in our

purpose, we need deeper understandings about

own code, nap[2]. And several MD simulation

the atomic structure and precise mechanisms ofruns and the local-ion flux analyses were

ion migration of the GBs, and the goal of thisperformed on the ISSP supercomputers.

project is to obtain new insights about them byusing large-scale molecular dynamics (MD)simulation.

References

In order to obtain atomistic insights on Liion

migrationmechanism

at

GBs,

we

[1] R. Kobayashi, K. Nakano, M. Nakayama,

performed non-equilibrium MD simulation of

Acta Materialia, 226 (2022) 117596.

large-scale poly-crystalline Li2Zr(PO4)3 (LZP)[2] Nagoya Atomistic-simulation Package (nap)system containing half a million atoms andhttp://github.com/ryokbys/nap

extracted local ion flux information around.

319

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Electronic structure in mismatched multilayer systems:
evaluation and application of the modeling scheme
Toshikaze KARIYADOInternational Center for Materials Nanoarchitectonics,
National Institute for Materials Science, Tsukuba, Ibaraki 305-0044
After the report of superconductivity inwhich gives us an intuitive understanding of thetwisted bilayer graphene, artificially stacked

physics behind the anisotropic band flattening.

two-dimensional (2D) materials with moiré

The first-principles calculations have been

pattern induced by some mismatches between

done using Quantum Espresso package, which

the layers attracts much attention. Generically,is adapted to the parallel computation andthe moiré pattern affects the electronic bandsuitable to use the supercomputing resources

structure, and can be used to realize uniqueefficiently.

band structures. Then, designing interesting

Not

only

calculating

electronic

band

band structures in artificially stacked systems is

structures itself, we also tried to extract somea current urgent topic to explore.

characteristic response tied to the unique bandIn this project, we have analyzed electronic

structure, focusing on the orbital magnetic

structures of twisted bilayer GeSe, where thesusceptibility. For that, we first derived a new

anisotropic band flattening is expected. Here,formula to calculate the orbital magnetic

the anisotropic band flattening means thatsusceptibility,

originally 2D band dispersion is squeezed into

validity using several types of toy models by

quasi 1D one in twisted bilayers. To analyze theour homemade program [2]. In order to accessband structure, we derived an effective model

the low temperature regime, we need fine meshfor twisted bilayer GeSe. There are multiple

in 𝑘-point sampling, where the parallelization

important quantities in the effective model suchby MPI is applied in our homemade program.

andnumericallytestedits

as the effective mass for each layer or theeffective interlayer tunneling. We obtain these

References

quantities making use of the first-principles[1] M. Fujimoto and T. Kariyado: Phys. Rev. B

calculations. Our analysis clarifies the relation

104 (2021) 125427.

between the crystal structure of GeSe and the[2] T. Kariyado, H. Matsuura, and M. Ogata: J.

anisotropy in the effective interlayer tunneling,

Phys. Soc. Jpn. 90 (2021) 124708.

320

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Compact spin qubits using the common gate
structure of ﬁn ﬁeld-eﬀect transistors
Tetsufumi Tanamoto
Department of Information and Electronic Engineering, Teikyo University
Utsunomiya 320-8511, Japan.

By using the ISSP supercomputer, we numerically investigate a transport properies of
the compact spin-qubit system embedded into
the common multi-gate FinFET transistors [1],where all gates are electrically tied togther as
the common gate. The quantum dots (QDs)
as qubits are coupled with their nearest Fin
conducting channels. The Hamiltonian of the
QDs and the channel is given by the tunneling
Hamiltonian:tance gyy (ω) is calculated from the Kubo for1
R
mula given by gyy (ω) = − iω[ΦRyy (ω) − Φyy (0)],iRΦyy [t] = − h̄V θ(t)⟨Jy (t)Jy (0) − Jy (0)Jy (t)⟩.
The current operator Jyi of the ith channel∑
is given by Jyi = (eh̄/(m∗ L)) ki ki c†ki s cki s ,where L is the channel length and the summation of ki is carried out over the channel.
(3)
The expression for gyy is

2e2
4[∆2 + δ 2 ]2,kdh[(∆2 − 2s33 ∆ − δ 2 )2 + 4∆2 Γ23 ]2
∑ ∑
(2)
†
†
†
c
H0 = E2 d2s d2s + E4 d4s d4s +Ek ci ki s ki s
2where k1 = 1, k2 = πne2 W , ∆ = (2EkF −i=1,3,5 ki ,s∑†ESL − ESR − s11 − s55 )/2, and δ = ESL −∗ †+[Vk1 ck1 s d2s + Vk1 d2s ck1 s ]ESR . ne2 is the number of the carriers per nm2 ,
k1
∫
∑
2
+
[Vk3 c†k3 s (d2s + d4s ) + Vk∗3 (d†2s + d†4s )ck3 s ] and sij ≡ |Vtun (ki )| /(Eki − Ekj ) is the selfenergy. Γi ≈ 2π|Vtun (ki )|2 ρF (ρF is the density
k3∑+[Vk5 c†k5 s d4s + Vk∗5 d†4s ck5 s ],(1) of state at Fermi energy EF , and Vtun is theoverlap of wave functions between the channel
k5
and the QDs in the tunneling Hamiltonian).
where the channels are numbered as 1, 3, andFigure 1(b) shows the conductance gyy of
5, and the two QDs are numbered as 2 and(i)the summation of the three current lines gyy
4. dis and ck,s are the annihilation operators(i ∈ 1, 3, 5) as a function of the energy levels ofof the QD i and the conducting electrons in
the two QDs, where ESL and ESR are either
the channel, respectively. The qubit states areES↓ or ES↑ . We can observe a double-peakdetected by the channel currents. The conducstructure around the Fermi energy where ESL
is close to ESR but ESL ̸= ESR . The symmetDEΓ Γ Γ Γric case δ = 0 gives the conventional resonant*DWH
tunneling form g = 4/[(∆ − 2s33 )2 + 4Γ23 ]2 .
1

ESL

3

3

(3)
gyy
=

5

ESR

VXEVWUDWH

References

ESL /EF
ESR /EF

Figure 1: (a) Three current lines. (b)gyy as
functions of energy levels of two quantum dots.

[1] T. Tanamoto and K. Ono, AIP Advances
11 (4), 045004 (2021).

321

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Change in period of ordinary earthquakes due to theinteraction with slow earthquakes
Takehito SUZUKI
Dept. Phys. Sci., Aoyama Gakuin University
5-10-1, Fuchinobe, Chuo-ku, Sagamihara, Kanagawa 252-5258

Two qualitatively diﬀerent behaviors of
earhtquakes have been known. One is the ordinary earthquake, which we feel naturally. The
other one is slow earthquakes, which generate
negligible seismic waves. Although the slow
earthquakes are not disastrous, they are considered to sometimes change to the ordinary
earthquakes after several repetitions. Whether
this transition occurs or not is a fatal problem
to the human society, and we should clarify thecondition for the transition to occur.

constant is kp . As widely known, this systemrepeats the dynamic slip and cessation. The
healing of pores in the cessation time is also
taken into account. However, the choice of thehealing law does not induce qualitative changes
in the result below.
We neglect the heat and ﬂuid diﬀusions during the dynamic slips. The governing equations for the ﬂuid pressure, porosity, and temperature in the slip zone during the dynamic
slip are given by

The fault rocks can be considered as poroelastic media, including pores inside it. The
pores are usually considered to be ﬁlled withwater. If the dynamic earthquake slip (frictional slip) occurs, we can consider the interaction among heat, ﬂuid pressure, and porosity[1, 2]. The slip is interpreted as the deformation around the contact area, called slip zone,
which has a ﬁnite width. During the dynamic
slip, the generation of pores [frictional heating] reduces [raises] the ﬂuid pressure in theslip zone, inducing the increase [reduction] in
the friction stress and the reduction [increase]in the slip velocity [1, 2]. Therefore, the slow
and ordinary earthquakes are dominated by
the generation of pores and the frictional heating, respectively.

ṗ = C1 Ṫ − M0 ϕ̇,The spring-block model and the interaction
between three quantities are employed to analyze the slow-ordinary transition. The single
block is assumed here. The upper substrateis drived with the constant speed Vp , and it
also loads the block via a spring whose spring

(

(1)

)

ϕ
,
ϕ∞

(2)

Ṫ = −C2 (σn0 + p)u̇,(3)ϕ̇ = α0 u̇ 1 −respectively, where C1 and C2 are positive constants. From here and below, quantities not
explained are summarized in Ref. [2]. From
Eq. (2), we obtainϕ = ϕ∞ − (ϕ∞ − ϕ0 )e−α0 u/ϕ∞ ,(4)

where ϕ0 is the porosity at the intant of theslip onset. Note that this value need not equal
to the value at time t = 0. Additionally, from
Eqs. (1)–(4), we obtain
(

(

)

)

ϕ0
ṗ =
1−
α0 e−α0 u/ϕ∞ u̇,ϕ∞(5)
where γ = C1 C2 > 0. From this representation, we can write p in terms of u to obtain−C1 C2 (σn0 + p) − M0

(

p=

322

M ′ α0σn0 + p0 − α0 0
ϕ∞ − γ)M ′ α0 −α0 u/ϕ∞ 0e−γu + α0 0e−σn ,ϕ∞ − γ(6)

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

where M0′ ≡ M0 (1 − ϕ0 /ϕ∞ ) and p0 is the ﬂuid
pressure at the instant of slip onset.
We now consider the energy conservation
law. First, note that the loading stress fromthe upper substrate must be equal to themacroscopic static friction stress at the instantof the slip onset, which leads tokp Vp ti = −µstat (σn0 + p0 ),(7)

where ti is the time when the slip initiated.
Using Eq. (7), the energy stored in the upper
spring just before the dynamic slip is given by1
1 µ2stat 0(σn + p0 )2 .
E1 = kp (Vp ti )2 =
2
2 kp

(8)

Moreover, the energy stored in the upper
spring after the cessation is written as (we assume that the upper spring does not move during the dynamic slip)1
kp (Vp ti − uf )22()2
1µstat 0(σn + p0 ) − uf , (9)
kp −
2
kp

E2 =
=

where uf is the ﬁnal slip distance for the single
slip. Furthermore, the work done to the blockby the friction stress during the dynamic slip
is obtained using Eq. (6):∫ uf (

Efric =
= −µslid[= −µslid1γ∫ uf [(
0(0)−µslid (σn0 + p) du

M 0 α0σn0 + p0 − α0
ϕ∞ − γ)e−γu]

M ′ ϕ∞+ α0 0(1 − e−α0 uf /ϕ∞ ) = 0.(11)−γϕ∞We deﬁne F (uf ) as the left hand side of Eq.
(11). The condition F (uf ) = 0 corresponds tothe condition where the elastic energy change
is equal to the energy loss due to the friction
during the single slip. It is also important that
F (uf ) includes p0 and ϕ0 . As mentioned, these
initial values are not values at t = 0, but thevalues at the slip onset of each slip.
Notably, F (uf ) is the double-well form, andthe ﬁrst well is much shallower than the second one. If F (uf ) = 0 has a solution between the wells, the slow earthquakes occur
because we can consider that the slip is inhibited. On the other hand, if F (uf ) = 0 does
not have a solution there, the solution jumps
to almost two orders larger one. This behavior
is interpreted as the ﬁrst-order phase change.
The slow-ordinary earthquake transition canbe understood as the ﬁrst-order phase change.
Additionally, we can conclude that this phasechange is governed by p0 and ϕ0 .
The analytical result described here was conﬁrmed by ISSP supercomputer. The numerical study can treat the BK model with several
blocks, and we conﬁrmed that the results here
can give useful implications to such a severalblock case. Detailed and comprehensive numerical treatments will be a potential future
work.

]

M0 α0 −α0 u/ϕ∞
+ α0
e
du
ϕ∞ − γM0 α0
σn0 + p0 − α0
ϕ∞ − γ)(1 − e−γuf )References][1] T. Suzuki, and T. Yamashita: J. Geophys.
M0 ϕ ∞+ α0(1 − e−α0 uf /ϕ∞ ) .(10)Res. 119 (2014)
ϕ∞ − γTherefore, from the energy conservation law,
we found an equation which uf must satisfy:[2] T. Suzuki: Phys. Rev. E 96 (2017)1
kp u2f + µstat (σn0 + p0 )uf
2
[ (
)
1
M0′ α00
σn + p0 − α0
(1 − e−γuf )−µslid
γ
−
γ
ϕ∞

323

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

3.5

SCCMS Projects

324Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of machine learning-aided simulations
methods for molecular liquids
Hayato SHIBA
Information Technology Center, University of Tokyo
6-2-3 Kashiwa-no-ha, Kashiwa, Chiba 277-0882

Thanks to the present status of the art where
basic simulation methodology for parallel MD
simulations is approaching its maturity, many
open source packages are commonly available
for usage on supercomputers. However, how tosimulate long-time phenomena remains a longstanding unresolved issue in molecular dynamics simulations. It is difficult to perform numerical time integration over 1010 steps whichcorresponds to 10 µs in all-atom modeling. I
am pursuing a methodology for realizing simulation that can allow computations on bothlarge-scale and long-time. The key to realizing this is the efficient usage machine learning for capturing the dynamical paths in thephase space. For a class of glassy materials,
it is recently found that static structure havethe power to predict in which regions particles
have a high tendency to move over a long timeby means of deep learning in terms of the graphneural networks (GNNs) [1]. In FY 2021, after
October, we have started to further extend thepredictive power of GNN.
Firstly I confirmed that results of a previous study [1] can be fully reproduced, bothquantitatively and qualitatively, by using thedataset provided by its authors. The system I
consider is Kob-Andersen-type Lennard-Jones(KALJ) liquid, wherein two types of particles
are enclosed in a box with different interaction
parameters and particle radii to bypass crystallization.
In Fig. 1, predicted propensity map is compared with the ground data in which the parti-

Figure 1: Color map indicating the predictive
ability of particle propensity in KALJ liquid ata low temperature. where the 2D cross sections
are shown here in the 3D system.
cle propensity is evaluated from direct molecular dynamics simulation. Further, I haveextended the GNN learning model so thatchangeover in each neighbor pair distances canbe learned as an edge feature on the GNN. As
a result, the predictive ability has been extended into a wider temporal range, exceeding the propensity ability of the node feature(particle propensity) in Ref. [1] in the rangefrom 103 to 108 MD steps. I have also clarified
that predictive ability of the original model isdecreased because of its inability to treat thecollective motion induced by strain displacement.
Most of the resources allocated for my ISSP
project in FY2021 are spent on extending
the dataset to longer-time. I have extended
the dataset to cover the time region up to100τα , where τα represents glassy relaxation
time called α-relaxation time. As a large num-325

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

ber of simulation snapshot is required for learning, the dataset is, in fact, very large. By
providing 32 different random initial velocities
500 independent initial particle configurations
which are fully relaxed at a target temperatureof consideration, I have conducted 16,000 simulation in total of 3D KALJ liquids with 4,096
particles by my in-house simulation code. As
a result, I have successfully revealed that the
GNN begins to lose its predictive ability at thetime scale close to τα . All the above results
mentioned will be soon submitted as an original paper [2]. In association with this work,
we have conducted machine learning performance evaluation by using the same model on
NVIDIA A100 GPUs, wherein the evaluation
itself is performed on Wisteria/BDEC-01 supercomputer at ITC, Univ. of Tokyo [3].
Further, I have analyzed the internal structure of the code and rewritten it in full for PyTorch Geometric (PyG) code which is a libraryfor training on GNNs on PyTorch, while all
the original code written for TensorFlow and
JAX is distributed by the authors of Ref. [1].
This PyTorch extension will enable the community to further combine these prediction
methods with existing tools used in molecular simulations, because PyTorch has now become the most popular frameworks used in
ML-aided molecular simulations. The PyG
code will soon be made publicly available via
our GitHub repository [4].

References[1] V. Bapst et al.: Nat. Phys. 16, 448-454(2020).
[2] H. Shiba et al.: in preparation.
[3] H. Shiba and T. Shimokawabe: IPSJ SIG
Technical Report, Vol. 2020-HPC-183(22),1-11 (2022) (in Japanese).
[4] https://github.com/h3-Open-BDEC/

326

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Finite temperature dependence of ab-initio Hamiltonians andits analysis for two-dimensional organic conductors Pd(dmit) 2 Salts
Kazuyoshi YOSHIMI1, Takao TSUMURAYA2, and Takahiro MISAWA3
1Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
2

Priority Organization for Innovation and Excellence, Kumamoto University,
Kumamoto 860-8555, Japan

3Beijing Academy of Quantum Information Sciences, Haidian District, Beijing 100193, China

The molecular solids β’-X[Pd(dmit)2]2 (where

In this study [4,5], we used the program

X represents a cation) exhibit various phases

RESPACK [6], which can derive the effective

such as an antiferromagnetic phase, a quantum

Hamiltonian describing low-energy degrees ofspin liquid, and a charge-ordered phase

freedom based on band structures obtained bydependingfirst-principles

on

the

choice

of

X

[1].

calculations,toderiveanComprehensive analyses of band calculations

effective Hamiltonian for the crystal structures

and transfer integrals based on the extended

reported in Ref. [3]. As a result, the transfer

Hückel method and first-principles calculations

integrals tend to increase with decreasing

have

and quantitative

temperature, while the effective interactions

evaluation of the electronic states has been

tend to decrease. The ratio of the transfer

successfully performed [2]. However, electron

integral to the effective interaction was found tocorrelation effects are expected to play a major

be about 20% smaller than that at roomrole in order to elucidate the origin of thesetemperature.

phenomena. Therefore, a quantitative derivation

effectiveofthediagonalization method with the boundary

constrained Random Phase Approximation

condition average by HΦ[7]. We find that the(cRPA)

thespin correlation function varies with themicroscopic origin of the stability of thetemperature dependence of the effective model,

quantum spin liquid. Moreover, it has been

and in particular, the antiferromagnetic orderreported that the temperature dependence of the

moment decreases at β’-EtMe3Sb[Pd(dmit)2]2,

transfer integral is large for these materials [3].

where the emergence of the quantum spin liquid

The effective interactions are expected to have ais reported experimentally.

similar temperature dependence.

The overall tendency of the compound

been carried out,theeffectiveisinteractions

necessary

for

using

clarifying

327

We also analyzed the obtained

Hamiltonians

using

the

exact

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

dependence of the antiferromagnet ordered

References

moment is consistent with the available[1] R. Kato, Chem. Rev., 104, 5319–5346

experimental results. Our results demonstrate(2004).

that the comprehensive derivation of the[2] K. Kanoda and R. Kato, Annu. Rev. Condens.

effective Hamiltonian and its analysis is a

Matter, Phys. 2, 167 (2011).

powerful[3] K. Ueda, T. Tsumuraya and R. Kato, Crystals

methodforelucidatingthemicroscopic origin of exotic quantum states

8, 138(2018).

found in organic materials. In future research,[4] T. Misawa, K. Yoshimi, T. Tsumuraya, Phys.

we plan to apply this method to other organic

Rev. Research 2, 032072(R) (2020).

materials that exhibit exotic quantum phases.

[5] K. Yoshimi, T. Tsumuraya, T. Misawa, Phys.
Rev. Research 3, 043224 (2021).
[6] K. Nakamura, Y. Yoshimoto, Y. Nomura etal., Comp. Phys. Comm. 261, 100781(2021).
[7] M Kawamura, K Yoshimi, T Misawa et al.,Comp. Phys. Comm. 217, 180(2017).

328

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Large-Scale GW/BSE electronic structure
calculations for metal-organic hybrid materials
Takatoshi Fujita
National Institutes for Quantum Science and Technology
Tokai-mura, Naka-gun, Ibaraki 319-1106

Accurate calculations of electronic states
are essential for computational studies of organic materials which are directed toward understanding of fundamental processes in organic electronic devices. We have recently
developed the large-scale GW method basedon the fragment molecular orbital method.
The fragmentation approximation for the total polarization function and the ∆COHSEX
approximation have been employed for eﬃcient evaluations of GW quasiparticle energies
from localized molecular orbitals. More recently, we have proposed the novel large-scale
excited-state methods based on the FMO, exicton model, and GW/BSE with Tamm-Dancoﬀ
approximation (TDA). In this method, theexcited-state Hamiltonian matrix elements at
the GW/TDA-BSE level is calculated in thebasis of fragment conﬁguration state functions
which describe intrafragment excitations or interfragment charge-transfer excitations. The
excited-state Hamiltonian is then diagonalized
to approximate the adiabatic excited states ofan entire system. We have conﬁrmed thatfor molecular clusters, the novel fragmentbased GW/TDA-BSE can reasonably reproduce the excited states obtained from conventional GW/TDA-BSE method. Our developments enables the applications of GW/TDABSE method to large molecular assemblies,
which will be useful for investigating charge
separation in condensed phase.

systematically improved by including the twobody correction terms. At the static COHSEX
level, errors of less than 10 meV relative canbe achieved for realistic molecular aggregates.
However, residual errors of up to 100 meV are
still present, originating from the ∆ COHSEX
approximation. In addition, we assessed thedependence of the total polarization function
on the threshold distance and found that theconvergence with respect to the threshold isslow. However, the threshold distance rangeof 1.5–2.0 nm was determined to be a reasonable compromise between the accuracy andcomputational eﬀort, and the HOMO–LUMO
gap and excitation energies reasonably reproduced in comparison with the results obtained
without the cutoﬀ. The present implementation oﬀers a practical scheme for investigating large molecular systems. Applications torealistic molecular systems, such as organic
light-emitting device materials and organic solar cells, are currently underway.

References[1] T. Fujita, Y. Noguchi, J. Phys. Chem. A
13 (2020) 2728.

Recently, we have demonstrated that the accuracy of the total polarization function can be329

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Doping effects on P2 NaxMn1−yMyO2 (M=Li, Mg, Al, Ti, V, Cr,
Fe, Co, Ni) for sodium-ion rechargeable batteries: Ab initio
investigations
Huu Duc LUONG1,2, Hiroyoshi MOMIDA2,3, Tamio OGUCHI2,3
1

Graduate School of Engineering, Osaka University, Suita, Osaka 565-0871, Japan
2

SANKEN, Osaka University, Ibaraki, Osaka 567-0047, Japan
3

ESICB, Kyoto University, Kyoto 615-8245, JapanP2 layered oxide NaxMnO2 exhibits a voltage

Throughthehighlymethodaccuratehybrid(HSE06),wewindow from 2.0 to 3.5V and high specificfunctional

capacity up to 220mAh/g. However, the material

computationally evaluate the doping influences

suffers from the serious phase transformationon the lattice distortions, stabilities, electronic

during its charging/discharging.

structures, redox potentials, and diffusion
mechanisms [1]. The model for calculation isshown in Fig. 1. Our calculations indicate that
dopants not only reduce the lattice distortion
degree, especially for Li, Mg, Ti, and V cases,
but also increase the stability of the structure,
implying the dopants would alleviate the JahnTeller lattice distortion, as shown in Figs. 2(a)and 2(b). Figure 2(c) illustrates that at full Na
concentrations, all the considered dopants,
except for Ti and V, have a small effect on theredox potential. At low Na concentrations, the Li

Crystal structure of doped structure

dopant preferably diffuses out of the MnO2 layer,

NaMn1–yMyO2(y=0.0625, M = Li, Mg, Al, Ti, V, Cr,

but hardly moves to the Na layer, suggesting that

Fe, Co, and Ni) along c-axis. Purple, red, blue,

P2-layered oxides can prevent the dopant's

yellow and green balls illustrate Mn, O, M, upper-migrations during the Na extractions due to thelayered and lower-layered Na atoms. Surrounding

high relative energies.

Fig. 1:each dopant, there are two nearest Mn1NN and four

The effect on the diffusion mechanism issecond nearest Mn2NN atoms.

described through the diffusion of a Na ion–

330

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Fig. 2: a) Lattice distortion. b) Formation energy. c) Redox potential of NaMn1–yMyO2. d) Dopant’s
migration path from Mn-layer site (blue balls) to intermediate site (brown balls) and to Na-layer faceshared sites (green balls) or edge-shared site (pink balls). e) Relative site energies of structures containing
dopants at the Mn-layer site, intermediate site, edge-shared site and face-shared site in the Na-layer
calculated along the dopant’s migration paths (M=Li, Mg) at rich and poor Na contents. f) Diffusion pathof a Na ion near the dopants. Green, yellow, red, purple, blue and black balls represent Na atoms at lower
and upper layers, O, Mn, dopant M, and Na-vacancy trace. A and B stand for the initial and final positionof Na ion for diffusion. An arrow indicates the polaron hopping between two adjacent Mn sites.

polaron complex near the dopant's environments,

increase significantly. It is found that the doping

as shown in Fig. 2(f). Fe, Mg, Ti, and Cr dopants

influence on the activation energy for Na ion

can hinder the Na ion-polaron complex diffusion

diffusion is associated with the M–O bondwith significantly higher activation energies,change and charges of the neighboring dopants.

respectively, while the Al dopant almost remains
the activation energy as well as the perfectstructure. However, Li, V, Co, and Ni dopants

References

benefit from such complex diffusion with much

[1] H. D. Luong, H. Momida, V. A. Dinh, T.

lower activation energy so the ion diffusivities

Oguchi, Phys. Rev. Materials 6, 015802 (2022).

331

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio study toward abundant element
nanocatalysts with less precious metals
Tetsuya TAKETSUGU
Faculty of Science, Hokkaido University
N10W8, Sapporo, Hokkaido 060-0810

DFT computations with QuantumEspresso(QE) are used to gain chemical insights andto design novel catalysts with abundant elements such as hexagonal boron-nitride (h-BN)
for reducing costs and dependences on precious
metals used in various heterogeneous catalysts.
We have elucidated the catalytic activity ofoxygen functionalized hexagonal boron nitride(h-BN) with B-O-O-B and B-O-B active sites
at the zigzag edges for oxidative dehydrogenation (ODH) of light alkanes, speciﬁcally ethane(C2 H6 ), propane (C3 H8 ), butane (C4 H10 ), andisobutane (HC(CH3 )3 ) [1]. It has been foundthat the reaction pathway involves two H atomtransfer steps with small activation energies.
We have demonstrated that the synergy of two
active sites, B-O-O-B and B-O-B, is crucial forthe ﬁrst and second H-transfer, respectively.
We have demonstrated that these active sites
play an important role in producing alkenes
counterpart of the mentioned alkanes. The
charge redistribution during H-transfers andlocalized oxygen atomic states in the conduction band are explored to suggest possible descriptors for the rational design of new catalysts. The universal action of the B-O-O-B
and B-O-B active sites for ODH of the lightalkanes paves the way for metal-free BN-basedmaterials for future catalytic applications.
Alumina-supported nickel-based catalysts,
Ni@Al2 O3 , constitute an important class ofcatalytic materials with a wide range of industrial applications, such as natural gas reforming for syngas production and oxidative dehy-

drogenation (ODH) of alkanes. When used in
ODH catalysis, it has been assumed that theactive species in these materials are NiO crystallites dispersed on alumina and nickel aluminate species (NiAl2 O4 ), both with Ni in its
common +2 oxidation state. These morphologies are believed to be responsible for the highselectivity of this class of catalysts as compared
to unsupported pure NiO crystallites. However, more recently, the formation of a Ni3+
species, which promotes the isolation of electrophilic oxygen (O− ), has been invoked to explain the high selectivity for ethylene formation from ethane. The complexity and inhomogeneity of the condensed phase reaction environment often preclude a complete molecularlevel understanding of the active species andunderlying reaction mechanisms. Therefore, it
proves helpful to study small metal oxide clusters in the gas phase. Such clusters provide
atom-speciﬁc insights into the interactions governing structure-reactivity correlations at themolecular level and ultimately can serve as isolated model systems for active sites in real catalysts. Therefore, we have studied the geometric and electronic structures of Nix Aly O+zclusters to identify such model systems for
Ni@Al2 O3 ODH catalysts [2]. As charged clusters are required for mass selection, we havechosen mixed metal oxide cations with thecomposition (NiOm )(Al2 O3 )n (AlO)+ with m= 1-2 and n = 1-3. For m = 1, the addition of the NiO moiety ensures formally fully
oxidized clusters with all metal atoms in their332

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

most common oxidation state (Al3+ and Ni2+ ).
Addition of one more O atom in the m = 2 series allows for the study of oxygen-rich species,
which may contain less common Ni3+ centersin combination with O− species such as those
invoked to explain enhanced ODH selectivity.
Borophene is a collective name for twodimensional (2D) boron sheets or crystalline
atomic monolayers of boron. Typically, such
sheets have to contain periodic B vacancies tomaintain structural stability, and these vacancies may appear in a great variety of diﬀerent motifs. This makes borophene a highly
polymorphic material. A great variety ofborophene structures were extensively studied
in the past decade in the quest for graphenelike materials with potential for advanced applications in catalysis and technology. Amongthem, the 2D honeycomb boron is of speciﬁc
interest as a structural analog of graphene. Recently it has been synthesized on the Al(111)substrate; however, it remains unknown towhat extent does honeycomb boron behaves
like graphene. Therefore, we have elucidated
the structural and electronic properties of thisunusual 2D material using extensive DFT calculations in order to explain recent experimental ﬁndings [3]. We have demonstrated thatin contrast to graphene on lattice-mismatched
metal surfaces, honeycomb boron cannot wiggle like a blanket on Al(111), but rather induces reconstruction of the top metal layer,
forming a stoichiometric AlB2 sheet on top of
Al. Our conclusions from theoretical modelingare fully supported by X-ray absorption spectra showing strong similarity in the electronic
structure of honeycomb boron on Al(111) andthick AlB2 ﬁlms. On the other hand, a clear
separation of the electronic states of the honeycomb boron into π− and σ−subsystems indicates an essentially 2D nature of the electronicsystem in both one-layer AlB2 and bulk AlB2 .
In other words, honeycomb boron essentiallymatched the metallic substrate aluminum s
structure so closely that it could not be con-sidered an independent, freestanding layeredmaterial.

References[1] S. Kumar, A. Lyalin, Z. Huang, and T.
Taketsugu, Catalytic Oxidative Dehydrogenation ofLight Alkanes over Oxygen Functionalized Hexagonal Boron Nitride, ChemistrySelect 7, e202103795(2022).
[2] Y. Li, M. C. Babin, S. Debnath, T. Iwasa, S. Kumar, T. Taketsugu, K. R. Asmis, A. Lyalin, D. M.
Neumark, Structural Characterization of NickelDoped Aluminum Oxide Cations by Cryogenic Ion
Trap Vibrational Spectroscopy, J. Phys. Chem. A
125, 9527-9535 (2021).
[3] A. Preobrajenski, A. Lyalin, T. Taketsugu,
N. A. Vinogradov, and A. S. Vinogradov, Honeycomb Boron on Al(111): from the Concept ofBorophene to the Two-Dimensional Boride, ACS
Nano 15, 15153 ‒ 15165 (2021).

333

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of fundamental simulation code for magnetic
materials
Tetsuya FUKUSHIMA
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

This year, we have developed a fundamental simulation code for calculating the magnetic properties of permanent magnets andspintronics materials. The automatic exhaustive calculations in this study are based on
the all-electron full-potential (Korringa-KohnRostoker) KKR Green’s function method (FPKKR). Since the potential is anisotropic rather
than spherically symmetric, we can calculate not only the magnetization and Curie
temperature but also the magnetocrystalline
anisotropy energy constant (Ku ) with high accuracy. The KKR Green’s function method
can also be conveniently combined with thecoherent potential approximation (CPA). It
is free from using supercells, resulting in reduced computational costs drastically. Therefore, it is possible to perform efficient calculations for a huge number of compositions of disordered alloys. We have applied this calculation method to YCo5 SmCo5 , and Sm2 Fe17 N3
based alloys.
Fig. 1 shows the calculated Ku and magnetization (Js ) of Y(Co,Fe,Ni,Cu)5 . The addition of low concentrations of iron, nickel, andcopper alone increases Ku as compared to thevalue of YCo5 . On the other hand, Js decreases at low concentrations regardless of thetype of added elements. For high concentration ranges, the addition of cobalt and nickel
constantly decreases the Js . In contrast, an increase in Js can be confirmed for the iron additions in the high concentration region; fromthe upper right of Fig. 1, YFe3 Co2 can be rec-Figure 1: Calculated Ku and Js for disordered
Y(Co,Fe,Ni,Cu)5 .

ognized as the material with the largest Ku
and Js among calculated compositions.
In practice, the 1-5 phases cannot exist stably at high iron concentrations. In samarium
systems, nickel has been added as a stabilizing
element to the 1-5 phases [1]. A similar composition, YFe3 (Co1−z Niz )2 , is also considered forthe yttrium system. However, the performance
deteriorates as a trade-off for phase stability;
thus it is necessary to search for the optimum
composition. In the present study, it was confirmed that up to z ∼ 0.5, the anisotropy field
is comparable to that of YCo5 .

334

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[1] A. Landa, P. Söderlind, E. E. Moore, and
A. Perron, Appl. Sci. 10, 1 (2020).

335

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Novel chloride solid electrolytes for all solid-state sodium
metal battery (2)Masanobu NAKAYAMA, Naoto TANIBATA, Ryo KOBAYASHI
Department of Advanced Ceramics,
Nagoya Institute of Technology, Gokiso-chi, Showa-ku, Nagoya, Aichi 466-8555
Since discovery of fast Li+ conductive

containing compound calculated by FPMD andchloride, Li3YCl6, by Asano et al. in 2018[1],FFMD, showing good accordance between twomuch attention

approaches.

hasbeen developed forHence,

theoptimizedFF

searching high ionic conductive chlorides. In

parameters are reliable.

this study, we focused on search for novel Na+

histogram of Na ion conductivity at room

conductive chlorides in terms of “element

temperature for 86 Na-Cl containing materials.

strategy” (Japanese government policy in

The results indicate a few samples show fastscience and technology since 2007).

Na+ conductivities, > 10-3 S/cm. Currently, we

Usinghigh-throughput force field (FF) calculations,

are

Na

conductivity experimentally.

ion

conductivities

areevaluatedsynthesizing

andFigure 2 displays

evaluating

ionic

exhaustively for chloride materials registered in
the Materials Project database.[2]Total 135

compounds

and

which

contains

NaCl(excluding H, Li, B, C, N, O, F, S, and so on)
are selected from the database, and their FF
potential parameters are optimized by using
cuckoo search algorithm.

So far, ~ 80compounds are optimized by referring firstprinciples

molecular

dynamics(FPMD)

datasets and their Na ionic conductivities areevaluated by using FF molecular dynamics

Fig. 1: Comparison between FPMD and(FFMD) approach.

FFMD derived RDF. FF parameters are

Note that FF parameter

optimized by cuckoo search algorithm.

optimization and FFMD calculations were
performed using NAP software.[3,4]Figure 1 shows a typical example of radial
distribution function (RDF) for a Na and Cl-

336

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

dma.201803075.
[2]

A. Jain, S.P. Ong, G. Hautier, W. Chen,
W.D. Richards, S. Dacek, S. Cholia, D.
Gunter, D. Skinner, G. Ceder, K.A.
Persson, Commentary: The Materials
Project: A materials genome approachto accelerating materials innovation,

Fig. 2: Histogram of Na+ conductivities

APL Mater. 1 (2013) 11002.

for Na-Cl containing materials.

https://doi.org/10.1063/1.4812323.
[3]

References

R. Kobayashi, nap: A molecular
dynamics package with parameteroptimization programs for classical and[1]

T. Asano, A. Sakai, S. Ouchi, M.

machine-learning potentials, J. Open

Sakaida, A. Miyazaki, S. Hasegawa,Source Softw. 6 (2021) 2768.

Solid Halide Electrolytes with Highhttps://doi.org/10.21105/joss.02768.

Lithium-Ion Conductivity for[4]

R. Kobayashi, Y. Miyaji, K. Nakano, M.

Application in 4 V Class Bulk-Type

Nakayama, High-throughput production

All-Solid-State Batteries, Adv. Mater.

of force-fields for solid-state electrolyte

30 (2018) 1803075.

materials, APL Mater. 8 (2020).

https://doi.org/https://doi.org/10.1002/ahttps://doi.org/10.1063/5.0015373.

337

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of high-performance permanent
magnets by large-scale simulation and data-driven
approach
Takashi MIYAKE
CD-FMat, AIST
Umezono, Tsukuba, Ibaraki 305-8568

Rare-earth transition-metal compounds arepotential main-phase for strong permanent
magnets. High content of 3d transition metals(Fe or Co) leads to high saturation magnetization, whereas rare-earth elements are essential
for strong magnetocrystalline anisotropy. Because of this, structure search for Fe/Co-richrare-earth compounds have attracted greatinterest.
There are several known structures, such as the CaCu5 -type structure, theTh2 Zn17 -type structure and the ThMn12 -type
structure. The CaCu5 -type structure is thesimplest among them, and the others are obtained by substituting transition-metal pairs(dumbbells) for rare-earth sites. There are variety of other structures obtained by diﬀerent
arrangement of dumbbells. In this study, we
have investigated stability of these structures[1].
As a first step, we prepare a 2×2×2supercell of SmFe5 and SmCo5 in the CaCu5 type structure, and generate hypotheticalstructures by replacing a part of Sm atoms
with dumbbells. We compute the formationenergy of all possible arrangements by density
functional theory in the generalized gradientapproximation. We then construct a cluster
expansion model. We evaluate the formationenergy of complex structures using the cluster expansion model. The result is shown in
Fig.1, where the formation energies for various
structures are plotted against dumbbell concentration (x). We see many structures be-

tween x=1/3 and x=1/2 whose formation energy is comparable with those of the Th2 Zn17 and ThMn12 -type structures. In contrast, theformation energy increases for x > 1/2.
The black solid line in the figure is the formation energy of disordered phase (so-called
TbCu7 -type structure). We compute the configuration entropy in the Bragg-Williams approximation, and evaluate the formation freeenergy. We found that as the temperature increases, the disordered phase is stabilized, andthe solubility limits of dumbbells in SmFez and
SmCoz are estimated to be z ∼ 9 at high temperature (T =0.15 eV).

Figure 1: Formation energy of Sm-Fe and SmCo systems as a function of dumbbell concentrations [1].

References[1] Fumiaki Kuroda, Taro Fukazawa andTakashi Miyake, Phys. Rev. Materials 5,
124405 (2021).

338

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Search for the optimum interface structure withsodium ion and ion liquid on graphene using
topological descriptor and machine learning
Yohei Shimizu & Hitoshi Washizu
Graduate school of simulation studies, University of Hyogo
7-1-28 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047

1

Background and Objective

1.1

Importance of controlling the Interface of sodium ion battery

Inexpensive and large-capacity sodium-ion
batteries are attracting attention as a stationary secondary power source. Ionic liquids aselectrolyte is known to have the effect of increasing the diffusion of sodium ions, and optimal compounding is required.

1.2

Needs and challenges of Materials Informatics (MI)MI predicts the properties of unknown materials from information on known materials [1]and are expected to shorten the development
period. Interface MI is difficult and few previous research because of Unknown descriptor
representing interface state and Infinite combinations.

1.3

Objective of our research

We establish prediction method of optimizing
Interface condition of cathode sodium ion battery with physical backing using by new topolgical descriptor as persistent homology.

2

Simulation and Estimation
methodIn this research, the objective variable is theself-diffusion coefficient of sodium ion. we etsimate optimizing self-diffusion coefficient condition by using results of MD simulation asteaching data. Table 1 is the method of MD
simulation using LAMMPS. Considering machine learning model, we use topological descriptor as persistent homology. In general
method of MI estimation model, experimentail conditions such as temprature and quantity etc. is used as descriptor. The problemof these method applied to the interface simulation MI is that the search range of interface cannot be simulated infinitely and thesedescriptor cannot represent the physical phenomenon directly. In our previous research[2], persistent homology can express amorphas
structure of polymer as persistent diagram in
two dimensions based on atomic coordinates(Fig. 1). We consider persistent homology as
descriptor of interface MI.

3

Results

3.1

Ability to express Interface condition using persistent homology

We compare the bulk and the interface, thediffusion coefficient in the direction parallel tothe interface increased. The effect on the in-339

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

terface is clarified by the inverse analysis of thepersistent diagram. In this results, persistentdiagrams can describe the state of the interface
directly (Fig. 2). It can be found of the conditions for controlling the diffusion coefficient.

3.2

Prediction of self-diffusion coefficient

Regardless of the type of ionic liquid, the structure with a high diffusion coefficient shows theuniformity of the cluster. Predictions while
preserving the physical meaning by directly
machine learning the persistent diagram. The
predictability of the interface condition using
the persistent diagram as a descriptor is shown
although improving accuracy is an issue (Fig.
3).

4

Figure 2: Difference between ion liquid bulk
and interface by using persistent homology

Conclutions

Persistent homology can express differences
sodium ion and ion liquid state near graphene.
Optimal interface condition can be predictedfrom the search range by using a persistent diagram as a descriptor.

Figure 3: Prediction of the self-diffusion coefficient of sodium ion by random forest model

References[1] Fujimura, K., Seko, A. Tanaka, I, et al.:Adv. Energy Mater. 3 (2013) 980-985.
[2] Shimizu, Y., Kurokawa, T., Arai, H.
Washizu, H.: Sci. Rep. 11 (2021) 2274.

Figure 1: Principle of Persistent homology [3,4]Table 1: LAMMPS calculation conditions
conditions
value
Cell size
Boundary condition
Force field & Charge
Graphene LJ parameter
Ion liquid quantity
Calculation method
Temperature
Time[3] I.Obayashi: Siam J. Appl. Algebra Geometry vol.2 No.4 (2018) 508-534.
[4] http://www.wpi-aimr.tohoku.ac.jp/hiraoka labo/homcloudenglish.html

9.12 × 51.048 × 20ÅPeriodic
Lopes’ OPLS & AM1-BCC
σ = 0.319/nm,  = 0.392/KJ/mol
Na+ 79 ∼ 159, TFSI− 134 or BF4− 214, EMI+ (Total charge = 0)
NVT ensemble
250K, 300K, 350K, 400K, 450K
100ns (Used to create the initial structure)340

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

3.6

Software Advancement Projects
and Workshop Support341

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Improvement of Quantum ESPRESSO implementing
the ESM-RISM method
Minoru OTANICenter for Computational Sciences, University of Tsukuba
1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8577

In this project, we modiﬁed the source codeof the Quantum ESPRESSO (QE) package, a
popular open-source code for studying the electronic structure of materials with the density
functional theory (DFT).
Before starting the project, we implemented
several simulation techniques to elucidate a microscopic detail of an electrochemical reaction
and atomic geometry under an electrochemical
environment at the electrode and electrolyte
interface, called the electrochemical interface.
To reduce the calculation time for obtaining
the equilibrium electrolyte distribution, we utilized the classical liquid theory, called the reference interaction site model (RISM), in a particular part of the electrolyte region [1]. The
RISM region can describe the electric double
layer near the interface, which includes the accumulation and depletion of the counter-ionsin the electrolyte when introducing an excess
charge on the electrode surface by applying abias voltage. These techniques are made possible by introducing a grand canonical ensemble
for both electrons on the electrode [2] and ionsin the electrolyte [1] and solving the Poisson
equation of the system under the open boundary condition along the perpendicular direction of the interface [3]. We call this hybrid
simulation technique applicable to interfacial
electrochemistry the ESM-RISM method.
In the ESM-RISM method, we need to solve
the Laue represented Poisson and RISM equations.
{∂z2 − g∥2 }V (g ∥ , z) = −4πρ(g ∥ , z),(1)hγ (g ∥ , z) =∑∫dz ′ cα (g ∥ , z ′ )α×χαγ (g ∥ , |z − z ′ |),(2)

where g ∥ , g∥ , ρ, h, c, χ, α, and γ represent, respectively, a wave vector parallel to the interface, the absolute value of g ∥ , the total charge
density, the total correlation function, the direct correlation function, the solution susceptibility, the atomic sites of implicit and explicit
solutions. These two equations are related
through the electrostatic potential V (g ∥ , z) [1].
In the ﬁrst implementation of ESM-RISM, weused a common z mesh points for both Eqs. (1)and (2). Figure 1(a) shows the schematic illustration of the z mesh in the calculation cell.
Since the mesh points along the z direction
are common, the electrostatic potential can beeasily shared in the equations, and this modelis relevant for the thin electric double layer(EDL) system. However, we need to solve
the RISM equation in a wide range of solution regions at low electrolyte concentrations
because the EDL becomes thicker according to
the Debye-Hückel theory. In this situation, it
is more versatile to be able to solve the Eqs. (1)and (2) with diﬀerent mesh spacing and diﬀerent unit cell along z direction, LDFT
and LRISMzz(see Fig. 1(c)). Thus we modify our ESMRISM code from the original common mesh to
an individual one.
To accomplish the goal, we need to map anarbitrary function f on the common mesh ontof˜ on the individual mesh. As seen in the ﬁgure. 1(d), we employ the Fourier interpolation

342

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo(a) Common mesh (

(d)

)

Slab

DFT unit cell

RISM
RISM unit cell(b) Common mesh
h(

)

Slab

(e)

)

Slab

(c) Individual mesh (

RISM

RISM

Figure 1: Schematic illustrations of a calculation cell. The z-mesh points used in DFT and RISM
calculations for (a) a common mesh with same cell sizes along z-direction (LDFT= LRISM), (b)zz
a common mesh with diﬀerent cell sizes, and (c) an individual mesh with diﬀerent cell size. The
horizontal red and blue lines with grids represent the unit cell size along the z-direction for the
DFT and RISM calculations. Conceptually, the zxy indicates a grid point of x (= long or short)unit cell for y (= DFT or RISM) calculation. (d) The mapping sequence of an arbitrary function
dense ) to f˜(g sparce ), where F and F −1 are the forward and backward Fourier transform,f (gcut
cut
dense and g sparse ).
respectively. (e) Schematic illustration of cutoﬀ radii in the reciprocal space (gcutcut
sparceThe “sparse” in (c) means a sparse mesh with a small cutoﬀ radius, gcut .
scheme. First, we did the backward Fourier
dense ) to f (z DFT ), and thentransform from f (gcutshort
we map the f in the DFT cell onto the f˜ in
the RISM cell by the following condition:{
DFT ,f (z) z = zshortf˜(z) =(3)DFT .
0z ̸= zshort
After the forward Fourier transformation, thedense is reduced to the sparsedense FFT grids gcut
sparseFFT grids gcut (see Fig. 1(e)). In the program, we ﬁrst apply the mapping sequence
from ρ to ρ̃. Secondly, by solving the Eq. (1)with ρ̃, the electrostatic potential in the RISM
cell can include the contribution from the DFT
charge. Finally, we solve the RISM equation
RISM,sparse
Eq. (2) on the sparse grids zlong.
After ﬁnishing the code development, we
checked the validity of our implementation bycomparing the total energy and the force acting on atoms between the two calculations with

Figs. 1 (a) and (c) conﬁgurations.
I would like to acknowledge Dr. Y. Motoyama, Dr. K. Yoshimi, and Dr. S. Hagiwara
for their enthusiastic contribution to code development. This function is implemented under the support of Project for advancementof software usability in materials science inﬁscal year 2021 by The Institute for Solid State
Physics, The University of Tokyo.

References[1] S. Nishihara and M. Otani: Phys. Rev. B
96 (2017) 115429.
[2] N. Bonnet, T. Morishita, O. Sugino, andM. Otani: Phys. Rev. Lett. 109 (2012)
266101.
[3] M. Otani and O. Sugino: Phys. Rev. B 73
(2006) 115407.

343

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Unified platform of experiment-data analysis
for 2D material structure
Takeo HOSHI1,2
1

Department of Mechanical and Physical Engineering, Tottori University,
4-101 Koyama-Minami, Tottori 680-8550, Japan.

2

Slow Positron Facility, Institute of Materials Structure Science, High Energy Accelerator
Research Organization (KEK), Oho 1-1, Tsukuba, Ibaraki, 305-0801, Japan

In a PASUMS project at FY2021, an open-

also for supercomputers. Among the above fivesource data-analysis framework 2DMAT [1-4]methods, the PAMC method was implemented

has

experimental

in the present project. In addition, the forward

measurements of two-dimensional material

problem solver of TRHEPD was also publishedstructures. The present project is the successor

as an open-source software package by theof one at FY2020. The current version ofpresent project [6,7].

beendeveloped

for

2DMAT is an unified platform for the analysis

2DMAT was applied to the structure

experimental

measurement

analysis of Si4O5N3 / 6H-SiC(0001)-( √3 ×total-reflection

high-energy√3 )R30 ° surface, a novel two-dimensional

positron diffraction (TRHEPD) [5], surface X-

semiconductor, by TRHEPD experiment [2]. A

raylow-energy

data-driven sensitivity analysis was proposed

electron diffraction (LEED) experiments byfor the quantitative analysis of experimental

installingproblem

uncertainties. The variation over individual

solvers that generate diffraction intensity data

fitting parameters was analyzed by solving thefrom a given dataset of the atomic positions.

eigenvalue problem of the variance-covariance

Among

were

matrix. 2DMAT was used also in othersupported as a result of the present project. The

application studies by TRHEPD experimentcurrent version of 2DMAT offers five analysis

and the study by T. Takeda (Waseda U.) et al.

methods: (i) Nelder-Mead optimization, (ii)

won a poster-session prize [8]. The analysis

grid search, (iii) Bayesian optimization, (iv)methods in 2DMAT are general and can be

replica exchange Monte Carlo (REMC) method,

applied also to other problems and was appliedand (v) population-annealing Monte Carloto a performance prediction of massively(PAMC) method. Methods (ii) through (v) are

parallel computation by Bayesian inference [4].

implemented by parallel computation, which isAs activities to promote 2DMAT, hands-on

efficient not only for personal computers but

workshops were held in April 2021 and Aprilofdifferent

techniques,diffraction(SXRD),

corresponding

them,

SXRD

and

forward

and

LEED

344

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

2022, and a study group was held in September[4] H. Kohashi, et al., JSIAM Letters 14, 13

2021. Test calculations in massively parallel(2022).

computations by the Fugaku supercomputer are[5] (Review) Y. Fukaya, et al, J. Phys. D: Appl.

underway (hp210228, hp210267).

Phys. 52, 013002 (2019).
[6] https://github.com/sim-trhepd-rheed/

References[7] T. Hanada, et al., Comp. Phys. Commun., in[1]press; Preprint: arXiv: 2110.09477

https://www.pasums.issp.utokyo.ac.jp/2DMAT[8] T. Takeda et al., the Best Poster Presentation[2] T. Hoshi, et al., Comp. Phys. Commun. 271

Award at the 2022 Kanto Chapter Conference

108186 (2022).

of the Surface and Vacuum Society of Japan.

[3] Y. Motoyama et al., Preprint:
arXiv:2204.04484

345

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Report of CCMS hands-on sessions in the 2021 fiscal year
Kota IDO
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
In the 2021 fiscal year, Center for

Table 1: List of CCMS hands-on sessions where

Computational Materials Science (CCMS) in thethe ISSP supercomputer was used in the 2021

Institute for Solid State Physics (ISSP) held

fiscal year.

three hands-on sessions where the ISSP

Date
Apr. 20
May 24Oct. 1supercomputer was used [1-3]. In this report, we
briefly summarize the hands-on sessions.
Table 1 shows the list of the hands-on

Lecturer
T. Hoshi et al.
K. Tsuda et al.
Y. Yamaji et al.

Software
2DMAT[4]PHYSBO[5]HΦ[6]References

sessions in the 2021 fiscal year. Software used in[1] https://ccms.issp.u-tokyo.ac.jp/event/4570

the hands-on sessions are 2DMAT, PHYSBO,[2] https://ccms.issp.u-tokyo.ac.jp/event/4881

and HΦ: 2DMAT is a Python package to search[3] https://ccms.issp.u-tokyo.ac.jp/event/5078

an optimal result by applying a search algorithm[4] https://www.pasums.issp.u-

to a direct-problem solver [4], PHYSBO is a

tokyo.ac.jp/2dmat/

Python library to perform a fast and scalable[5] https://www.pasums.issp.u-

Bayesian optimization [5], and HΦ is a package

tokyo.ac.jp/physbo/

of solvers for quantum many body systems [6].

[6] https://www.pasums.issp.u-tokyo.ac.jp/hphi/

Development of these software was supported[7] https://www.pasums.issp.u-tokyo.ac.jp/

by “Project for advancement of software[8] https://www.pasums.issp.u-

usability in materials science” (PASUMS) [7]. In

tokyo.ac.jp/2dmat/doc/paper/

all of the hands-on sessions, lecturers explained[9] https://www.pasums.issp.u-

the basics of each software and gave its tutorial.

tokyo.ac.jp/physbo/doc/paper/

Materials of these hands-on sessions are[10] https://www.pasums.issp.u-

available on each official page (in Japanese) [8-tokyo.ac.jp/hphi/doc/presentation/

10].

346

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Supercomputer course of Computational Materials Design(CMD®) workshop
Masaaki GESHI1, Yoshitada MORIKAWA2, Tomoya ONO3
1

Institute for NanoScience Design,

Osaka University, Machikaneyama, Toyonaka, Osaka 560-0043
2

Department of Precision Engineering,Osaka University, Yamada-oka, Suita, Osaka 565-0871
3

Center for Computational Science,

University of Tsukuba, Tenno-dai, Tsukuba, Ibaraki 305-8577

The 39th Computational Materials Design

oxygen reduction reaction on carbon electrodes,(CMD®) workshop (CMD39) has been heldand so on. The participants performed thefrom September 6th to September 10th and thecalculations and examined the results.

40th CMD® workshop (CMD40) has been done

In CMD38 two participants took thefrom February 21st to February 25th. Both weresupercomputer

held online. In this workshop we have thesupercomputer of ISSP. They got a tutorial onsupercomputer course to train up human

RSPACE developed by T. Ono. After giving theresources to advance research by using system B

introductory lecture of large-scale computing by

supercomputer of ISSP, the University of Tokyo.

M. Geshi and introducing the calculation

In CMD39 eight participants took themethod of electronic states and electron

supercomputer course and got a tutorial on

conduction property using RSPACE, exercises

STATE-Senri developed by Y. Morikawa. After

instructed in the manual were carried out. Then,giving the introductory lecture of large-scale

electronic structure calculations were carried out

computing by M. Geshi and explaining how tofor various molecules, and the electronic density

use the supercomputer of ISSP, participants

distribution was visualized. The attendees also

started constructing calculation models of theirperformed massively parallel calculations to

own research subjects with the help of theconfirm the efficiency for parallel computing.

lecturers. Then they carried out calculations

Finally, the electron conduction property ofusing supercomputers. Concrete themes weremolecules connected to atomic wires wasmolecular

analyzed.

adsorption

on

solid

surfaces,chemical reactions at electrode interfaces,

347

course

and

used

the

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

4

PUBLICATION LIST

348

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Example:LASTNAME, Firstname [ project class; # points (B), # points (C) ] (Page #)— Project title
1. First paper
Names of Authors, etc.
2. Second paper...

2 ISSP Joint Research Projects◦ B–E classes
AKAI, Hisazumi [ B class; 1300 (B), 90 (C) ] (24)— Finite temperature magnetic properties of permanent magnet materials— First-principles calculation of magnetocrystalline anisotropy of permanent magnet materials
1. First-principles investigation of Nd(Fe,M)12 (M = K–Br) and Nd(Fe,Cr,Co,Ni,Ge,As)12 : Possible
enhancers of Curie temperature for NdFe12 magnetic compounds
T. Fukazawa, H. Akai, Y. Harashima, and T. Miyake, Acta.Mater. 226, 117597 (2022).
DOI:10.1016/j.actamat.2021.117597
2.

Direct observation of magnetic Friedel oscillation at Fe(001) surface
T. Mitsui, S. Sakai, S. Li, T. Ueno, T. Watanuki, Y. Kobayashi, R. Masuda, M. Seto, and H. Akai
Hyperﬁne Interactions 242,37 (2021).
DOI:10.1007/s10751-021-01772-0

3.

Atomistic theory of thermally activated magnetization processes in Nd 2 Fe14 B permanent magnet
Seiji Miyashita, Masamichi Nishino, Yuta Toga, Taichi Hinokihara, Ismail Uysal, Takashi Miyake,Hisazumi Akai, Satoshi Hirosawa, and Akimasa Sakumaa Sci. Tech. Adv. Mater. 22,658 (2021).
DOI:10.1080/14686996.2021.1942197

4.

Data assimilation method for experimental and ﬁrst-principles data: Finite-temperature magnetization of (Nd, Pr, La, Ce)2 (Fe, Co, Ni)14 B
Y. Harashima, K. Tamai, S. Doi, M. Matsumoto, H. Akai, N. Kawashima, M. Itho, N. Sakuma,
K. Kato, T. Shoji, and T. Miyake, Phys. Rev. Mater. 5, 013806 (2021).
DOI:10.1103/PhysRevMaterials.5.013806

5.

Spin-wave dispersion and exchange stiﬀness in Nd2 Fe14 B and RFe11 Ti (R=Y, Nd, Sm) from ﬁrstprinciples calculations
Fukazawa, H. Akai, Y. Harashima, and T. Miyake, Phys. Rev. B 103, 024418 (2021).
DOI:10.1103/PhysRevB.103.024418

AKASHI, Ryosuke [ B class; 600 (B), 100 (C) ] (141)— Development of the ﬁrst-principles method for calculating Tc based on density functional theory forsuperconductors

349

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoAOYAMA, Kazushi [ B class; 1000 (B), 120 (C) ] (276)— Eﬀect of magnetic anisotropy on spin textures in pyrochlore antiferromagnets— Stability of the hedgehog-lattice topological spin texture in breathing-pyrochlore antiferromagnets
1. Emergent skyrmion-based chiral order in zero-ﬁeld Heisenberg antiferromagnets on the breathing
kagome lattice
K. Aoyama and H. Kawamura, Phys. Rev. B 105, (2022) L100407.
DOI:10.1103/PhysRevB.105.L100407
2.

Eﬀects of spin-lattice coupling and a magnetic ﬁeld in classical Heisenberg antiferromagnets on
the breathing pyrochlore lattice
K. Aoyama, M. Gen, and H. Kawamura, Phys. Rev. B 104, (2021) 184411.
DOI:10.1103/PhysRevB.104.184411

3.

Spin Dynamics Simulation of the Z2 -vortex Fluctuations
Yo. P. Mizuta, K. Aoyama, K. Tomiyasu, M. Matuura, and H. Kawamura, J. Phys. Soc. Jpn.
91, (2022) 035001 SHORT NOTES.
DOI:10.7566/JPSJ.91.035001

ARAI, Munehito [ C class; 7600 (B), 0 (C) ] (220)— Rational design of novel proteins for medical and industrial applications— Theoretical Design of Novel Artiﬁcial Proteins to Inhibit Viral Infection
ARAI, Toyoko [ C class; 1400 (B), 500 (C) ] (117)— RSDFT calculation of atomic displacement captured by energy dissipation channel of noncontact
atomic force microscope
ARIMA, Kenta [ B class; 600 (B), 110 (C) ] (288)— First-principles simulation of graphene nanoribbon and investigation of reactivity as machining catalyst— Investigations of electronic structures and reactivity of graphene nanoribbons with diﬀerent widths
1. Atomic-scale insights into the origin of rectangular lattice in nanographene probed by scanningtunneling microscopy
J. Li, S. Li, T. Higashi, K. Kawai, K. Inagaki, K. Yamamura, and K. Arima, Phys. Rev. B 103,245433 (2021).
DOI:10.1103/PhysRevB.103.245433

ARUGA, Tetsuya [ B class; 300 (B), 80 (C) ] (166)— Interaction between magnetic metal phthalocyanine molecules and bi-layer metal ﬁlms
ASANO, Yuta [ E class; 23500 (B), 2550 (C) ] (206)— Eﬀects of cavitation on soundwaves— Molecular Dynamics Simulation of Complex Fluids
1. Eﬀects of polymers on the cavitating ﬂow around a cylinder: A Large-scale molecular dynamics
analysis
Y. Asano, H. Watanabe, and H. Noguchi, J. Chem. Phys. 155, 014905 (2021).
DOI:10.1063/5.0056988
2.

Eﬀects of gas-liquid phase transitions on soundwave propagation: A molecular dynamics study
Y. Asano, H. Watanabe, and H. Noguchi, Phys. Rev. Fluids, (2022) in press.

BUI, VANPHO [ C class; 2200 (B), 350 (C) ] (110)— Study on removal mechanism of single crystalline Si planarized by catalyst referred etching in pure350

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

water

EGAMI, Yoshiyuki [ C class; 8600 (B), 1000 (C) ] (64)
— Development and application of ﬁrst-principles method for electron-transport calculations of largescale interface structures— First-principles study on electron-transport through semiconductor interface structures
FUCHIZAKI, Kazuhiro [ C class; 3000 (B), 0 (C) ] (256)— Kinetics of phase transition and polyamorphism
1. Thermodynamics of polyamorphism
K. Fuchizaki Mem. Fac. Sci. Ehime Univ. 24, 43 (2022).

FUJII, Susumu [ C class; 2600 (B), 0 (C) ] (260)— Nanoscale phonon transport across ceramics interfaces
1. Structure and lattice thermal conductivity of grain boundaries in silicon by using machine learningpotential and molecular dynamics
S. Fujii and A. Seko, Comput. Mater. Sci. 204, 111137 (2022).
DOI:10.1016/j.commatsci.2021.111137

FUJIMOTO, Satoshi [ B class; 600 (B), 90 (C) ] (196)— Topological nematic phase transition in Kitaev spin liquid
FUJIMOTO, Yoshitaka [ C class; 600 (B), 0 (C) ] (145)— Physical properties of layered graphene
1. Electronic states and modulation doping of hexagonal boron-nitride trilayer
T. Haga, Y. Matsuura, Y. Fujimoto and S. Saito, Physical Review Materials 5, 094003 (2021).
2.

Stability of Hydrogen Boride Sheets in Water
K. I. Rojas, N. T. Cuong, H. Nishino, R. Ishibiki, S. Ito, M. Miyauchi, Y. Fujimoto, S. Tominaka,
S. Okada, H. Hosono, N. Arboleda, T. Kondo, Y. Morikawa, and I. Hamada, Communications
Materials 2, 1 (2021).

3.

Chemistry and Physics of Carbon Nanotube Structures
Y. Fujimoto, Handbook of Carbon Nanotubes, pp.1-19, edited by J. Abraham, S. Thomas, and
N. Kalarikkal (Springer Nature 2021).

4.

Detection of environmentally toxic molecules using carbon nanotubes: A ﬁrst principles theoreticalstudy
Y. Fujimoto and S. Saito, Journal of The Electrochemical Society, 169, 037512 (2022).

5.

Theoretical study on quantum transport of carbon nanotubes for detecting toxic molecules: The
role of dopants
Y. Fujimoto, Journal of Electrochemical Science and Engineering, Accepted.

FUJINO, Tomoko [ D class; 2500 (B), 0 (C) ] (194)— Estimation of Coulomb repulsion in charge transfer salts of EDXT oligomers
1. Conjugation length eﬀect on the conducting behavior of single-crystalline oligo(3,4-ethylenedioxythiophene)(nEDOT) radical cation salts
R. Kameyama, T. Fujino, S. Dekura, and H. Mori, Chem. Phys. Phys. Chem, 2022, 24, 91309134.
DOI:10.1039/D2CP00250G

351

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

2.

Band-ﬁlling Eﬀects in Single-crystalline Oligomer Models for Doped PEDOT: 3,4-Ethylenedioxythiophene(EDOT) Dimer Salt with Hydrogen-bonded Inﬁnite Sulfate Anion Chains
R. Kameyama, T. Fujino, S. Dekura, S. Imajo, T. Miyamoto, H. Okamoto, and H. Mori, submitted to J. Mat. Chem. C, accepted.

FUJISHIRO, Hiroki [ C class; 2600 (B), 0 (C) ] ()— Strained Band-Structure Engineering for Antimonide-Based Terahertz Transistors
FUKUDA, Jun-ichi [ B class; 900 (B), 0 (C) ] (280)— Calculation of ordered structures, dynamics and optical properties of soft materials
1. Liquid Crystalline Half-Skyrmions and Their Optical Properties
Jun-ichi Fukuda, Andriy Nych, Uliana Ognysta, Slobodan Žumer, and Igor Muševič, Annalen
der Physik 534, 2100336 (2022).
DOI:10.1002/andp.202100336

FUKUDA, Masahiro [ B class; 400 (B), 70 (C) ] (156)— AB type 2D materials search by high-throughput DFT calculations
1. A structure map for AB2 type 2D materials using high-throughput DFT calculations
Masahiro Fukuda, Jingning Zhang, Yung-Ting Lee, and Taisuke Ozaki, Mater. Adv., 2, 4392
(2021).
DOI:10.1039/d0ma00999g

FUKUDA, Tuneo [ C class; 800 (B), 0 (C) ] (139)— Molecular dynamics simulation of substitution reaction on metal surface
FUKUMOTO, Yoshiyuki [ B class; 700 (B), 0 (C) ] (289, 290)
— Numerical studies on excitation spectra of Heisenberg antiferromagnets on the triangular and kagome
lattices— Towards a uniﬁed understanding of thermodynamic properties in S=1/2 spherical kagome systems
W72 V30 and Mo72 V30
GOHDA, Yoshihiro [ C class; 5200 (B), 800 (C) ] (79)— Maximization of interface magnetoelectric coupling with Bayesian optimization
1. Role of ferroelectricity, delocalization, and occupancy of d states in the electrical control ofinterface-induced magnetization
R. Costa-Amaral and Y. Gohda, Phys. Rev. Appl. 15, 064014 (2021).
DOI:10.1103/PhysRevApplied.15.064014
2.

Giant converse magnetoelectric eﬀect in a multiferroic heterostructure with polycrystalline Co 2 FeSi
S. Fujii, T. Usami, Y. Shiratsuchi, A.M. Kerrigan, A.M. Yatmeidhy, S. Yamada, T. Kanashima,
R. Nakatani, V.K. Lazarov, T. Oguchi, Y. Gohda, and K. Hamaya, NPG Asia Mater., in press.

3.

Intrinsic superconductivity of two-monolayer-thick indium ﬁlm
T. Ogino, I. Seo, H. Tajiri, M. Nakatake, S. Takakura, Y. Sato, Y. Hasegawa, Y. Gohda, K.
Nakatsuji, and H. Hirayama, submitted to Phys. Rev. Lett.

4.

Origin of anisotropic magnetoresistance tunable with electric ﬁeld in Co2FeSi/BaTiO3 multiferroic
inetrfaces
S. Tsuna, R. Costa-Amaral, and Y. Gohda, submitted to Phys. Rev. Mater.

GOHLKE, Matthias [ C class; 4400 (B), 600 (C) ] (233)352

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo— Ground state and dynamical properties of the J1 J2 K-Heisenberg model on the square lattice
HAGITA, Katsumi [ C class; 3600 (B), 0 (C) ] (254)— DPD simulations of cross-linked networks to study topological eﬀect using MP-SRP method
1. Viscosity Overshoot in Biaxial Elongational Flow: Coarse-Grained Molecular Dynamics Simulation of RingLinear Polymer Mixtures
T. Murashima, K. Hagita and T. Kawakatsu, Macromolecules 54, 7210–7225 (2021).
DOI:10.1021/acs.macromol.1c00267
2.

Molecular Dynamics Simulations of Ring Shapes on a Ring Fraction in Ring-Linear Polymer
BlendsK. Hagita and T. Murashima, Macromolecules 54, 8043–8051 (2021).
DOI:10.1021/acs.macromol.1c00656

3.

Role of chain crossing prohibition on chain penetration in ring-linear blends through dissipative
particle dynamics simulations
K. Hagita, T. Murashima, H. Shiba, N. Iwaoka, and T. Kawakatsu, Comput. Mater. Sci. 203,
111104 (2022).
DOI:10.1016/j.commatsci.2021.111104

HAMAGUCHI, Satoshi [ C class; 8800 (B), 1050 (C) ] (62)— Analysis of Surface Reactions in Atomic Layer Etching Processes
HAMAMOTO, Yuji [ C class; 1600 (B), 0 (C) ] (123)— Global search for the structures of two-dimensional materials by Gaussian process regression
HARADA, KENJI [ C class; 2200 (B), 0 (C) ] (263)— Data analysis method using a tensor network representation
HARASHIMA, Yosuke [ C class; 1000 (B), 0 (C) ] (134)— Critical concentration of metal-insulator transition in doped semiconductors and Coulomb gap— Critical exponent of metal-insulator transition in doped semiconductors and spin ordering
1. Analysis of Kohn-Sham Eigenfunctions Using a Convolutional Neural Network in Simulations of
the Metal-Insulator Transition in Doped Semiconductors
Y. Harashima, T. Mano, K. Slevin, and T. Ohtsuki, J. Phys. Soc. Jpn. 90, 094001 (2021).
DOI:10.7566/JPSJ.90.094001

HARUYAMA, Jun [ C class; 2800 (B), 750 (C) ] (100)— Electrochemical reaction analysis using density functional calculation + implicit solvation model 3
1. Thermodynamic Analysis of Li-Intercalated Graphite by First- Principles Calculations with Vibrational and Conﬁgurational Contributions
J. Haruyama, S. Takagi, K. Shimoda, I. Watanabe, K. Sodeyama, T. Ikeshoji, and M. Otani, J.
Chem. Phys. C 125, 27891 (2021).
DOI:10.1021/acs.jpcc.1c08992

HASHIMOTO, Tamotsu [ C class; 3000 (B), 600 (C) ] (253)— Molecular dynamics simulation of BaTiO3 nano structure
HATANO, Naomichi [ B class; 400 (B), 70 (C) ] ()— Novel Spectral Clustering Method of Directed Networks
HATSUGAI, Yasuhiro [ C class; 3200 (B), 600 (C) ] (251)353

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo— Topological phases and science of bulk-edge correspondence by numerical methods
1. Chiral edge modes in evolutionary game theory: A kagome network of rock-paper-scissors cycles
T. Yoshida, T. Mizoguchi, and Y. Hatsugai, Phys. Rev. E 104, 025003 (2021).
DOI:10.1103/PhysRevE.104.025003
2.

Bulk-edge correspondence in the adiabatic heuristic principle
K. Kudo, Y. Kuno, and Y. Hatsugai, Phys. Rev. B 104, L241113 (2021).
DOI:10.1103/PhysRevB.104.L241113

3.

Adiabatic Continuity of the Spinful Quantum Hall States
K. Kudo and Y. Hatsugai, arXiv:2201.07893
DOI:10.48550/arXiv.2201.07893

HATTORI, Ken [ B class; 300 (B), 60 (C) ] ()— Atomic structure and electronic states for silicide ﬁlms
HAYAMI, Satoru [ C class; 3400 (B), 650 (C) ] (191)— Searching for meron crystal in itinerant magnets
1. Essential role of anisotropic magnetic dipole in anomalous Hall eﬀect
S. Hayami and H. Kusunose, Phys. Rev. B 103, L180407 (2021).
DOI:10.1103/PhysRevB.103.L180407
2.

Skyrmion crystals in centrosymmetric itinerant magnets without horizontal mirror plane
R. Yambe and S. Hayami, Sci. Rep. 11, 11184 (2021).
DOI:10.1038/s41598-021-90308-1

3.

Field-Direction Sensitive Skyrmion Crystals in Cubic Chiral Systems: Implication to 4f-Electron
Compound EuPtSi
S. Hayami and R. Yambe, J. Phys. Soc. Jpn. 90, 073705 (2021).
DOI:10.7566/JPSJ.90.073705

4.

In-plane magnetic ﬁeld-induced skyrmion crystal in frustrated magnets with easy-plane anisotropy
S. Hayami, Phys. Rev. B 103, 224418 (2021).
DOI:10.1103/PhysRevB.103.224418

5.

Spin-orbital-momentum locking under odd-parity magnetic quadrupole ordering
S. Hayami and H. Kusunose, Phys. Rev. B 104, 045117 (2021).
DOI:10.1103/PhysRevB.104.045117

6.

Multipole classiﬁcation in 122 magnetic point groups for uniﬁed understanding of multiferroic
responses and transport phenomena
M. Yatsushiro, H. Kusunose, and S. Hayami Phys. Rev. B 104, 054412 (2021).
DOI:10.1103/PhysRevB.104.054412

7.

Meron-antimeron crystals in noncentrosymmetric itinerant magnets on a triangular lattice
S. Hayami and R. Yambe, Phys. Rev. B 104, 094425 (2021).
DOI:10.1103/PhysRevB.104.094425

8.

Charge density waves in multiple-Q spin states
S. Hayami and Y. Motome, Phys. Rev. B 104, 144404 (2021).
DOI:10.1103/PhysRevB.104.144404

9.

Nonreciprocal magnon excitations by the Dzyaloshinskii-Moriya interaction on the basis of bondmagnetic toroidal multipoles354

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

T. Matsumoto and S. Hayami, Phys. Rev. B 104, 134420 (2021).
DOI:10.1103/PhysRevB.104.134420
10. Temperature-driven transition from skyrmion to bubble crystals in centrosymmetric itinerantmagnets
S. Hayami, New J. Phys. 23, 113032 (2021).
DOI:10.1088/1367-2630/ac3683
11. Phase Shift in Skyrmion Crystals
S. Hayami, T. Okubo, and Y. Motome, Nat. Commun. 12, 6927 (2021).
DOI:10.1038/s41467-021-27083-0
12. Locking of skyrmion cores on a centrosymmetric discrete lattice: Onsite versus oﬀsite
S. Hayami and R. Yambe, Phys. Rev. Research 3, 043158 (2021).
DOI:10.1103/PhysRevResearch.3.043158
13. Spin excitation spectra in helimagnetic states: Proper-screw, cycloid, vortex-crystal, and hedgehog
lattices
Y. Kato, S. Hayami, and Y. Motome Phys. Rev. B 104, 224405 (2021).
DOI:10.1103/PhysRevB.104.224405
14. Essential model parameters for nonreciprocal magnons in multisublattice systems
S. Hayami and T. Matsumoto, Phys. Rev. B 105, 014404 (2022).
DOI:10.1103/PhysRevB.105.014404
15. Skyrmion crystal and spiral phases in centrosymmetric bilayer magnets with staggered DzyaloshinskiiMoriya interaction
S. Hayami, Phys. Rev. B 105, 014408 (2022).
DOI:10.1103/PhysRevB.105.014408
16. Mechanism of antisymmetric spin polarization in centrosymmetric multiple-Q magnets based on
eﬀective chiral bilinear and biquadratic spin cross products
S. Hayami, Phys. Rev. B 105, 024413 (2022).
DOI:10.1103/PhysRevB.105.024413
17. Multiple Skyrmion Crystal Phases by Itinerant Frustration in Centrosymmetric Tetragonal Magnets
S. Hayami, J. Phys. Soc. Jpn. 91, 023705 (2022).
DOI:10.7566/JPSJ.91.023705
18. Skyrmion crystals in centrosymmetric triangular magnets under hexagonal and trigonal single-ion
anisotropy
S. Hayami, J. Magn. Magn. Mater. 553, 169220 (2022).
DOI:10.1016/j.jmmm.2022.169220
19. Helicity locking of a square skyrmion crystal in a centrosymmetric lattice system without verticalmirror symmetry
S. Hayami and R. Yambe, Phys. Rev. B 105, 104428 (2022).
DOI:10.1103/PhysRevB.105.104428

HIDA, Kazuo [ B class; 400 (B), 70 (C) ] (309)— Numerical Study of One Dimensional Frustrated Quantum Spin Systems
1. Inﬁnite Series of Ferrimagnetic Phases Emergent from the Gapless Spin Liquid Phase of Mixed
Diamond Chains

355

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Kazuo Hida, J. Phys. Soc. Jpn. 90, 054701 (2021).
DOI:10.7566/JPSJ.90.054701
2.

First Order Transitions Between the Gapped Spin-Liquid and Ferrimagnetic Phases in (1/2,1/2,1)
Mixed Diamond Chains with Bond Alternation
Kazuo Hida, J. Phys. Soc. Jpn. 91, 024706 (2022).
DOI:10.7566/JPSJ.91.024706

HIGUCHI, Yuji [ C class; 4600 (B), 750 (C) ] (230)— Structure and mechanical properties of crystalline polymers absorbing water molecules
1. Hydrophobic immiscibility controls self-sorting or co-assembly of peptide amphiphiles
R. Wakabayashi, R. Imatani, M. Katsuya, Y. Higuchi, H. Noguchi, N. Kamiya, and M. Goto,
Chem. Commun. 58, 585 (2021).
DOI:10.1039/D1CC05560G

HINUMA, Yoyo [ B class; 800 (B), 80 (C) ] (135)— Exploration of exotic surface sites for catalyst informatics
1. Surface activation by electron scavenger metal nanorod adsorption on TiH2, TiC, TiN, and Ti2O3
Yoyo Hinuma, Shinya Mine, Takashi Toyao, Zen Maeno and Ken-ichi Shimizu, Phys. Chem.
Chem. Phys. 23, 16577 (2021).
2.

Factors determining surface oxygen vacancy formation energy in ternary spinel structure oxides
with zinc
Yoyo Hinuma, Shinya Mine, Takashi Toyao, Takashi Kamachi and Ken-ichi Shimizu, Phys.
Chem. Chem. Phys. 23, 23768 (2021).

HIRATSUKA, Masaki [ B class; 900 (B), 120 (C) ] ()— Calculation of Infrared and Raman spectra by molecular dynamics simulation using machine learning— Validation of a Machine Learning Method for Predicting Vibration Spectra
HIRAYAMA, Naomi [ C class; 1800 (B), 0 (C) ] ()— Development of inter-atomic potentials of Fe-based amorphous alloys and MD simulation of crystallization process
HIYAMA, Miyabi [ C class; 3200 (B), 800 (C) ] (249)— Theoretical analysis of absorption and ﬂuorescence spectra for ﬁreﬂy bioluminescence related molecules
1. Absorption Spectra for Fireﬂy Bioluminescence Substrate Analog: TokeOni in Various pH Solutions
H. Ogawa, R. Ono, Y. Noguchi, N. Kitada, R. Saito-Moriya, S. A. Maki, H. Akiyama, H. Itabashi,
and M. Hiyama, Photochem. Photobiol. 97, 1016 (2021).
DOI:10.1111/php.13458

HOSHI, Takeo [ C class; 5200 (B), 0 (C) ] (344)— HPC-based fusion of experiment analysis, simulation and data-driven science
1. Data-driven sensitivity analysis in a total-reﬂection high-energy positron diﬀraction (TRHEPD)
Takeo Hoshi, Daishiro Sakata, Shotaro Oie, Izumi Mochizuki, Satoru Tanaka, Toshio Hyodo, andKoji Hukushima, Comput. Phys. Commun. 271, 108186 (2022).
DOI:10.1016/j.cpc.2021.108186
2.

Performance prediction of massively parallel computation by Bayesian inference
Hisashi Kohashi, Harumichi Iwamoto, Takeshi Fukaya, Yusaku Yamamoto, and Takeo Hoshi

356

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

JSIAM Letters 14 13-16 (2022).
3.

sim-trhepd-rheed – Open-source simulator of total-reﬂection high-energy positron diﬀraction (TRHEPD)
and reﬂection high-energy electron diﬀraction (RHEED)
Takashi Hanada, Yuichi Motoyama, Kazuyoshi Yoshimi, and Takeo Hoshi, Comput. Phys. Commun. in press (arXiv:2110.09477).

4.

Data-analysis software framework 2DMAT and its application to experimental measurements for
two-dimensional material structures
Yuichi Motoyama, Kazuyoshi Yoshimi, Harumichi Iwamoto, Hayato Ichinose, and Takeo Hoshi,
arXiv:2204.04484
DOI:10.48550/arXiv.2204.04484

HOTTA, Chisa [ B class; 1000 (B), 80 (C) ] (278)— Development and application of methods to calculate thermodynamic properties in low dimensional
magnets
1. Dimensional reduction in quantum spin-1/2 system on a 1/7-depleted triangular lattice
R. Makuta and C. Hotta, Phys. Rev. B 104, 224415 (2021).
DOI:10.1103/PhysRevB.104.224415

HOTTA, Takashi [ C class; 5000 (B), 0 (C) ] (188)— Research of multi-channel Kondo eﬀect emerging from heavy rare-earth ions
1. Three-Channel Kondo Eﬀect Emerging from Ho Ions
Takashi Hotta, J. Phys. Soc. Jpn. 90, 113701 (2021).
DOI:10.7566/JPSJ.90.113701

IDO, Kota [ B,C class; 4700 (B), 390 (C) ] (232)— Development of COMPutation ARchive of Exact Diagonalization(COMPARED)— Neural network quantum states for excited states in strongly correlated electron systems
1. Unconventional dual 1D2D quantum spin liquid revealed by ab initio studies on organic solids
familyKota Ido, Kazuyoshi Yoshimi, Takahiro Misawa, Masatoshi Imada, npj Quantum Materials 7, 48(2022).
DOI:10.1038/s41535-022-00452-8
Data Repository
COMPAREDhttps://isspns-gitlab.issp.u-tokyo.ac.jp/compared/compared

IITAKA, Toshiaki [ C class; 2000 (B), 0 (C) ] (115)— Structure and Property of Basalt Melt and Glass
1. A comparative study on pressure-induced structural transformations in a basaltic glass and meltfrom Ab initio molecular dynamics calculations
S. Q. Feng, A. Majumdar, H. Y. Kuang, Y. M. Pan, T. Iitaka, and J. S. Tse Phys. Chem. Miner.
48, 41 (2021).
DOI:10.1007/s00269-021-01165-3

IKEDA, Hiroaki [ B class; 400 (B), 70 (C) ] ()— Electronic structure calculations in quantum liquid crystals

357

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

IKEDA, Tatsuhiko [ B class; 600 (B), 40 (C) ] (198)— Numerical study of nonequilibrium phases in periodically driven systems with dissipation
1. Criticality and rigidity of dissipative discrete time crystals in solids
K. Chinzei and T.N. Ikeda, Phys. Rev. Research 4, 023025 (2022).
DOI:10.1103/PhysRevResearch.4.023025

IKUHARA, Yuichi [ C class; 2000 (B), 0 (C) ] (113)— Determining grain-boundary stable atomic structure by ﬁrst-principle calculations— First principles calculations for proving stable grain-boundary structures in perovskite oxides
1. Oxygen Atom Ordering on SiO2/4H-SiC 0001 Polar Interfaces formed by Wet Oxidation
M. Saito, H. Li, K. Inoue, H. Matsuhata, Y. Ikuhara, Acta Mater. 221, 117360 (2021).
DOI:10.1016/j.actamat.2021.117360
2.

Arrangement of polyhedral units for [0001]-symmetrical tilt grain boundaries in zinc oxide
K. Inoue, J.Y. Roh, K. Kawahara, M. Saito, M. Kotani, Y. Ikuhara, Acta Mater. 212 116864(2021).
DOI:10.1016/j.actamat.2021.116864

IMADA, Masatoshi [ E class; 28500 (B), 3000 (C) ] (174)— Quantum Spin Liquids on Pyrochlore Lattice— Studies on Eﬀects of Non-Local Coulomb Interaction for High Termperature Superconductivity
1. Unconventional dual 1D-2D quantum spin liquid revealed by ab initio studies on organic solids
familyKota Ido, Kazuyoshi Yoshimi, Takahiro Misawa, and Masatoshi Imada, npj Quantum Mater. 7,
48 (2022).
DOI:0.1038/s41535-022-00452-8
2.

Hidden self-energies as origin of cuprate superconductivity revealed by machine learning
Youhei Yamaji, Teppei Yoshida, Atsushi Fujimori, and Masatoshi Imada Phys. Rev. Research 3,043099 (2021).
DOI:10.1103/PhysRevResearch.3.043099

3.

Order-N orbital-free density-functional calculations with machine learning of functional derivatives
for semiconductors and metals
Fumihiro Imoto, Masatoshi Imada, and Atsushi Oshiyama, Phys. Rev. Research 3, 033198(2021).
DOI:10.1103/PhysRevResearch.3.033198

4.

Ab initioderivation of low-energy Hamiltonians for systems with strong spin-orbit interaction: Application to Ca5 Ir3 O12Maxime Charlebois, Jean-Baptiste Morée, Kazuma Nakamura, Yusuke Nomura, Terumasa Tadano,
Yoshihide Yoshimoto, Youhei Yamaji, Takumi Hasegawa, Kazuyuki Matsuhira, and Masatoshi
Imada, Phys. Rev. B 104, 075153 (2021).
DOI:10.1103/PhysRevB.104.075153

5.

Dirac-type nodal spin liquid revealed by reﬁned quantum many-body solver using neural-network
wave function, correlation ratio, and level spectroscopy
Yusuke Nomura and Masatoshi Imada, Phys. Rev. X 11, 031034 (2021).
DOI:10.1103/PhysRevX.11.031034

6.

Charge Order and Superconductivity as Competing Brothers in Cuprate High-Tc Superconductors
Masatoshi Imada J. Phys. Soc. Jpn. 90, 111009 (2021).
DOI:10.7566/JPSJ.90.111009

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

7.

Resonant Inelastic X-Ray Scattering Spectra of Cuprate Superconductors Predicted by Model ofFractionalized Fermions
Masatoshi Imada J. Phys. Soc. Jpn. 90, 074702 (2021).
DOI:10.7566/JPSJ.90.074702

8.

High-temperature superconductivity
Xingjiang Zhou, Wei Sheng Lee, Masatoshi Imada, Nandini Trivedi, Philip Phillips, Hae Young
Kee, Päivi Törmä, Mikhail Eremets Nat. Rev. Phys. 3, 125137 (2021).
DOI:10.1038/s42254-021-00324-3

9.

Local moments versus itinerant antiferromagnetism: Magnetic phase diagram and spectral properties of the anisotropic square lattice Hubbard model
Marcin Raczkowski, Fakher F. Assaad, Masatoshi Imada Phys. Rev. B 103, 462 (2021).
DOI:10.1103/PhysRevB.103.125137

INAGAKI, Kouji [ B class; 400 (B), 70 (C) ] (155)— First-principles calculation of graphitization of diamond surface and its exfoliation process
ISHIBASHI, Shoji [ C class; 1800 (B), 0 (C) ] (121)— Prediction of properties of organic ferroelectrics and piezoelectrics by ﬁrst-principles calculation
1. Hydrogen-bonded single-component organic ferroelectrics revisited by van der Waals densityfunctional theory calculations
S. Ishibashi, S. Horiuchi, and R. Kumai, Phys. Rev. Mater. 5, 094409 (2021).
DOI:10.1103/PhysRevMaterials.5.094409
2.

Large Polarization and Record-High Performance of Energy-Storage Induced by a Phase Change
in Organic Molecular Crystals
S. Horiuchi and S. Ishibashi, Chem. Sci. 12, 14198 (2021).
DOI:10.1039/d1sc02729h

ISHII, Fumiyuki [ C class; 5200 (B), 850 (C) ] (74)
— First-Principles Calculation of Spin Splitting and Anomalous Hall Conductivity in Energy Conversion
Materials— First-principles study of interface structure prediction and electronic structures
1. First-principles calculation of anomalous Hall and Nernst conductivity by local Berry phase
H. Sawahata, N. Yamaguchi, S. Minami, and F. Ishii, arXiv:2204.05949, submitted to Phys. Rev.
B.
2.

First-principles LCPAO Approach to Insulators Under Finite Electric Fields
N. Yamaguchi and F. Ishii, arXiv:2203.10441

3.

Statistical analysis of properties of non-fullerene acceptors for organic photovoltaics
N. Yamaguchi, H. Sano, H. Sawahata, M. Nakano, T. Taima, F. Ishii, M. Karakawa Jpn. J. Appl.
Phys. 61, 030905 (2022).

ISOBE, Masaharu [ B class; 800 (B), 0 (C) ] (281)— Equilibration and phase transition in the dense hard sphere systems— Nonequilibrium response and phase transition in the dense hard sphere systems
1. Non-equilibrium response and equilibration in hard disk systems
D. Mugita and M. Isobe, EPJ Web Conferences 249, 14004 (2021).
DOI:10.1051/epjconf/202124914004

359

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo2.

Diﬀusional characteristics of a Newtonian event-chain Monte Carlo in hard disk systems
H. Banno, D. Mugita, and M. Isobe, J. of Phys.: Conf. Ser. 2207 012011 (2022).
DOI:10.1088/1742-6596/2207/1/012011

3.

Molecular dynamics study of a nano-scale beta-type Stirling engine
K. Kitaya and M. Isobe, J. of Phys.: Conf. Ser. 2207 012006 (2022).
DOI:10.1088/1742-6596/2207/1/012006

ITOH, Satoru [ C class; 1800 (B), 0 (C) ] (270)— Formation of lipid rafts studied by molecular dynamics simulation
JESCHKE, Harald [ C class; 3800 (B), 0 (C) ] ()— Magnetism and superconductivity in ternary chromium chalcogenides
JOUTSUKA, Tatsuya [ B,C class; 1800 (B), 0 (C) ] (119, 120)
— Elucidation of Photocatalytic Reaction Mechanism by Ab Initio Calculations— Theoretical Analysis of Metal Film Growth Mechanism in Chemical Vapor Deposition
1. Eﬃcient Free-Energy Calculation of Proton Transfer by Constrained Density Functional Theory
and Geometrically Restrained Molecular Dynamics Simulation
Tatsuya Joutsuka and Koji Ando, Chem. Lett. 50, 1325 (2021).
DOI:10.1246/cl.210132
2.

Understanding the structure of Cu-doped MgAl2O4 for CO2 hydrogenation catalyst precursor
using experimental and computational approaches
Tatsuya Joutsuka, Ryu Hamamura, Kakeru Fujiwara, Tetsuo Honma, Masahiko Nishijima, andShohei Tada, submitted.

3.

Active sites on ZnxZr1 − xO2 − x solid solution catalysts for CO2-to-methanol hydrogenation
Shohei Tada, Nagomu Ochiai, Hiroka Kinoshita, Mitsuhiro Yoshida, Natsumi Shimada, Tatsuya
Joutsuka, Masahiko Nishijima, Tetsuo Honma, Noriko Yamauchi, Yoshio Kobayashi, Kenta Iyoki,
submitted.

4.

Molecular Mechanism of Autodissociation in Liquid Water: Density Functional Theory Molecular
Dynamics Simulations
Tatsuya Joutsuka, submitted.
DOI:10.26434/chemrxiv-2022-9t6vf

KAGESHIMA, Hiroyuki [ C class; 1200 (B), 0 (C) ] (129)— Study on structural elementary excitations at semiconductor surfaces and interfaces
KANEKO, Ryui [ B class; 700 (B), 90 (C) ] (284, 286)
— tensor-network calculation of real time dynamics in two-dimensional cold atom systems— tensor-network study of the magnetization process of the SU(N) Heisenberg model
1. Reentrance of the Disordered Phase in the Antiferromagnetic Ising Model on a Square Latticewith Longitudinal and Transverse Magnetic Fields
R. Kaneko, Y. Douda, S. Goto, and I. Danshita, J. Phys. Soc. Jpn. 90, 073001 (2021).
DOI:10.7566/JPSJ.90.073001
2.

Symmetry-protected topological phases and competing orders in a spin-1/2 XXZ ladder with afour-spin interaction
T. Ogino, S. Furukawa, R. Kaneko, S. Morita, and N. Kawashima, Phys. Rev. B 104, 075135(2021).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

DOI:10.1103/PhysRevB.104.075135
3.

Multiple magnetization plateaus induced by farther neighbor interactions in an S = 1 two-leg
Heisenberg spin ladder
H. Kohshiro, R. Kaneko, S. Morita, H. Katsura, and N. Kawashima, Phys. Rev. B 104, 214409(2021).
DOI:10.1103/PhysRevB.104.214409

4.

Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard
model
R. Kaneko and I. Danshita, Commun. Phys. 5, 65 (2022).
DOI:10.1038/s42005-022-00848-9

KARIYADO, Toshikaze [ B class; 300 (B), 0 (C) ] (320)— Electronic structure in mismatched multilayer systems: evaluation and application of the modelingscheme1. Eﬀective continuum model of twisted bilayer GeSe and origin of the emerging one-dimensionalmode
M. Fujimoto and T. Kariyado, Phys. Rev. B 104, 125427 (2021).
DOI:10.1103/PhysRevB.104.125427
2.

Disentangling Orbital Magnetic Susceptibility with Wannier Functions
T. Kariyado, H. Matsuura, and M. Ogata, J. Phys. Soc. Jpn. 90, 124708 (2021).
DOI:10.7566/JPSJ.90.124708

KASAMATSU, Shusuke [ C class; 10000 (B), 1150 (C) ] (51)
— Understanding superionic conduction in disordered materials systems— Understanding superionic conductivity in disordered systems using machine learning potential molecular dynamics
1. Enabling ab initio conﬁgurational sampling of multicomponent solids with long-range interactions
using neural network potentials and active learning
Shusuke Kasamatsu, Yuichi Motoyama, Kazuyoshi Yoshimi, Ushio Matsumoto, Akihide Kuwabara,
and Takafumi Ogawa, submitted.

KATO, Takeo [ B class; 1100 (B), 180 (C) ] (271, 272)
— Numerical study of heat transport through a mesoscopic device— Theoretical study of spin Hall magnetoresistance by the quantum Monte Carlo method
KATO, Yusuke [ C class; 8800 (B), 800 (C) ] (215, 217)
— Eﬀects of non-diagonal spin interactions and dipole interaction on quantum spin liquids— Quantum eﬀects on chiral magnets
1. Feasibility of Kitaev quantum spin liquid in ultracold polar molecules
Kiyu Fukui, Yasuyuki Kato, Joji Nasu, and Yukitoshi Motome, submitted to Phys. Rev. B

KAWAKAMI, Norio [ C class; 8200 (B), 1100 (C) ] (182)— Excitation modes and transport phenomena in strongly correlated systems— Topological phases, transport phenomena and eﬀects of exceptional points in strongly correlated systems
1. Mott transition and magnetism in a fragile topological insulator
Ashish Joshi and Robert Peters, Phys. Rev. B 103, 165130 (2021).
DOI:10.1103/PhysRevB.103.165130

361

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo2.

Eﬀects of renormalization and non-Hermiticity on nonlinear responses in strongly correlated electron systems
Yoshihiro Michishita and Robert Peters, Phys. Rev. B 103, 195133 (2021).
DOI:10.1103/PhysRevB.103.195133

3.

Eﬀects of strong correlations on the nonlinear response in Weyl-Kondo semimetals
Akira Kofuji, Yoshihiro Michishita, and Robert Peters, Phys. Rev. B 104, 085151 (2021).
DOI:10.1103/PhysRevB.104.085151

4.

Surface exceptional points in a topological Kondo insulator
Robert Peters, Kazuhiro Kimura, Yoshihiro Michishita, Tsuneya Yoshida, and Norio Kawakamia
Phys. Rev. B 104, 235153 (2021).
DOI:10.1103/PhysRevB.104.235153

5.

Magnetism of magic-angle twisted bilayer graphene
Javad Vahedi, Robert Peters, Ahmed Missaoui, Andreas Honecker, Guy Trambly de Laissardire
SciPost Phys. 11, 083 (2021).
DOI:10.21468/SciPostPhys.11.4.083

6.

Probing three-state Potts nematic ﬂuctuations by ultrasound attenuation
Kazuhiro Kimura, Manfred Sigrist, and Norio Kawakami, Phys. Rev. B 105, 035130 (2022).
DOI:10.1103/PhysRevB.105.035130

KAWAKATSU, Toshihiro [ C class; 4600 (B), 0 (C) ] (238)— Hybrid simulations on ﬂuid-viscoelastic membrane system using multiscale simulation platform oncomplex ﬂuids (MSSP)
1. Lagrangian multiscale simulation of complex ﬂows
Y. Morii and T. Kawakatsu, Phys. Fluids 33, 093106 (2021).
DOI:10.1063/5.0063059

KAWAMURA, Hikaru [ C class; 3800 (B), 0 (C) ] (250)— Novel order in frustrated magnets
1. Hedgehog-lattice spin texture in classical Heisenberg antiferromagnets on the breathing pyrochlore
lattice
K. Aoyama and H. Kawamura, Phys. Rev. B 103, 014406 (2021).
DOI:10.1103/PhysRevB.103.014406
2.

Frustration-induced quantum spin liquid behavior in the s = 1/2 random-bond Heisenberg antiferromagnet on the zigzag chain
K. Uematsu, T. Hikihara, and H. Kawamura, J. Phys. Soc. Jpn. 90, 124703 (2021).
DOI:10.7566/JPSJ.90.124703

3.

Eﬀects of spin-lattice coupling and a magnetic ﬁeld in classical Heisenberg antiferromagnets on
the breathing pyrochlore lattice
K. Aoyama, M. Gen, and H. Kawamura, Phys. Rev. B 104, 184411 (2021).
DOI:10.1103/PhysRevB.104.184411

4.

Replica symmetry breaking in the RKKY skyrmion crystal system
K. Mitsumoto and H. Kawamura, Phys. Rev. B 104, 184432 (2021).
DOI:10.1103/PhysRevB.104.184432

5.

Skyrmion crystal in the RKKY system on the two-dimensional triangular lattice362

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

K. Mitsumoto and H. Kawamura, Phys. Rev. B 105, 094427(2022).
DOI:10.1103 /PhysRevB.105.094427
6.

Emergent skyrmion-based chiral order in zero-ﬁeld Heisenberg antiferromagnets on the breathing
kagome lattice
K. Aoyama and H. Kawamura, Phys. Rev. B 105, L100407 (2022).
DOI:10.1103/PhysRevB.105.L100407

7.

Spin Dynamics Simulation of the Z2 -vortex Fluctuations
Y.P. Mizuta, K. Aoyama, K. Tomiyasu, M. Matsuura, and H. Kawamura, J. Phys. Soc. Jpn.
91, 035001 (2022).
DOI:10.7566/JPSJ.91.035001

KAWAMURA, Mitsuaki [ B class; 400 (B), 80 (C) ] (305)— Crystal structure search guided by multicomponent sphere packing
KAWANO, Shoya [ D class; 1000 (B), 0 (C) ] (132)— Optical conductivity of Ca5 Ir3 O12 by ﬁrst-principles calculations
KAWASHIMA, Naoki [ E class; 38000 (B), 3600 (C) ] (172)— Tensor-Network Renormalization-Group Study of Critical Phenomena
1. Anisotropy as a diagnostic test for distinct tensor-network wave functions of integer- and halfinteger-spin Kitaev quantum spin liquids
H.-Y. Lee, T. Suzuki, Y. B. Kim and N. Kawashima, Phys. Rev. B 104, 024417(1-13) (2021).
DOI:10.1103/PhysRevB.104.024417
2.

Generating function for tensor network diagrammatic summation
W.-L. Tu, H.-K. Wu, N. Schuch, N. Kawashima and J.-Y. Chen, Phys. Rev. B 103, 205155(2021).
DOI:10.1103/PhysRevB.103.205155

3.

Multiple magnetization plateaus induced by farther neighbor interactions in an S=1 two-leg
Heisenberg spin ladder
H. Kohshiro, R. Kaneko, S. Morita, H. Katsura and N. Kawashima, Phys. Rev. B 104, 214409(2021).
DOI:10.1103/PhysRevB.104.214409

4.

Open spin chain realization of a topological defect in a one-dimensional Ising model:
Boundary and bulk symmetry: Y. Fukusumi and S. Iino, Phys. Rev. B 104, 125418 (2021).
DOI:10.1103/PhysRevB.104.125418

5.

Symmetry-protected topological phases and competing orders in a spin-1/2 XXZ ladder with afour-spin interaction
T. Ogino, S. Furukawa, R. Kaneko, S. Morita and N. Kawashima, Phys. Rev. B 104, 075135(2021).
DOI:10.1103/PhysRevB.104.075135

6.

Mott-insulator-like Bose-Einstein condensation in a tight-binding system of interacting bosons
with a ﬂat band
H. Katsura, N. Kawashima, S. Morita, A. Tanaka and H. Tasaki, Phys. Rev. Research 3, 033190(2021).
DOI:10.1103/PhysRevResearch.3.033190

7.

Scaling dimensions from linearized tensor renormalization group transformations

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

X. Lyu, R. G. Xu and N. Kawashima, Phys. Rev. Research 3, 023048 (2021).
DOI:10.1103/PhysRevResearch.3.023048
8.

Universal and non-universal correction terms of Bose gases in dilute region: a quantum Monte
Carlo study
A. Masaki-Kato, Y. Motoyama and N. Kawashima, J. Phys. Soc. Jpn. 90, 034711(1-8) (2022).
DOI:10.7566/JPSJ.91.024001

KITAO, Akio [ C class; 6600 (B), 0 (C) ] (225)— Eﬃcient sampling simulation of the soft modes signiﬁcantly contribute to protein properties
1. Binding free energy of protein/ligand complexes calculated using dissociation Parallel Cascade
Selection Molecular Dynamics and Markov state model
H. Hata, D. Phuoc Tran, M. Marzouk Sobeh and A. Kitao, Biophys. Physicobiol. 18, 305 (2021).
2.

The role of the half-turn in determining structures of Alzheimer’s Abeta wild-type and mutants
S. Hayward and A. Kitao, J. Struct. Biol. 213, 107792 (2021).

3.

Regulatory Switching by Concerted Motions on the Microsecond Time Scale of the Oxygen Sensor
Protein FixL
T. Yamawaki, M. Mizuno, H. Ishikawa, K. Takemura, A. Kitao, Y. Shiro and Y. Mizutani, J.
Phys. Chem. B. 16, 2835 (2021).

4.

Dissociation Pathways of the p53 DNA Binding Domain from DNA and Critical Roles of Key
Residues Elucidated by dPaCS-MD/MSM
M. M. Sobeh and A. Kitao, J. Chem. Inf. Model 62, 1294 (2021).

KOBAYASHI, Akito [ B class; 400 (B), 80 (C) ] (199)— Ordered states in strongly correlated Dirac electron systems of organic conductors
KOBAYASHI, Katsuyoshi [ B class; 400 (B), 70 (C) ] (154)— Theoretical study on electronic properties of new nanoscale surfaces and interfaces
1. Short-range magnetic interaction in a monolayer 1T-VSe2 ﬁlm revealed by element-speciﬁc x-ray
magnetic circular dichroism
K. Sumida, Y. Takeda, S. Kusaka, K. Kobayashi, and T. Hirahara, Phys. Rev. Materials 6,014006 (2022).
DOI:10.1103/PhysRevMaterials.6.014006

KOBAYASHI, Nobuhiko [ C class; 3400 (B), 600 (C) ] (92)
— First-principles study of quantum transport in nanostructures
KOBAYASHI, Ryo [ B class; 300 (B), 0 (C) ] (319)— Molecular dynamics analyses of ion migration at grain boundaries in solid state electrolyte
1. Non-equilibrium molecular dynamics study on atomistic origin of grain boundary resistivity in
NASICON-type Li-ion conductor
R. Kobayashi, K. Nakano, and M. Nakayama, Acta Materialia 226, 117596 (2022).
DOI:10.1016/j.actamat.2021.117596

KOGA, Akihisa [ C class; 4400 (B), 750 (C) ] (231)— Spin transport through Kitaev spin liquids
1. Role of Majorana fermions in spin transport of anisotropic Kitaev model
H. Taguchi, Y. Murakami, A. Koga and J. Nasu, Phys. Rev. B 104, 125139 (2021).

364

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2.

Ferrimagnetically ordered states in the Hubbard model on the hexagonal golden-mean tiling
A. Koga and S. Coates, Phys. Rev. B 105, 104410 (2022).

3.

Photoinduced dynamics of a quasicrystalline excitonic insulator
K. Inayoshi, Y. Murakami, and A. Koga, Phys. Rev. B 105, 104307 (2022).

4.

Thermally enhanced Majorana-mediated spin transport in the Kitaev model
H. Taguchi, Y. Murakami and A. Koga, Phys. Rev. B 105, 125137 (2022).

KOMATSU, Yu [ C class; 4000 (B), 700 (C) ] (89)
— A uniﬁed understanding of thermodynamic properties in icy planets and icy moons
KONDO, Kenji [ C class; 2000 (B), 100 (C) ] (264)— Numerical Analysis for Stability and Dynamics of Magnetic Structures such as Skyrmions
KOURA, Akihide [ C class; 1400 (B), 0 (C) ] (127)— Ab initio molecular dynamics study on static structure of glass materials
1. Reproduction of Melting and Crystallization of Sodium by Machine-Learning Interatomic Potential Based on Artiﬁcial Neural Networks
A. Irie, S. Fukushima, A. Koura, K. Shimamura and F. Shimojo, J. Phys. Soc. Jpn. 90 (2021)
094603.
DOI:10.7566/JPSJ.90.094603
2.

Importance of Adjusting Coeﬃcients in Cost Function for Construction of High-Accuracy MachineLearning Interatomic Potential
A. Irie, K. Shimamura, A. Koura, and F. Shimojo, J. Phys. Soc. Jpn. 91 (2022) 045002.

3.

Thermal conductivity calculation based on GreenKubo formula using ANN potential for β-Ag2 Se
Y. Takeshita, K. Shimamura, S. Fukushima, A. Koura, and F. Shimojo, J. Phys. Chem. Solids
163, 110580 (2022).

KUNISADA, Yuji [ C class; 6200 (B), 0 (C) ] (73)
— Reduction of Rare Metals in Formic Acid Decomposition Catalysts and Oxygen Storage Materials
1. Anisotropic Growth of Copper Nanorods Mediated by Cl Ions
M. J. Saw, M. T. Nguyen, Y. Kunisada, T. Tokunaga, T. Yonezawa, ACS Omega 7 (2022)
74147420.
DOI:10.1021/acsomega.2c00359

KUROKI, Kazuhiko [ C class; 10000 (B), 900 (C) ] (53, 55)— First principles study on defect formations in new thermoelectric materials— Study on new-type of nickelate superconductors based on multiorbital models
1. Development of an eﬃcient impurity solver in dynamical mean ﬁeld theory for multiband systems:
Iterative perturbation theory combined with parquet equations
R. Mizuno, M. Ochi, and K. Kuroki, Phys. Rev. B 104, 035160 (2021).
DOI:10.1103/PhysRevB.104.035160
2.

Simpliﬁcation of the Local Full Vertex in the Impurity Problem in DMFT and Its Applications
for the Nonlocal Correlation
R. Mizuno, M. Ochi, and K. Kuroki, J.Phys. Soc. Jpn. 91, 034002 (2022).
DOI:10.7566/JPSJ.91.034002

365

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

3.

First-principles study of defect formation energies in LaOXS2 (X =Sb,Bi)
M. Ochi and K. Kuroki, Phys.Rev.B 105, 094110 (2022).
DOI:10.1103/PhysRevB.105.094110

KUSAKABE, Koichi [ C class; 2600 (B), 300 (C) ] (104)— Evolutionary algorithm for simulation of fast chemical reaction process
1. Eﬀect of on-site Coulomb repulsion on ferromagnetic ﬂuctuations in heavily overdoped cuprates
S. Teranishi, K. Nishiguchi, S. Yunoki, and K. Kusakabe, J. Phys. Soc. Jpn. 90, 094707 (2021).
DOI:10.7566/JPSJ.90.094707
2.

Material Optimization of Potenetial High-Tc Superconducting Single-layer Cuprates
S. Teranishi, K. Nishiguchi, and K. Kusakabe, J. Phys. Soc. Jpn. 90, 054705 (2021).
DOI:10.7566/JPSJ.90.054705

3.

High magnetoresistance of a hexagonal boron nitride-graphene heterostructure-based MTJ throughexcited-electron transmission
H. Harfah, Y. Wicaksono, G. K. Sunnardianto, M. A. Majidi, and K. Kusakabe, Nanoscale Adv.
4, 117 (2022).
DOI:10.1039/D1NA00272D

4.

S=1 antiferromagnetic electron-spin systems on hydrogenated phenalenyl-tessellation molecules
for material-based quantum-computation resources
N. Morishita, Y. Oishi, T. Yamaguchi, and K. Kusakabe, Appl. Phys. Express 14, 121005 (2021).
DOI:10.35848/1882-0786/ac3b9d

5.

Zero-energy modes in a super-chiral nanographene network of phenalenyl-tessellation molecules
N. Morishita, and K. Kusakabe, Phys. Lett. A 408, 127462 (2021).
DOI:10.1016/j.physleta.2021.127462

6.

Terahertz-induced martensitic transformation in partially stabilized zirconia
M. Nagai, Y. Higashitani, M. Ashida, K. Kusakabe, H. Niioka, A. Hattori, H. Tanaka, G. Isoyama,
and N. Ozaki Research square, DOI:10.21203/rs.3.rs-130295/v1 (Preprint)
DOI:10.21203/rs.3.rs-130295/v1

LEE, Minhyeok [ C class; 1800 (B), 0 (C) ] (268)— Development of the Low-Temperature Oxidation Model for Alternative Fuels Using Machine Learning
LIAO, YUXUAN [ C class; 4200 (B), 800 (C) ] ()— Machine-learning-assisted Development of Giant Thermal-Property Database for Polymer Materials— Ultimate Suppression of Nanoheat Transport with Quasi-phononic Crystal
1. Akhiezer mechanism dominates relaxation of propagons in amorphous material at room temperature
Yuxian Liao, Junichiro Shiomi, J. Appl. Phys. 130, 035101 (2021).
DOI:10.1063/5.0050159

MAEHIRA, Takahiro [ B class; 300 (B), 30 (C) ] (168)— Electronic Structure and Fermiology of d-electron compounds
MAKINO, Takayuki [ B class; 400 (B), 0 (C) ] (164)— Electron-phonon interaction under electric ﬁelds in oxides— Parallel nonlinear regression analysis for spectroscopic data with existing Julia packages
1. Contactless Determination of Optimal Chloride Concentration for Power Conversion Eﬃciency in

366

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoPVKMAI Using Photoluminescence Spectroscopy
T. Asai et al., Photonics 8, 412 (2021).
DOI:10.3390/photonics8100412
2.

Optical properties of LiNbO2 thin ﬁlms
T. Kurachi et al., Physica B 621, 413259 (2021).
DOI:10.1016/j.physb.2021.413259

MAO, WEI [ C class; 1600 (B), 500 (C) ] ()— First-principles calculation of microscopic behaviors of hydrogen in metal oxides
MASAKI, Yusuke [ B class; 400 (B), 0 (C) ] ()— Fractional Vortices in Topological Nematic Superﬂuids
MATSUKAWA, Hiroshi [ C class; 1600 (B), 500 (C) ] ()— Physics of Friction
MATSUMOTO, Munehisa [ C class; 2000 (B), 650 (C) ] ()— Data assimilation of measurement and simulation for rare-earth permanent magnets
MATSUNAKA, Daisuke [ B class; 300 (B), 0 (C) ] (170)— First-principles Study of Defects of Magnesium Alloys
MATSUSHITA, Katsuyoshi [ C class; 200 (B), 300 (C) ] (301)— Numerical Study of Rotation-Translation Motion Transition of Cell Clusters— Simulation of Cell Collective Rotatopm
MATSUSHITA, Yu-ichiro [ C class; 9600 (B), 1100 (C) ] (58)
— Identiﬁcation of interface-state defects in power semiconductors: Approach from ab-initio calculations
1. Eﬀect of magnetocrystalline anisotropy on magnetocaloric properties of an AlFe2 B2 compound
Hung Ba Tran, Hiroyoshi Momida, Yu-ichiro Matsushita, Kazunori Sato, Yukihiro Makino, Koun
Shirai, and Tamio Oguchi, Phys. Rev. B 105, 134402 (2022).
DOI:10.1103/PhysRevB.105.134402
2.

Insight into anisotropic magnetocaloric eﬀect of CrI3
Hung Ba Tran and Hiroyoshi Momida and Yu-ichiro Matsushita and Koun Shirai and Tamio
Oguchi, Acta Materialia 231, 117851 (2022).
DOI:10.1016/j.actamat.2022.117851

MAYUMI, Koichi [ C class; 3400 (B), 800 (C) ] (245)— Molecular Dynamics Simulations of Strain-Induced Crystallization in Robust and Tough Polymer
Gels
MISAWA, Masaaki [ B class; 500 (B), 0 (C) ] (149)— Large-Scale Molecular Dynamics Simulations on Non-Equilibrium Phenomena Using First-Principles
Calculation and Machine Leaning
1. 第一原理計算と機械学習による固体材料における衝撃圧縮特性の分子動力学解析
三澤賢明, 島村孝平, 下條冬樹, セラミックス 56, 674 (2021).
2.

第一原理計算と機械学習に基づく衝撃圧縮挙動の分子動力学計算
三澤賢明, 島村孝平, 下條冬樹, 高圧力の科学と技術 31, 132 (2021).
DOI:10.4131/jshpreview.31.132

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoMIZUKAMI, Wataru [ C class; 4200 (B), 0 (C) ] (244)— Simulations of quantum-classical-hybrid algorithms for sensor materials with considering noise
1. Variational quantum simulation for periodic materials
Nobuyuki Yoshioka, Takeshi Sato, Yuya O. Nakagawa, Yu-ya Ohnishi, and Wataru Mizukami,
Phys. Rev. Research 4, 013052 (2022).
DOI:10.1103/PhysRevResearch.4.013052
2.

Solving quasiparticle band spectra of real solids using neural-network quantum states
Nobuyuki Yoshioka, Wataru Mizukami, and Franco Nori, Commun. Phys. 4, 106 (2021).
DOI:10.1038/s42005-021-00609-0

MIZUSHIMA, Takeshi [ B class; 400 (B), 80 (C) ] (304)— Numerical study on the tolerance of Majorana-based qubits in topological superconductors
1. Manipulation of Majorana Kramers Qubit and its Tolerance in Time-Reversal-Invariant Topological Superconductor
T. Sanno, M. G. Yamada, T. Mizushima, and S. Fujimoto, submitted
2.

Engineering Yang-Lee anyons via Majorana bound states
Y. Tanaka, T. Sanno, T. Mizushima, and S. Fujimoto, submitted

MOCHIZUKI, Masahito [ B,C,D class; 12100 (B), 0 (C) ] (180, 181)
— Novel dynamics of magnetic skyrmion crystal phases due to extra degrees of freedom— Numerical studies on the photoinduced phenomena of magnetic skyrmion lattices in metallic magnets— Theoretical study on the spin-wave excitations of multiple-Q magnetic hedgehogs
1. Dynamical switching of magnetic topology in microwave-driven itinerant magnet
R. Eto and M. Mochizuki, Phys. Rev. B 104, 104425 (2021).
DOI:10.1103/PhysRevB.104.104425
2.

Low-energy excitations of skyrmion crystals in a centrosymmetric Kondo-lattice magnet: Decoupled spin-charge excitations and nonreciprocity
R. Eto, R. Pohle, and M. Mochizuki, arXiv:2203.01496
DOI:10.48550/arXiv.2203.01496

3.

Dynamical phase transitions in the photodriven charge-ordered Dirac-electron system
Y. Tanaka and M. Mochizuki, arXiv:2203.04542
DOI:10.48550/arXiv.2203.04542

MOMIDA, Hiroyoshi [ C class; 2600 (B), 400 (C) ] (102)— Structure stability and electronic structures of point defects in wide-gap oxide materials
1. Tavorite-like orthorhombic Ax VPO4 F (A = Li, Na) for novel high-voltage cathodes in rechargeable
batteries
H. D. Luong, V. A. Dinh, H. Momida, and T. Oguchi, J. Alloys Compd. 875, 159963 (2021).
DOI:10.1016/j.jallcom.2021.159963
2.

First-principles study on cathode properties of Li2 M TiO4 and Na2 M TiO4 (M = V, Cr, Mn, Fe,
Co, Ni)K. Yamauchi, H. Momida, and T. Oguchi, J. Phys. Soc. Jpn. 91, 034704 (2022).
DOI:10.7566/JPSJ.91.034704

3.

Performance and reaction mechanisms of tin compounds as high-capacity negative electrodes oflithium and sodium ion batteries

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H. Kotaka, H. Momida, and T. Oguchi, Mater. Adv. 3, 2793 (2022).
DOI:10.1039/d1ma00967b
4.

Understanding doping eﬀects on P2 Nax Mn1−x My O2 (M = Li, Mg, Al, Ti, V, Cr, Fe, Co, Ni)
cathode materials for Na-ion batteries
H. D. Luong, H. Momida, V. A. Dinh, and T. Oguchi, Phys. Rev. Materials 6, 015802 (2022).
DOI:10.1103/PhysRevMaterials.6.015802

5.

Insight into anisotropic magnetocaloric eﬀect of CrI3
H. B. Tran, H. Momida, Y. Matsushita, K. Shirai, and T. Oguchi, Acta Materialia, Accepted.
DOI:10.1016/j.actamat.2022.117851

6.

Eﬀect of magnetocrystalline anisotropy on magnetocaloric properties of AlFe2 B2 compound
H. B. Tran, H. Momida, Y. Matsushita, K. Sato, Y. Makino, K. Shirai, and T. Oguchi, Phys.
Rev. B, Accepted.

MORIKAWA, Yoshitada [ C,E class; 10100 (B), 1500 (C) ] (49)
— Quantum Simulations on Dynamical Heterogeneous Catalysts
1. Theoretical study on adsorption and reaction of polymeric formic acid on the Cu(111) surface
S. E. M. Putra, F. Muttaqien, Y. Hamamoto, K. Inagaki, A. Shiotari, J. Yoshinobu, Y. Morikawa,and I. Hamada, Phys. Rev. Materials 5, 075801 (2021).
DOI:10.1103/PhysRevMaterials.5.075801
2.

A ﬂat-lying dimer as a key intermediate in NO reduction on Cu(100)K. Kuroishi*, M. R. Al Fauzan*, T. N. Pham, Y. Wang, Y. Hamamoto, K. Inagaki, A. Shiotari,
H. Okuyama, S. Hatta, T. Aruga, I. Hamada, and Y. Morikawa, Phys. Chem. Chem. Phys. 23,
16880 (2021).
DOI:10.1039/D1CP02746H

3.

Chemical stability of hydrogen boride nanosheets in water
K. I. M. Rojas, N. T. Cuong, H. Nishino, R. Ishibiki, S. Ito, M. Miyauchi, Y. Fujimoto, S.
Tominaka, S. Okada, H. Hosono, N. B. Arboleda Jr., T. Kondo, Y. Morikawa and I. Hamada,Commun. Mater. 2, 81 (2021).
DOI:10.1038/s43246-021-00184-5

4.

Isotope eﬀect of methane adsorbed on fcc metal (111) surfaces
S. E. M. Putra, Y. Morikawa, and I. Hamada, Chem. Phys. Lett. 780, 138943 (2021).
DOI:10.1016/j.cplett.2021.138943

5.

Mechanistic insight into oxygen vacancy migration in SrFeO3 δ from DFT+U simulations
M. Alaydrus, I. Hamada, and Y. Morikawa, Phys. Chem. Chem. Phys. 23, 18628-18639 (2021).
DOI:10.1039/D1CP02452C

6.

Dry reforming of methane on Co catalysts: DFT-based insight into carbon deposition vs removal
Y.-J. Wong, H. H. Halim; N. F. Khairudin, T. N. Pham, S. E. M. Putra, Y. Hamamoto, K.
Inagaki, I. Hamada, A. R. Mohamed, and Y. Morikawa, J. Phys. Chem. C 125, 21902-21913(2021).
DOI:10.1021/acs.jpcc.1c04819

7.

Adsorption of CO2 on Terrace, Step, and Defect Sites on Pt Surfaces: A Combined TPD, XPS,
and DFT Study
Y.-J. Wong, Y.-H. Choi, S. Tanaka, H. Yoshioka, K. Mukai, H. H. Halim, A. R. Mohamed, K.
Inagaki, Y. Hamamoto, I. Hamada, J. Yoshinobu, Y. Morikawa, J. Phys. Chem. C 125, 2365723668 (2021).

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DOI:10.1021/acs.jpcc.1c05228
8.

Analysis of atomic structure, magnetic ordering, and oxygen diﬀusion in oxygen deﬁcient Sr 3 Fe2 O7 −
δ perovskite: Toward rational catalysts design
T. Ota, M. Alaydrus, H. Kizaki and Y. Morikawa, Phys. Rev. Materials 6, 015801 (2022).
DOI:10.1103/PhysRevMaterials.6.015801

MORITA, Satoshi [ B class; 600 (B), 90 (C) ] (295)— Improvement of tensor network renormalization for high-dimensional systems
1. Symmetry-protected topological phases and competing orders in a spin-1/2 XXZ ladder with afour-spin interaction
Takuhiro Ogino, Shunsuke Furukawa, Ryui Kaneko, Satoshi Morita, and Naoki Kawashima, Phys.
Rev. B 104, 075135 (2021).
DOI:10.1103/PhysRevB.104.075135
2.

Mott Insulator-like Bose-Einstein Condensation in a Tight-Binding System of Interacting Bosons
with a Flat Band
Hosho Katsura, Naoki Kawashima, Satoshi Morita, Akinori Tanaka, and Hal Tasaki, Phys. Rev.
Research 3, 033190 (2021).
DOI:10.1103/PhysRevResearch.3.033190

MOTOME, Yukitoshi [ C class; 11600 (B), 1250 (C) ] (178)— Theoretical study of symmetry breaking and quantum transport phenomena in charge-spin-orbital
coupled systems
1. Fractional corner magnetization of collinear antiferromagnets
H. Watanabe, Y. Kato, H. C. Po, and Y. Motome, Phys. Rev. B 103, 134430 (2021).
DOI:10.1103/PhysRevB.103.134430
2.

Spin moiré engineering of topological magnetism and emergent electromagnetic ﬁelds
K. Shimizu, S. Okumura, Y. Kato, and Y. Motome, Phys. Rev. B 103, 184421 (2021).
DOI:10.1103/PhysRevB.103.184421

3.

Crystal-chirality-dependent control of magnetic domains in a time-reversal-broken antiferromagnet
K. Kimura, Y. Kato, S. Kimura, Y. Motome, and T. Kimura, npj Quantum Mater. 6, 54 (2021).
DOI:10.1038/s41535-021-00355-0

4.

Spin dynamics in the Kitaev model with disorder: Quantum Monte Carlo study of dynamical spin
structure factor, magnetic susceptibility, and NMR relaxation rate
J. Nasu and Y. Motome, Phys. Rev. B 104, 035116 (2021).
DOI:10.1103/PhysRevB.104.035116

5.

Topological spin crystals by itinerant frustration
S. Hayami and Y. Motome, J. Phys.: Condens. Matter 33, 443001 (2021).
DOI:10.1088/1361-648X/ac1a30

6.

Vortex creation and control in the Kitaev spin liquid by local bond modulations
S.-H. Jang, Y. Kato, and Y. Motome, Phys. Rev. B 104, 085142 (2021).
DOI:10.1103/PhysRevB.104.085142

7.

Charge density waves in multiple-Q spin states
S. Hayami and Y. Motome, Phys. Rev. B 104, 144404 (2021).
DOI:10.1103/PhysRevB.104.144404

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8.

Quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An
application to the Kitaev model in a magnetic ﬁeld
P. A. Mishchenko, Y. Kato, and Y. Motome, Phys. Rev. D 104, 074517 (2021).
DOI:10.1103/PhysRevD.104.074517

9.

Electronic and magnetic properties of iridium ilmenites AIrO3 (A=Mg, Zn, and Mn)
S.-H. Jang and Y. Motome, Phys. Rev. Materials 5, 104409 (2021).
DOI:10.1103/PhysRevMaterials.5.104409

10. Quadratic optical responses in a chiral magnet
S. Okumura, T. Morimoto, Y. Kato, and Y. Motome, Phys. Rev. B 104, L180407 (2021).
DOI:10.1103/PhysRevB.104.L180407
11. Determinant-free fermionic wave function using feed-forward neural networks
K. Inui, Y. Kato, and Y. Motome, Phys. Rev. Research 3, 043126 (2021).
DOI:10.1103/PhysRevResearch.3.043126
12. Phase shift in skyrmion crystals
S. Hayami, T. Okubo, and Y. Motome, Nat. Commun. 12, 6927 (2021).
DOI:10.1038/s41467-021-27083-0
13. Phase degree of freedom and topology in multiple-Q spin textures
K. Shimizu, S. Okumura, Y. Kato, and Y. Motome, arXiv:2201.03290.
DOI:10.48550/arXiv.2201.03290
14. Feasibility of Kitaev quantum spin liquids in ultracold polar molecules
K. Fukui, Y. Kato, J. Nasu, and Y. Motome, arXiv:2204.06144
DOI:10.48550/arXiv.2204.06144

MURASHIMA, Takahiro [ B class; 600 (B), 90 (C) ] (293)— Development of multiscale simulation technique for liquids and solids
1. Viscosity Overshoot in Biaxial Elongational Flow: Coarse-Grained Molecular Dynamics Simulation of Ring-Linear Polymer Mixtures
T. Murashima, K. Hagita and T. Kawakatsu, Macromolecules 54, 7210 (2021).
DOI:10.1021/acs.macromol.1c00267

NADA, Hiroki [ B,C class; 500 (B), 750 (C) ] (274, 275)
— Creation of a Method for Design of Scale Formation Control Molecules by a Metadynamics Method— Elucidation of pathways for the crystallization of ionic liquids by large-scale metadynamics simulation
1. Stable Binding Conformations of Polymaleic and Polyacrylic Acids at a Calcite Surface in the
Presence of Countercations: A Metadynamics Study
H. Nada, submitted to Langmuir

NAKAGAWA, Naoko [ C class; 3800 (B), 700 (C) ] (240)— Steady states realized by a global thermodynamic balance in nonequilibrium
1. Work relation for determining the mixing free energy of small-scale mixtures
A. Yoshida and N. Nakagawa, Phys. Rev. Research, to appear (2022).

NAKAMURA, Kazuma [ C class; 2600 (B), 0 (C) ] (108)— Ab initio calcualtion for reﬂectivity for SrVO3/SrTiO3 CaCuO2/SrTiO3, and Ca5Ir3O12— Ab initio derivation of eﬀective low-energy models for SrVO3/SrTiO3 and CaCuO2/SrTiO3 multi-

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layer system
1. Ab initio derivation of low-energy Hamiltonians for systems with strong spin-orbit interaction:
Application to Ca5 Ir3 O12
M. Charlebois, J. B. Moree, K. Nakamura, Y. Nomura, T. Tadano, Y. Yoshimoto, Y. Yamaji, T.
Hasegawa, K. Matsuhira, and M. Imada, Phys. Rev. B 104, 075153 (2021).
DOI:10.1103/PhysRevB.104.075153
2.

RESPACK: An ab initio tool for derivation of eﬀective low-energy model of material
Kazuma Nakamura, Yoshihide Yoshimoto, Yusuke Nomura, Terumasa Tadano, Mitsuaki Kawamura, Taichi Kosugi, Kazuyoshi Yoshimi, Takahiro Misawa, and Yuichi Motoyama, Comput.
Phys. Commun. 261, 107781 (2021).
DOI:10.1016/j.cpc.2020.107781

NAKANO, Hiroki [ C class; 1400 (B), 450 (C) ] (266)— Numerical study on low-energy states of quantum spin systems
1. Magnetization process of the S=1/2 Heisenberg antiferromagnet on the ﬂoret pentagonal lattice
R. Furuchi, H. Nakano, N. Todoroki, and T. Sakai, J. Phys. Commun. 5 125008 (2021).
DOI:10.1088/2399-6528/ac3f7a

NAKANO, Hiroyoshi [ C class; 4000 (B), 0 (C) ] (247)— Molecular dynamics study of surface nanobubbles under non-equilibrium conditions
1. Molecular dynamics study of shear-induced long-range correlations in simple ﬂuids
Hiroyoshi Nakano and Yuki Minami, Phys. Rev. Research in press.

NAKAYAMA, Takashi [ C class; 3000 (B), 700 (C) ] (93)— First-principles study on charging-induced structure phase transitions of thin ﬁlm oxides
1. Clustering feature of metal atoms in pentacene molecular solids: the ﬁrst-principles study
S. Watanabe, Y. Tomita, K. Kawabata, T. Nakayama, Jpn. J. Appl. Phys. 61, 021003 (2022).
DOI:10.35848/1347-4065/ac41e22.

Impacts of terminal molecules on metal-atom diﬀusion into alkane self-assembled-monolayer ﬁlms:
ﬁrst-principles study
S. Watanabe, T. Nakayama, Jpn. J. Appl. Phys. 60, 125505 (2021).
DOI:10.35848/1347-4065/ac3181

3.

New types of resonant tunneling currents at Si-p/n junctions: One-dimensional model calculation
S. Cho, T. Nakayama, Jpn. J. Appl. Phys. 60, 054002 (2021).
DOI:10.35848/1347-4065/abf782

NASU, Joji [ C class; 3800 (B), 800 (C) ] (190)— Numerical study of topological thermal transport in Kitaev-related systems
1. Role of Majorana fermions in spin transport of anisotropic Kitaev model
H. Taguchi, Y. Murakami, A. Koga, and J. Nasu, Phys. Rev. B 104, 125139 (2021).
2.

Field-angle dependence of thermal Hall conductivity in a magnetically ordered Kitaev-Heisenberg
system
S. Koyama and J. Nasu, Phys. Rev. B 104, 075121 (2021).

3.

Spin dynamics in the Kitaev model with disorder: Quantum Monte Carlo study of dynamical spin
structure factor, magnetic susceptibility, and NMR relaxation rate
J. Nasu and Y. Motome, Phys. Rev. B 104, 035116-1-17 (2021).

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4.

Majorana correlations in the Kitaev model with ordered-ﬂux structures
A. Koga, Y. Murakami, and J. Nasu, Phys. Rev. B 103, 214421 (2021).

5.

Field-angle dependence of thermal transport in Kitaev-Γ model
S. Koyama and J. Nasu, J. Phys.: Conf. Ser. 2164, 012071 (2022).

NIKI, Kaori [ B,C class; 400 (B), 250 (C) ] (143)— Calculation of photoelectron angle distribution in the photoexcitation process on the organic molecules
adsorbed surface— Development of time-resolved analysis method for molecular crystal surface
1. A Faster Method of Photoelectron Intensity Calculation Based on Multiple Scattering Theory
M. Haniuda, M. Nozaki, and K. Niki, J. Surf. Sci. and Nanotech.
2.

The electronic and structural dynamics of CuPc
Kiana Baumgartner, Misa Nozaki, Christian Metzger, Masato Haniuda, Kaori Niki, Daria PopovaGorelova, Kai Rossnage, Markus Scholz, Science

NISHIDATE, Kazume [ C class; 400 (B), 0 (C) ] (163)— First-principles electronic structure calculation of double-perovskite photocatalyst
NISHIGUCHI, Kazutaka [ B class; 400 (B), 0 (C) ] (314)— Theoretical study of thermoelectric properties in doped Fe2 VAl: A weak-coupling approach
1. Possibility of N-type Doping in CaAl2 Si2 -type Zintl Phase Compound CaZn2 X2 (X = As, P)
K. Nishiguchi, M. Ochi, C. H. Lee, and K. Kuroki, J. Phys. Soc. Jpn., in press.

NOGUCHI, Hiroshi [ C class; 11600 (B), 1250 (C) ] (212)— structure formation of biomembrane
1. Binding of anisotropic curvature-inducing proteins onto membrane tubes
H. Noguchi, C. Tozzi, and M. Arroyo Soft Matter 18, 3384 (2022).
DOI:10.1039/D2SM00274D
2.

Hydrophobic immiscibility controls self-sorting or co-assembly of peptide amphiphiles
Rie Wakabayashi, Rino Imatani, Mutsuhiro Katsuya, Yuji Higuchi, Hiroshi Noguchi, Noriho
Kamiya, and Masahiro Goto Chem. Commun. 58, 585 (2022).
DOI:10.1039/D1CC05560G

3.

Eﬀects of gas-liquid phase transitions on soundwave propagation: A molecular dynamics study
Y. Asano, H. Watanabe, and H. Noguchi Phys. Rev. Fluids, (2022) in press.

NOGUCHI, Yoshifumi [ C class; 5200 (B), 800 (C) ] (78)
— XAS simulations by ﬁrst-principles GW+Bethe-Salpeter method
1. Absorption Spectra for Fireﬂy Bioluminescence Substrate Analog: TokeOni in Various pH Solutions
Haruhisa Ogawa, Ryohei Ono, Yoshifumi Noguchi, Nobuo Kitada, Ryohei Saito-Moriya, Shojiro
A. Maki, Hidefumi Akiyama, Hideyuki Itabashi, and Miyabi Hiyama, Photochem. Photobiol.
97, 1016 (2021).
DOI:10.1111/php.13458
2.

Exciton maps for thermally activated delayed ﬂuorescence active/inactive carbazole benzonitrile
derivatives

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Yoshifumi Noguchi, J. Chem. Phys. 155, 204302 (2021).
DOI:10.1063/5.0068402
3.

Fragment-Based Excited-State Calculations Using the GW Approximation and the Bethe −Salpeter Equation
Takatoshi Fujita and Yoshifumi Noguchi, J. Phys. Chem. A 125, 10580 (2021).
DOI:10.1021/acs.jpca.1c07337

NOMURA, Yusuke [ C class; 5200 (B), 800 (C) ] (184)— Finite-temperature calculations for quantum many-body systems using Boltzmann machine
1. RESPACK: An ab initio tool for derivation of eﬀective low-energy model of material
Kazuma Nakamura, Yoshihide Yoshimoto, Yusuke Nomura, Terumasa Tadano, Mitsuaki Kawamura, Taichi Kosugi, Kazuyoshi Yoshimi, Takahiro Misawa, and Yuichi Motoyama, Comput.
Phys. Commun. 261, 107781 (2021).
DOI:10.1016/j.cpc.2020.107781
2.

Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
Yusuke Nomura, J. Phys.: Condens. Matter 33, 174003 (2021).

3.

qeirreps: An open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
Akishi Matsugatani, Seishiro Ono, Yusuke Nomura, and Haruki Watanabe, Comput. Phys. Commun. 264, 107948 (2021).
DOI:10.1016/j.cpc.2021.107948

4.

Purifying Deep Boltzmann Machines for Thermal Quantum States
Yusuke Nomura, Nobuyuki Yoshioka, and Franco Nori, Phys. Rev. Lett. 127, 060601 (2021).

5.

Dirac-Type Nodal Spin Liquid Revealed by Reﬁned Quantum Many-Body Solver Using NeuralNetwork Wave Function, Correlation Ratio, and Level Spectroscopy
Yusuke Nomura and Masatoshi Imada, Phys. Rev. X 11, 031034 (2021).

6.

Ab initio derivation of low-energy Hamiltonians for systems with strong spin-orbit interaction:
Application to Ca5Ir3O12
Maxime Charlebois, Jean-Baptiste More, Kazuma Nakamura, Yusuke Nomura, Terumasa Tadano,
Yoshihide Yoshimoto, Youhei Yamaji, Takumi Hasegawa, Kazuyuki Matsuhira, and Masatoshi
Imada, Phys. Rev. B 104, 075153 (2021).
DOI:10.1103/PhysRevB.104.075153

NOZAWA, Kazuki [ C class; 400 (B), 400 (C) ] (137)— First-principles calculations of complex metallic alloy surfaces
OBATA, Masao [ B class; 700 (B), 120 (C) ] (136)— Analysis of ferroelectric-ferromagnetic interface and magnetic material with an anisotropic crystal
structure— Analysis of insulator-ferromagnetic interface and magnetic material with an anisotropic crystal structure
1. Eﬀect of electron localization in theoretical design of Ni-Mn-Ga based magnetic shape memory
alloysZelený, Martin and Sedlák, Petr and Heczko, Oleg and Seiner, Hanuš and Vertát, Petr andObata, Masao and Kotani, Takao and Oda, Tatsuki and Straka, Ladislav, Mater. Des. 209,
109917 (2021).
DOI:10.1016/j.matdes.2021.109917

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ODA, Tatsuki [ C class; 4800 (B), 950 (C) ] (83)
— Analyses on electronic structure and magnetoelectric eﬀect in high-performance spintronics and magnetic materials
1. Eﬀect of electron localization in theoretical design of Ni-Mn-Ga based magnetic shape memory
alloysMartin Zelen, Petr Sedlk, Oleg Heczko, Hanu Seiner, Petr Vett, Masao Obata, Takeo Kotani,
Tatsuki Oda, and Ladislav Straka, Materials & Design 209, 109917 (2021).

OGUCHI, Tamio [ C class; 3200 (B), 350 (C) ] (99)
— Magnetocaloric Eﬀect of Transition-Metal Alloys
1. Tavorite-type orthorhombic Ax VPO4 F (A = Li, Na) for novel high-voltage cathodes in rechargeable batteries
Huu Duc Luong, Van An Dinh, Hiroyoshi Momida, Tamio Oguchi, J. Alloys Compd. 875, 159963(2021).
2.

CrySPY: a crystal structure prediction tool accelerated by machine learning
Tomoki Yamashita, Shinichi Kanehira, Nobuya Sato, Hiori Kino, Kei Terayama, Hikaru Sawahata,
Takumi Sato, Futoshi Utsuno, Koji Tsuda, Takashi Miyake, Tamio Oguchi, Sci. Technol. Adv.
Mater.: Methods 1, 87 (2021).

3.

Atomic-layer stacking dependence of the magnetocrystalline anisotropy in Fe-Co multilayer thinﬁlms at MgO(001) interface
K. Nakamura, K. Nozaki, K. Hayashi, A.-M. Pradipto, M. Weinert, T. Oguchi, J. Magn. Magn.
Mater. 537, 168175 (2021).

4.

Electric-ﬁeld tuning of magnetic properties of bilayer VI3 : A ﬁrst-principles study
Thi Phuong Thao Nguyen, Kunihiko Yamauchi, Tamio Oguchi, Danila Amoroso, Silvia Picozzi,
Phys. Rev. B 104, 014414 (2021).

5.

First-Principles Study on Cathode Properties of Li2 M TiO4 and Na2 M TiO4 (M = V, Cr, Mn, Fe,
Co, Ni)Kunihiko Yamauchi, Hiroyoshi Momida, Tamio Oguchi:, J. Phys. Soc. Jpn. 91, 034704 (2022).

6.

Understanding doping eﬀects on P2 Nax Mn1−y My O2 (M =Li, Mg, Al, Ti, V, Cr, Fe, Co, Ni)
cathode materials for Na-ion batteries
Huu Duc Luong, Hiroyoshi Momida, Van An Dinh, Tamio Oguchi, Phys. Rev. Mater. 6, 015802(2022).

7.

Performance and reaction mechanisms of tin compounds as high-capacity negative electrodes oflithium and sodium ion batteries
Hiroki Kotaka, Hiroyoshi Momida, Tamio Oguchi, Mater. Adv. 3, 2793-2799 (2022).

8.

Spin-Polarized Band Structure in MoTe2 /Bi2 Se3 Heterostructure Designed from First Principles
Kunihiko Yamauchi, Ryoma Shimazu, Tamio Oguchi, J. Phys. Soc. Jpn. 91, 044705 (2022).

9.

Insight into anisotropic magnetocaloric eﬀect of CrI3
Hung Ba Tran, Hiroyoshi Momida, Yu-ichiro Matsushita, Koun Shirai, Tamio Oguchi,
Mater. 231, 117851 (2022).

Acta

10. Eﬀect of magnetocrystalline anisotropy on magnetocaloric properties of an AlFe2 B2 compound
Hung Ba Tran, Hiroyoshi Momida, Yu-ichiro Matsushita, Kazunori Sato, Yukihiro Makino, Koun
Shirai, Tamio Oguchi, Phys. Rev. B 105, 134402 (2022).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoOHKUBO, Yuji [ B class; 400 (B), 0 (C) ] (161)— Clariﬁcation of atomistic mechanism application of process design for adhesion interface between
metal and plasma-treated ﬂuoropolymers using ﬁrst principles calculation
OHMURA, Satoshi [ C class; 2200 (B), 0 (C) ] (112)— Ab initio molecular dynamics study on ion-conduction mechanisms of perovskite-type oxide
1. Liquid Structure of Tantalum under Internal Negative Pressure
Katagiri, K. and Ozaki, N. and Ohmura, S. and Albertazzi, B. and Hironaka, Y. and Inubushi,
Y. and Ishida, K. and Koenig, M. and Miyanishi, K. and Nakamura, H. and Nishikino, M. andOkuchi, T. and Sato, T. and Seto, Y. and Shigemori, K. and Sueda, K. and Tange, Y. and Togashi,
T. and Umeda, Y. and Yabashi, M. and Yabuuchi, T. and Kodama, R., Phys. Rev. Lett. 126,
175503 (2021).
DOI:10.1103/PhysRevLett.126.175503
2.

Tracking the light-driven layer stacking of graphene oxide
Yajima and Ryo Shikata and Tomohiro Iguchi and Keishi Akada and Shoji Yoshida and Jun-ichi
Fujita and Shin-ya Koshihara and Yuta Nishina, Carbon 183, 612 (2021).
DOI:10.1016/j.carbon.2021.07.058

OHNISHI, Masato [ C class; 4600 (B), 750 (C) ] (87)
— Low Thermal Conductance Generated by van der Waals Interaction
1. Strain-induced band modulation of thermal phonons in carbon nanotubes
Masato Ohnishi, Junichiro Shiomi, Phys. Rev. B 104, 014306 (2021).

OHNO, Akira [ B class; 400 (B), 70 (C) ] ()— Correlation between Order Parameter and Electron Transport Mechanism in Liquid Crystal
OHNO, Kaoru [ C class; 6600 (B), 950 (C) ] (68)— Improvement and application of all-electron mixed basis program
1. Study on Ni-Ti alloys around equiatomic composition by the ﬁrst-principles phase ﬁeld method
K. Ohno, M. Tsuchiya, R. Kuwahara, R. Sahara, S. Bhattacharyya, and T. N. Pham, Comp.
Mat. Sci. 191, 110284 (2021).
DOI:10.1016/j.commatsci.2021.110284
2.

Eﬀect of the Pt concentration on microstructures of Ti-Pt alloys using the ﬁrst-principles phaseﬁeld method
Thi Nu Pham, Kaoru Ohno, Ryoji Sahara, Riichi Kuwahara, and Swastibrata Bhattacharyya,
Acta Materialia 215, 117050 (2021).
DOI:10.1016/j.actamat.2021.117050

OHSAWA, Kazuhito [ C class; 400 (B), 0 (C) ] (159)— Study of interaction between radiation damage and interstitial atom
OHTO, Tatsuhiko [ C class; 4000 (B), 0 (C) ] (91)
— First-principles transport calculations for single-molecular junctions
OHTSUKI, Tomi [ C class; 5600 (B), 850 (C) ] (228)— Critical phenomena in novel Anderson transitions
1. Analysis of KohnSham Eigenfunctions Using a Convolutional Neural Network in Simulations of
the MetalInsulator Transition in Doped Semiconductors

376

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Y. Harashima, T. Mano, K. Slevin, T. Ohtsuki, J. Phys. Soc. Jpn. 90, 094001 (2021).
DOI:10.7566/JPSJ.90.094001

OKADA, Ken [ C class; 3600 (B), 650 (C) ] ()— Variational Monte Carlo study of twisted bilayer graphene
OKAZAKI, Susumu [ C class; 3600 (B), 700 (C) ] (243)— Investigation of the molecular origins of the mechanical and thermal properties of realistic biopolymers using all-atomistic molecular dynamics
1. Algorithm to minimize MPI communications in the parallelized fast multipole method combinedwith molecular dynamics calculations
Yoshimichi Andoh,Shin-ichi Ichikawa,Tatsuya Sakashita,Noriyuki Yoshii,Susumu Okazaki, J. comput. chem. 42, 1073 (2021),
DOI:10.1002/jcc.26524
2.

A comparison of the brittle PMMA with the ductile PC on the elasticity and yielding from amolecular dynamics perspective
Zhiye Tang, Kazushi Fujimoto, Susumu Okazaki, Polymer 226,123809 (2021),
DOI:10.1016/j.polymer.2021.123809

3.

Three-dimensional free-energy landscape of hydrogen and oxygen molecules in polymer electrolyte
membranes: Insight into diﬀusion paths
Tetsuro Nagai, Kazushi Fujimoto, Susumu Okazaki, J. Chem. Phys. 156, 044507 (2022),
DOI:10.1063/5.0075969

4.

Dynamic Monte Carlo calculation generating particle trajectories which satisfy diﬀusion equation
for heterogeneous systems with position-dependent diﬀusion coeﬃcient and free energy
Tetsuro Nagai, Akira Yoshimori, Susumu Okazaki, J. Chem. Phys. 156, 154506 (2022),
DOI:10.1063/5.0086949

OKUBO, Masashi [ B class; 400 (B), 30 (C) ] (157)— Development of all-solid-state capacitors using sulﬁde-based solid electrolytes
OKUBO, Tsuyoshi [ C class; 11600 (B), 1300 (C) ] (210)— Finite temperature property of the Kitaev models— Finite temperature property of the Kitaev spin liquid
1. Bond-weighted Tensor Renormalization GroupD. Adachi, T. Okubo and S. Todo, Phys. Rev. B, 105, L060402 (2022).
DOI:10.1103/PhysRevB.105.L060402
2.

Phase Shift in Skyrmion Crystals
S. Hayami, T. Okubo, and Y. Motome, Nature Commun., 12, 6927 (2021).
DOI:10.1038/s41467-021-27083-0

3.

TeNeS: Tensor Network Solver for Quantum Lattice Systems
Y. Motoyama, T. Okubo, K. Yoshimi, S. Morita, T. Kato, and N. Kawashima, arXiv:2112.13184
DOI:10.48550/arXiv.2112.13184

4.

Possibility of a topological phase transition in two-dimensional frustrated Heisenberg spin systems
T. Okubo and N. Kawashima, arXiv:2112.15053
DOI:10.48550/arXiv.2112.15053

377

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

OKUMURA, Hisashi [ C class; 5600 (B), 850 (C) ] (227)— Molecular dynamics simulations for assembly and disassembly of protein aggregates
1. Role of water molecules in the laser-induced disruption of amyloid ﬁbrils observed by nonequilibrium molecular dynamics simulations
H. Okumura, S. G. Itoh, K. Nakamura, and T. Kawasaki, J. Phys. Chem. B 125, 4964 (2021).
DOI:10.1021/acs.jpcb.0c11491
2.

Implementations of replica-permutation and replica sub-permutation methods into LAMMPS
M. Yamauchi, G. La Penna, S. G. Itoh, and H. Okumura, Comput. Phys. Commun. 276, 108362(2022).
DOI:10.1016/j.cpc.2022.108362

ONO, Atsushi [ B class; 300 (B), 0 (C) ] (204)— Photoinduced nonequilibrium dynamics in correlated electron systems
1. Ultrafast reorientation of the Néel vector in antiferromagnetic Dirac semimetals
A. Ono and S. Ishihara, npj Comput. Mater. 7, 171 (2021).
DOI:10.1038/s41524-021-00641-2

ONO, Shota [ B,C class; 1100 (B), 300 (C) ] (126)— Stability of atomically thin alloys— Stability of atomically thin alloys: II
1. Theoretical prediction on the immiscible Pb-Sn alloy stabilized on metal surfaces
S. Ono, J. Yuhara, and J. Onoe, Chem. Phys. Lett. 776, 138696 (2021).
DOI:10.1016/j.cplett.2021.138696
2.

Metastability relationship between two- and three-dimensional crystal structures: a case study of
the Cu-based compounds
S. Ono, Sci. Rep. 11, 14588 (2021).
DOI:10.1038/s41598-021-94034-6

3.

Comprehensive search for buckled honeycomb binary compounds based on noble metals (Cu, Ag,
and Au)S. Ono, Phys. Rev. Materials 5, 104004 (2021).
DOI:10.1103/PhysRevMaterials.5.104004

ONO, Tomoya [ C class; 9400 (B), 800 (C) ] (60)
— Development of ﬁrst-principles electronic-structure and transport calculation code RSPACE and simulations for device
1. Theoretical investigation of vacancy related defects at 4H-SiC(0001̄)/SiO2 interface after wet
oxidation
M. Tsunasaki, T. Ono and M. Uemoto, Jpn. J. Appl. Phys. 61 (2022) SH1001.
2.

First-Principles Study on Structure and Anisotropy of High N-atom Density Layer in 4H-SiC
M. Uemoto, N. Komatsu, Y. Egami and T. Ono, J. Phys. Soc. Jpn. 90 (2021) 124713.

ORIMOTO, Yuuichi [ C class; 1600 (B), 350 (C) ] (116)— First principles calculations of two-dimensional ordering process at organic/inorganic materials interface
OSHIKAWA, Masaki [ B class; 600 (B), 90 (C) ] (291)— Study on gapless SPT phases in quantum spin systems

378

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo1.

Z2 -enriched symmetry indicators for topological superconductors in the 1651 magnetic spacegroupsSeishiro Ono, Hoi Chun Po, and Ken Shiozaki, Phys. Rev. Research 3, 023086 (2021).
DOI:10.1103/PhysRevResearch.3.023086

2.

qeirreps: An open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
Akishi Matsugatani, Seishiro Ono, Yusuke Nomura, and Haruki Watanabe, Comput. Phys. Commun. 264, 107948 (2021).
DOI:10.1016/j.cpc.2021.107948

3.

Resolving the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XY model withtensor-network-based level spectroscopy
Atsushi Ueda and Masaki Oshikawa, Phys. Rev. B 104, 165132 (2021).
DOI:10.1103/PhysRevB.104.165132

4.

Tensor Network Renormalization Study on the Crossover in Classical Heisenberg and RP2 Models
in Two Dimensions
Atsushi Ueda and Masaki Oshikawa, arXiv.2202.07042
DOI:10.48550/arXiv.2202.07042

OSHIYAMA, Atsushi [ E class; 32500 (B), 3300 (C) ] (42)— Clariﬁcation of Microscopic Mechanisms of Semiconductor Epitaxial Growth and Device-Interface
Formation by Large-Scale Quantum-Theory-Based Computations
1. Gallium-gallium weak bond that incorporates nitrogen at atomic steps during GaN epitaxial
growthK. M. Bui, K. Shiraishi and A. Oshiyama, Appl. Surf. Sci. 557, 149542 (2021).
2.

Microscopic mechanism of adatom diﬀusion on stepped SiC surfaces revealed by ﬁrst-principles
calculations
K. Seino and A. Oshiyama, Appl. Surf. Sci. 561, 149927 (2021).

3.

Defect-free interface between amorphous (Al2 O3 )1−x (SiO2 )x revealed by ﬁrst-principle molecular
dynamics simulations
K. Chokawa, K. Shiraishi and A. Oshiyama, Appl. Phys. Lett. 119, 011602 (2021).

4.

Order-N orbital-free density-functional calculations with machine learning of functional derivatives for semiconductors and metals
F. Imoto, M. Imada adn A. Oshiyama, Phys. Rev. Research 3, 033198 (2021).

OTANI, Minoru [ E class; 14500 (B), 2200 (C) ] (342)— Development and Application of electrochemical-reaction simulation methods at the solid/solution
interfaces
OTSUKI, Michio [ C class; 2200 (B), 550 (C) ] (258)— Three-Dimensional Finite Element Analysis of Friction between solids
OZAKI, Taisuke [ C class; 5000 (B), 350 (C) ] (85)
— Prediction of new crystal structures based on the densest ternary sphere packings
1. Densest ternary sphere packings
Ryotaro Koshoji and Taisuke Ozaki, Phys. Rev. E 104, 024101 (2021).
DOI:10.1103/PhysRevE.104.024101

379

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoOZEKI, Yukiyasu [ C class; 7600 (B), 0 (C) ] (218)— Development and improvement of dynamical scaling analysis for critical phenomena— Development and improvement of dynamical scaling analysis for critical phenomena II
RAEBIGER, Hannes [ C class; 5000 (B), 800 (C) ] (81)— First principles theory of carrier localization in transition metal compounds
1. Parallel alignment of methylammonium cations in orthorhombic CH3 NH3 PbCl3 single crystal
observed by polarized micro-Raman scattering spectroscopy
Y. Kim, S. Bae,J. Park, T. T. .T. Nguyen, H. R. Jung, W. Jo, Y.-H. Kim, H. Raebiger, S. Yoon,
Chem. Mater. 34, 2972 (2022).
DOI:10.1021/acs.chemmater.1c03744
2.

Strain engineering to release trapped hole carriers in p-type haeckelite GaN
S. Bae, Y.-G. Kang, K. Ichihashi, M. Khazaei, V. Swamy, M. J. Han, K. J. Chan, K.-i. Shudo,
H. Raebiger, ACS Appl. Electron. Mater. 3, 5257 (2021).
DOI:10.1021/acsaelm.1c00765

3.

MXene Phase with C3 Structure Unit: A Family of 2D Electrides
S. Bae, W. Espinoza-Garcı́a, J-G. Kang, N. Egawa, J. Lee, K. Kuwahata, M. Khazaei, K. Ohno,
Y-H. Kim, M. J. Han, H. Hosono, G. M. Dalpian, and H. Raebiger, Adv. Funct. Mater. 31,
2100009 (2021).
DOI:10.1002/adfm.202100009

SAITO, Mineo [ C class; 8200 (B), 0 (C) ] (67)— First-principles calculations on muon in solids
1. Electronic Band Structures of Group-IV Two-Dimensional Materials: Spin-Orbit Coupling andGroup Theoretical Analysis
S. A. Puturi, Y. Yamaguchi, T. A. Ariasoca, M. Y. H. Widianto, K. Tagami and M. Saito, Surf.
Sci. 714, 121917 (2021) .
DOI:10.1016/j.susc.2021.121917
2.

Electronic Structures of Puckered Bilayer Group-V Two-Dimensional Materials: Group Theoretical analysis
M. Y. H. Widianto, A. Zaharo, N. A. P. Namari1, and M. Saito, Jpn. J. Appl. Phys. 60, 061001(2021) .
DOI:10.35848/1347-4065/ac0004

3.

Analysis of Band Structures of Phosphorene and Bithemauthene Based on the Double Group
TheoryM. Y. H. Widianto and M. Saito, Jpn. J. Appl. Phys. 61, 035503 (2022) .
DOI: 10.35848/1347-4065/ac4c4e

SAKAGUCHI, Norihito [ C class; 6200 (B), 0 (C) ] (72)
— Reduction of Rare Metals in Fuel Cell Catalysts and Hydrogen Permeable Membrane
1. Anisotropic Growth of Copper Nanorods Mediated by Cl− Ions
M. J. Saw, M. T. Nguyen, Y. Kunisada, T. Tokunaga, T. Yonezawa, ACS Omega 7, 7414 (2022).
DOI:10.1021/acsomega.2c00359

SAKAI, Masatoshi [ B class; 500 (B), 100 (C) ] (298)— Charge order structure in organic charge order materials— Origin of the electronic conductivity on organic charge order materials

380Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

SAKAI, Toru [ C class; 4800 (B), 150 (C) ] (235, 236)
— Numerical Diagonalization Study on Magnetization Process of Quantum Spin Chain with the Biquadratic Interaction— Numerical Diagonalization Study on Quantum Phase Transitions of Frustrated Spin Systems
1. Quantum spin nematic liquid in the S=1 antiferromagnetic chain with the biquadratic interaction
T. Sakai, AIP Advances 11, 015306 (2021).
2.

EPR Theories for Selection Rules to Observe the Spin Gap
T. Sakai, Applied Magnetic Resonance 52, 507 (2021).

3.

Magnetization process of the S=1/2 Heisenberg antiferromagnet on the ﬂoret pentagon lattice
R. Furuchi, H. Nakano, N. Todoroki and T. Sakai, J. Phys. Commun. 5, 125008 (2021).

4.

Field-Induced Quantum Spin Nematic Liquid Phase in the S=1 Antiferromagnetic Heisenberg
Chain with Additional Interactions
T. Sakai, H. Nakano, R. Furuchi and K. Okamoto, J. Phys.: Conf. Ser. 2164, 012030 (2022).

5.

Magnetization plateau of the distorted diamond spin chain with anisotropic ferromagnetic interaction
T. Sakai, K. Okamoto, H. Nakano and R. Furuchi, AIP Advances 12, 035030 (2022).

SAKAKIBARA, Hirofumi [ B class; 400 (B), 70 (C) ] (152)— Automatic generation of ﬁrst-principle eﬀective models based on MLO
SAKASHITA, Tatsuya [ B class; 200 (B), 120 (C) ] (318)— Development of integrated interface of eigensolvers Rokko and application to quantum spin systems
SASAKI, Takehiko [ C class; 2200 (B), 400 (C) ] (106)— Study on Hydration Process of Cellobiose by First Principles Calculations
1. The mechanism of sorbitol dehydration in hot acidic solutions
T. Kondo, T. Sasaki, M. Shiga, J. Comput. Chem. 42, 1783 (2021).
DOI:10.1002/jcc.26710
2.

X-ray absorption spectra of aqueous cellobiose: Experiment and theory
D. Akazawa, T. Sasaki, M. Nagasaka, M. Shiga, J. Chem. Phys. 156, 044202 (2022).
DOI:10.1063/5.0078963

SATO, Kazunori [ B class; 500 (B), 40 (C) ] (147)— Computational materials design of Ag, Cu chalcogenide based thermoelectric materials
SATO, Taku [ B class; 400 (B), 70 (C) ] ()— Magnetic excitations in the quantum pyrochlore magnet
SEKI, Yuya [ B class; 400 (B), 30 (C) ] (311)— Quantum simulation using Ising models
SHAO, Cheng [ C class; 5200 (B), 850 (C) ] ()— First principles based investigation of phonon-magnon coupling in ferromagnetic insulator— Machine-learning optimization of metal-insulator superlattice thermoelectric materials
SHIMADA, Toshihiro [ B class; 400 (B), 70 (C) ] (151)— Electronic structure calculation of organic crystals with high molecular weight381

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

1.

Interaction between alkali metals and diamond: etching and charge states of NV centers
Hiroki Takehana, Ichiro Yamane, Takashi Yanase, Taro Nagahama, Toshihiro Shimada, Carbon,
182, 585 (2021).
DOI:10.1016/j.carbon.2021.06.059

2.

DFT Calculation of Square MoS2 Nanotubes
Meiqi Zhang, Mengting Weng, Takahiro Tamura, Manami Goto, Ichiro Yamane, Takashi Yanase,Taro Nagahama, Toshihiro Shimada, Physica E, 130, 114693 (2021).
DOI:10.1016/j.physe.2021.114693

SHIMAMURA, Kohei [ C class; 2600 (B), 900 (C) ] (101)— Study of Eﬃcient Training Data Generation Method for Constructing Artiﬁcial Neural Network Force
Field III
1. Estimating Thermal Conductivity of α-Ag2 Se Using ANN Potential with Chebyshev Descriptor
K. Shimamura, Y. Takeshita, S. Fukushima, A. Koura, and F. Shimojo, Chem. Phys. Lett. 778,
138748 (2021).
DOI:10.1016/j.cplett.2021.138748

SHIMOJO, Fuyuki [ C class; 9400 (B), 1150 (C) ] (59)— First-Principles Molecular-Dynamics Study of Structural and Electronic Properties of Covalent Liquids and Glasses under Pressure
1. Estimating Thermal Conductivity of α-Ag2 Se Using ANN Potential with Chebyshev Descriptor
K. Shimamura, Y. Takeshita, S. Fukushima, A. Koura, and F. Shimojo, Chem. Phys. Lett. 778,
138748 (2021).
DOI:10.1016/j.cplett.2021.138748
2.

Reproduction of Melting and Crystallization of Sodium by Machine-Learning Interatomic Potential based on Artiﬁcial Neural Networks
A. Irie, S. Fukushima, A. Koura, K. Shimamura, and F. Shimojo, J. Phys. Soc. Jpn. 90, 094603(2021).
DOI:10.7566/JPSJ.90.094603

SHIMOKAWA, Tokuro [ C class; 4000 (B), 500 (C) ] (239)— Thermal eﬀects on quantum frustrated magnetisms
1. Quantum spin solver near saturation: QS3
H. Ueda, S. Yunoki, and T. Shimokawa, Comput. Phys. Commun. 277, 108369 (2022).
DOI:10.1016/j.cpc.2022.108369

SHINODA, Wataru [ E class; 13500 (B), 2150 (C) ] (208)— Molecular Simulation of Soft Materials using All-Atom and Coarse-Grained Force Field
1. Hemimicelle formation of semi-ﬂuorocarbon chains at airwater interface: coarse-grained molecular
dynamics study with an extension of the SPICA force ﬁeld
Hari OS Yadav, Shogo Harada, An-Tsung Kuo, Shingo Urata, Wataru Shinoda, Mol. Phys. 119,e21910355 (2021).
DOI:10.1080/00268976.2021.1910355
2.

Analyzing the Role of Surfactants in the Colloidal Stability of Nanoparticles in Oil through CoarseGrained Molecular Dynamics Simulations
Mark Z Griﬃths, Wataru Shinoda, J. Phys. Chem. B 125, 6315 (2021).
DOI:10.1021/acs.jpcb.1c01148

382

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo3.

All-atom molecular dynamics study of hepatitis B virus containing pregenome RNA in solution
Kazushi Fujimoto, Youhei Yamaguchi, Ryo Urano, Wataru Shinoda, Tetsuya Ishikawa, Katsumi
Omagari, Yasuhito Tanaka, Atsushi Nakagawa, Susumu Okazaki, J. Chem. Phys. 155, 145101(2021).
DOI:10.1063/5.0065765

4.

SPICA Force Field for Proteins and Peptides
Shuhei Kawamoto, Huihui Liu, Yusuke Miyazaki, Sangjae Seo, Mayank Dixit, Russell DeVane,
Christopher MacDermaid, Giacomo Fiorin, Michael L Klein, Wataru Shinoda, J. Chem. Theory
Comput. 18, 3204 (2022).
DOI:10.1021/acs.jctc.1c01207

SHINOHARA, Yasushi [ C class; 1200 (B), 0 (C) ] (128)— Atomistic simulations for optical absorption of solids
1. Semiclassical description of electron dynamics in extended systems under intense laser ﬁelds
Mizuki Tani, Tomohito Otobe, Yasushi Shinohara, and Kenichi L. Ishikawa, Phys. Rev. B 104,
075157 (2021).
DOI:10.1103/PhysRevB.104.075157

SHIOMI, Junichiro [ C class; 10000 (B), 1100 (C) ] (213)— Analysis for Thermal Functional Materials using Multi-scale Simulation
1. Akhiezer mechanism dominates relaxation of propagons in amorphous material at room temperature
Yuxian Liao, Junichiro Shiomi, J. Appl. Phys. 130, 035101 (2021).
DOI:10.1063/5.0050159
2.

Strain-induced band modulation of thermal phonons in carbon nanotubes
Masato Ohnishi, Junichiro Shiomi, Phys. Rev. B 104, 014306 (2021).

3.

Heat conduction below diﬀusive limit in amorphous superlattice structures
Yuxian Liao, Sotaro Iwamoto, Michiko Sasaki, Masahiro Goto, Junichiro Shiomi, Nano Energy
84, 105903 (2021).

4.

Exploring diamondlike lattice thermal conductivity crystals via feature-based transfer learning
Shenghong Ju, Ryo Yoshida, Chang Liu, Stephen Wu, Kenta Hongo, Terumasa Tadano, Junichiro
Shiomi, Phys. Rev. Materials 5 , 053801 (2021).

5.

Nanoconﬁnement between Graphene Walls Suppresses the Near-Wall Diﬀusion of the Ionic Liquid
Cheng Shao, Wee-Liat Ong, Junichiro Shiomi, Alan JH McGaughey, J. Phys. Chem. B 125,4527 (2021).

6.

Phonon transport in multiphase nanostructured silicon fabricated by high-pressure torsion
Cheng Shao, Kensuke Matsuda, Shenghong Ju, Yoshifumi Ikoma, Masamichi Kohno, Junichiro
Shiomi, J. Appl. Phys. 129, 085101 (2021).

SHIRAI, Tatsuhiko [ B class; 900 (B), 0 (C) ] (279)— Circuit-depth dependence of quantum approximate optimization algorithm— The eﬀect of quantum phase transition on the performance of QAOA
1. Exact bounds for dynamical critical exponents of transverse-ﬁeld Ising chains with a correlateddisorderT. Shirai and S. Tanaka, Ann. Phys. (N. Y.) 435, 168483 (2021).
DOI:10.1016/j.aop.2021.168483

383

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoSHIRAISHI, Kenji [ C class; 10800 (B), 0 (C) ] (56, 57)— First Pricnciples Study of N Vacancies in Si3N4 for Flash Memory Application— First principles studies of impurity-dislocation complexes in GaNSHUDO, Ken-ichi [ B class; 300 (B), 30 (C) ] ()— Virtical Magnetic distribution of nano-scale Co ﬁlm
SUGINO, Osamu [ E class; 24500 (B), 3200 (C) ] (45)— First-principles calculation of functionality of hydrogen— First-principles prediction of stability and functionality of complex materials
1. Machine-learning-based exchange correlation functional with physical asymptotic constraints
R Nagai, R Akashi, O Sugino, Phys. Rev. Research 4, 013106 (2022).
DOI:10.1103/PhysRevResearch.4.013106
2.

Optical representation of thermal nuclear ﬂuctuation eﬀect on band-gap renormalization
Kohei Ishii, Jun Haruyama, Osamu Sugino, Phys. Rev. B 104, 245144 (2021).
DOI:10.1103/PhysRevB.104.245144

3.

Functional-renormalization-group approach to classical liquids with short-range repulsion: A
scheme without repulsive reference system
Takeru Yokota, Jun Haruyama, Osamu Sugino, Phys. Rev. E 104, 014124 (2021).
DOI:10.1103/PhysRevE.104.014124

SUWA, Hidemaro [ C class; 5200 (B), 0 (C) ] (187)— Charge-spin-orbital entanglement of iridates
1. Extraordinary magnetic response due to emergent isotropic ﬂuctuations in an anisotropic 2D antiferromagnet
Junyi Yang, Hidemaro Suwa, D. Meyers, Han Zhang, Lukas Horak, Zhan Zhang, Jenia Karapetrova, Jong-Woo Kim, Philip J. Ryan, M. P. M. Dean, Lin Hao, and Jian Liu, submitted toPhys. Rev. Lett.
2.

Nematicity and fractional magnetization plateaus induced by spin-lattice coupling in the classicalkagome-lattice Heisenberg antiferromagnet
Masaki Gen and Hidemaro Suwa, submitted to Phys. Rev. B

SUZUKI, Takafumi [ C class; 3800 (B), 800 (C) ] (237)— Supersolid phases in the hard-core bosonic hubbard model on a triangular lattice— Supersolid state in a square-lattice Bose-Hubbard model with dipole interactions
1. Anisotropy as a diagnostic test for distinct tensor-network wave functions of integer- and halfinteger-spin Kitaev quantum spin liquids
Hyun-Yong Lee, Takafumi Suzuki, Yong Baek Kim, Naoki Kawashima, Phys. Rev B 104, 024417(2021).
DOI:10.1103/physrevb.104.024417
2.

Ground-state phase diagram of anisotropically interacting Heisenberg-Γ models on a honeycomb
lattice
Takafumi Suzuki, Takuto Yamada, and S.-I. Suga, Phys. Rev B 103, 224425 (2021).
DOI:10.1103/physrevb.103.224425

SUZUKI, Takehito [ B class; 100 (B), 10 (C) ] (322)384

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo— Change in period of ordinary earthquakes due to the interaction with slow earthquakes
SUZUKI, Yuji [ C class; 8400 (B), 0 (C) ] (65)
— Development of Polymer Electret Materials for Energy Harvesting Using Machine Learning
1. Discovery of Polymer Electret Material via de Novo Molecule Generation and Functional Group
Enrichment Analysis
Zhang, Y., Zhang, J., Suzuki, K., Sumita, M., Terayama, K., Li, J., Mao, Z., Tsuda, K., andSuzuki, Y., Appl. Phys. Lett. 118, 223904 (2021).
DOI:10.1063/5.0051902

TAKAYAMA, Akari [ B class; 500 (B), 0 (C) ] (299)— Structure analysis of 2D materials by using 2DMATTAMURA, Ryo [ B class; 200 (B), 80 (C) ] (32)
— Evaluation method of error in eﬀective model estimation
1. Structural analysis based on unsupervised learning: Search for a characteristic low-dimensional
space by local structures in atomistic simulations
R. Tamura, M. Matsuda, J. Lin, Y. Futamura, T. Sakurai, and T. Miyazaki, Phys. Rev. B 105,
075107 (2022).
DOI:10.1103/PhysRevB.105.075107
2.

Bayesian optimization package: PHYSBO
Y. Motoyama, R. Tamura, K. Yoshimi, K. Terayama, T. Ueno, and K. Tsuda, submitted.

TANAKA, Shu [ B class; 400 (B), 70 (C) ] (307)— Development of Algorithms for Ising Machines Based on Statistical Mechanics
1. Exact bounds for dynamical critical exponents of transverse-ﬁeld Ising chains with a correlateddisorderT. Shirai and S. Tanaka, Ann. Phys. (N. Y.) 435, 168483 (2021).
DOI:10.1016/j.aop.2021.168483
2.

Continuous black-box optimization with an Ising machine and random subspace coding
S. Izawa, K. Kitai, S. Tanaka, R. Tamura, and K. Tsuda, Physical Review Research, 4 (2022)
023062.
DOI:10.1103/PhysRevResearch.4.023062

3.

Structural analysis based on unsupervised learning: Search for a characteristic low-dimensional
space by local structures in atomistic simulations
R. Tamura, M. Matsuda, J. Lin, Y. Futamura, T. Sakurai, and T. Miyazaki, Phys. Rev. B 105,
075107 (2022).
DOI:10.1103/PhysRevB.105.075107

4.

Bayesian optimization package: PHYSBO
Y. Motoyama, R. Tamura, K. Yoshimi, K. Terayama, T. Ueno, and K. Tsuda, submitted.

TANAMOTO, Tetsufumi [ B class; 200 (B), 60 (C) ] (321)— Analysis of transport properties of spin-qubit based on FinFET
TATETSU, Yasutomi [ C class; 2600 (B), 350 (C) ] (103)— Theoretical analyses for surfaces and grain boundaries with magnetic elements from ﬁrst-principles
calculations
1. Inter-element miscibility driven stabilization of ordered pseudo-binary alloy

385

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

K. Matsumoto, R. Sato, Y. Tatetsu, R. Takahata, S. Yamazoe, M. Yamauchi, Y. Inagaki, Y.
Horibe, M. Kudo, T. Toriyama, M. Auchi, M. Haruta, H. Kurata, and T. Teranishi, Nat. Commun., 13, 1047 (2022).
DOI:10.1038/s41467-022-28710-0

TERAO, Takamichi [ B class; 700 (B), 90 (C) ] (283)— Structural formation of patchy particles
1. Eigenvalue analysis of the three-dimensional tight-binding model with non-Hermitian disorder
T. Terao, Phys. Rev. B 103, 224201 (2021).

TERASAWA, Asako [ B class; 400 (B), 80 (C) ] ()— First-principles analysis of structure and exchange coupling constants of subphases and interface in
Nd-based permanent magnets
TEZUKA, Masaki [ C class; 4400 (B), 0 (C) ] (242)— Scrambling and eﬀect of dissipation in quantum many-body systems
TODO, Synge [ C class; 6000 (B), 900 (C) ] (222)— Topological order and quantum operation in quantum many-body systems
1. Bond-weighted tensor renormalization group
D. Adachi, T. Okubo, and S. Todo, Phys. Rev. B 105, L060402 (2022).
DOI:10.1103/PhysRevB.105.L060402

TOHYAMA, Takami [ C class; 3000 (B), 700 (C) ] (193)— Analysis of string excitations in the optical conductivity of doped Mott insulators
1. Resonating dimer-monomer liquid state in a magnetization plateau of a spin-12 kagome-strip
Heisenberg chain
K. Morita, S. Sota, and T. Tohyama, Commun. Phys. 2, 161 (2021).
DOI:10.1038/s42005-021-00665-6
2.

Coexistence of strong and weak Majorana zero modes in an anisotropic XY spin chain with secondneighbor interactions
K. Wada, T. Sugimoto, and T. Tohyama, Phys. Rev. B 104, 035119 (2021).
DOI:10.1103/PhysRevB.104.075119

3.

Density-matrix renormalization group study of optical conductivity of the Mott insulator for twodimensional clusters
K. Shinjo, Y. Tamaki, S. Sota, and T. Tohyama, Phys. Rev. B 104, 205123 (2021).
DOI:10.1103/PhysRevB.104.205123

4.

Magnetic phase diagrams of the spin-12 Heisenberg model on a kagome-strip chain: Emergenceof a Haldane phase
K. Morita, S. Sota, and T. Tohyama, Phys. Rev. B 104, 224417 (2021).
DOI:10.1103/PhysRevB.104.224417

5.

Discord eﬀects of inter-cluster interactions on a cluster-based Haldane state in a triangular spin
tube
T. Sugimoto and T. Tohyama, J. Phys.: Conf. Ser. 2164, 012029 (2022).
DOI:10.1088/1742-6596/2164/1/012029

6.

Antiphase oscillations in the time-resolved spin structure factor of a photoexcited Mott insulator
on a square lattice386

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

T. Tohyama, K. Shinjo, and K. Tsutsui, J. Phys.: Conf. Ser. 2164, 012049 (2022).
DOI:10.1088/1742-6596/2164/1/012049
7.

Numerical simulations of spectroscopic properties in two-dimensional Mott insulator
T. Tohyama, K. Shinjo, S. Sota, and K. Tsutsui, J. Phys.: Conf. Ser. 2207, 012028 (2022).
DOI:10.1088/1742-6596/2207/1/012028

TOKUMOTO, Yuki [ B class; 400 (B), 70 (C) ] (150)— Defect formation energy and band structure of Pb-based topological insulators
TONEGAWA, Takashi [ B class; 600 (B), 0 (C) ] (296)— Numerical Study of the One-Dimensional Quantum Spin Systems with Spatial Structures
TOYODA, Masayuki [ B class; 500 (B), 0 (C) ] (148)— Thickness-dependent electronic structure of exfoliated boron monosulﬁde
TSUMURAYA, Takao [ C class; 1000 (B), 550 (C) ] (124)— Origins of phase stabilities and physical properties in Mg based alloys: A ﬁrst-principles study
1. Origin of phase stability in Fe with long-period stacking order as an intermediate phase in cyclic
γ-ϵ martensitic transformation
Takao Tsumuraya and Ikumu Watanabe and Takahiro Sawaguchi Phys. Rev. Research 3, 033215(2021).
DOI:10.1103/PhysRevResearch.3.033215

TSUNEYUKI, Shinji [ C class; 6000 (B), 900 (C) ] (70)
— Elucidation of mechanism and theoretical prediction of super-functional materials using high-density
hydrogen
1. Superionic Conductivity Combined CB9H10 − Rotation and Li-ion Concerted Motion in LiCB9H10:An Ab Initio and Neural-Net Potential Molecular Dynamics Study
Ryuhei Sato, Shigeyuki Takagi, Tamio Ikeshoji, Toyota Sato, Takashi Honda, Toshiya Otomo,
Shin-ichi Orimo, Shinji Tsuneyuki, submitted to J. Phys. Chem. Lett.

TSURUTA, Kenji [ C class; 600 (B), 550 (C) ] (130)— Ab-initio and artiﬁcial neural-network molecular-dynamics calculations for molecule-modiﬁed nanointerfaces
UCHIDA, Takashi [ B class; 300 (B), 90 (C) ] (316)— Multiple spin density waves in inversion-symmetric two-dimensional Hubbard models— Spontaneous formation of multiple-Q orders in inversion-symmetric Hubbard models
UMEMOTO, Koichiro [ C class; 2200 (B), 650 (C) ] ()— Order-disorder transitions in post-post-perovskite phases in Mg-Si-O system
WAKABAYASHI, Daisuke [ B class; 400 (B), 0 (C) ] (312)— Large-scale molecular-dynamics simulation of silica melt and glass under high pressure with ANN
potentials by active learning
WATANABE, Haruki [ B class; 500 (B), 100 (C) ] ()— Comprehensive material search based on symmetry indicators
WATANABE, Hiroshi [ B,C class; 5300 (B), 430 (C) ] (229)— Analysis of the phase boundary under the steady-state heat conduction

387

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo— Development of an Eﬃcient Phase Diagram Exploration Method Using Gaussian Process Regression
WATANABE, Hiroshi [ B class; 400 (B), 70 (C) ] (200)— Study of cuprate high-temperature superconductors using 4-band d-p model
1. Uniﬁed description of cuprate superconductors using a four-band d-p model
H. Watanabe, T. Shirakawa, K. Seki, H. Sakakibara, T. Kotani, H. Ikeda, S. Yunoki, Phys. Rev.
Research 3, 033157 (2021).
DOI:10.1103/PhysRevResearch.3.033157

WATANABE, Satoshi [ C class; 10800 (B), 1150 (C) ] (47)
— Analyses related to atomic structures and atom dynamics at complex structures such as surfaces,interfaces and defects
1. ニューラルネットワークポテンシャルによる金–リチウム合金化過程の解析
清水康司, E. F. Arguelles, 李文文, 安藤康伸, 南谷英美, 渡邉聡表面と真空 64, 369 (2021).
DOI:10.1380/vss.64.3692.

窒化物半導体におけるフォノン関連物性の解析のための 機械学習ポテンシャルの開発
渡邉聡, 清水康司, 南谷英美日本結晶成長学会誌 48, 48-4-05 (2021).

3.

Ionic Rectiﬁcation across Ionic and Mixed Conductor Interfaces
K. Nishio, S. Ichinokura, A. Nakanishi, K. Shimizu, Y. Kobayashi, N. Nakamura, D. Imazeki, R.
Shimizu, T. Hirahara, S. Watanabe, and T. Hitosugi, Nano Lett. 21, 10086 (2021).
DOI:10.1021/acs.nanolett.1c03872

4.

Neural network potential study of point defect properties in multiple charge states: GaN withnitrogen vacancy
K. Shimizu, Y. Dou, E. F. Arguelles, T. Moriya, E. Minamitani, and S. Watanabe, arXiv.2203.16789
DOI:10.48550/arXiv.2203.16789

YAMADA, Atsuo [ C class; 6200 (B), 900 (C) ] (69)
— First principles analysis on novel energy storage device materials
1. Soft X-ray Emission Studies on Hydrate-Melt Electrolytes
T. Shimada, N. Takaneka, E. Watanabe, Y. Yamada, Y. T. Cui, Y. Harada, M. Okubo, A.
Yamada, J. Phys. Chem. B 125, 11534 (2021).
DOI:10.1021/acs.jpcb.1c07246
2.

Relationship between Electric Double-Layer Structure of MXene Electrode and Its Surface Functional Groups
T. Shimada. N. Takenaka, Y. Ando, M. Otani, M. Okubo, A. Yamada, Chem. Mater. 34, 2069
(2022).
DOI:10.1021/acs.chemmater.1c03328

YAMADA, Atsushi [ C class; 600 (B), 400 (C) ] (195)— Studies of the superconductivity and magnetic states in the strongly correlated electron systems basedon Hubbard models.
YAMADA, Masahiko [ C class; 6000 (B), 650 (C) ] (223, 224)
— Glass transition in the disordered Kitaev model— Heat capacity and magnetic susceptibility of the SU(N) Heisenberg models
YAMAGUCHI, Naoya [ B class; 900 (B), 110 (C) ] (131)— First-principles Calculations of Magnetic Insulators Under Uniform Electric Fields

388

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo— First-principles Calculations of Spin-to-charge Conversion Materials Utilizing Organic Molecules
1. First-principles LCPAO Approach to Insulators Under Finite Electric Fields
N. Yamaguchi and F. Ishii, submitted to Comp. Phys. Commun.
2.

First-principles calculation of anomalous Hall and Nernst conductivity by local Berry phase
H. Sawahata, N. Yamaguchi, S. Minami and F. Ishii, submitted to Phys. Rev. B

YAMAJI, Youhei [ E class; 14500 (B), 2150 (C) ] (177)— Numerical studies of Mott transitions in quantum spin liquid candidates
1. Ab initio derivation of low-energy Hamiltonians for systems with strong spin-orbit interaction:
Application to Ca5 Ir3 O12Maxime Charlebois, Jean-Baptiste More, Kazuma Nakamura, Yusuke Nomura, Terumasa Tadano,
Yoshihide Yoshimoto, Youhei Yamaji, Takumi Hasegawa, Kazuyuki Matsuhira, Masatoshi Imada,
Phys. Rev. B 104, 075153 (2021).
DOI:10.1103/PhysRevB.104.075153

YAMASHITA, Tomoki [ C class; 5200 (B), 800 (C) ] (76)— Development of crystal structure prediction methods using machine learning
1. CrySPY: a crystal structure prediction tool accelerated by machine learning
T. Yamashita, S. Kanehira, N. Sato, H. Kino, H. Sawahata, T. Sato, F. Utsuno, K. Tsuda, T.
Miyake, and T. Oguchi, Sci. Technol. Adv. Mater. Meth. 1, 87 (2021).
DOI:10.1080/27660400.2021.1943171
2.

Hybrid algorithm of Bayesian optimization and evolutionary algorithm in crystal structure prediction
T. Yamashita, H. Kino, K. Tsuda, T. Miyake, and T. Oguchi, Sci. Technol. Adv. Mater. Meth.
2, 67 (2022).
DOI:10.1080/27660400.2022.2055987

3.

Improvement of look ahead based on quadratic approximation for crystal structure prediction
T. Yamashita and H. Sekine, Sci. Technol. Adv. Mater. Meth. 2, 84 (2022).
DOI:10.1080/27660400.2022.2059335

YAMATO, Takahisa [ B class; 400 (B), 80 (C) ] (303)— Non-uniform thermal transport properties in proteins
1. Computational study on the thermal conductivity of a protein
T. Yamato, T. Wang, W. Sugiura, O. Laprvote, T. Katagiri, J. Phys. Chem. B 126, 16, 3029
(2022).
DOI:10.1021/acs.jpcb.2c00958

YAMAUCHI, Kunihiko [ C class; 5000 (B), 800 (C) ] (80)— First-principles design of topological interfaces toward next-generation spintronics application
1. Electric-ﬁeld tuning of the magnetic properties of bilayer VI3: A ﬁrst-principles study
Thi Phuong Thao Nguyen, Kunihiko Yamauchi, Tamio Oguchi, Danila Amoroso, and Silvia Picozzi, Phys. Rev. B 104, 014414 (2021).
DOI:10.1103/PhysRevB.104.014414
2.

First-principles Study on Piezoelectricity and Spontaneous Polarization in Bi(Fe,Co)O3
Hiroshi Katsumoto, Kunihiko Yamauchi, and Tamio Oguchi, J. Phys. Soc. Jpn. 90, 124712(2021).
DOI:10.7566/JPSJ.90.124712

389

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

3.

First-Principles Study on Cathode Properties of Li2MTiO4 and Na2MTiO4 (M = V, Cr, Mn, Fe,
Co, Ni)Kunihiko Yamauchi, Hiroyoshi Momida, and Tamio Oguchi, J. Phys. Soc. Jpn. 91, 034704(2022).
DOI:10.7566/JPSJ.91.034704

4.

Spin-Polarized Band Structure at MoTe2=Bi2Se3 Interface Designed from First Principles
Kunihiko Yamauchi, Ryoma Shimazu1, and Tamio Oguchi, J. Phys. Soc. Jpn. 91, 044705(2022).
DOI:10.7566/JPSJ.91.044705

YANAGISAWA, Susumu [ C class; 5800 (B), 650 (C) ] ()— First-principles band structure calculation of organic crystals at ﬁnite-temperature— First-principles investigation on the electronic properties of polymer organic semiconductors
YANAGISAWA, Takashi [ B class; 300 (B), 30 (C) ] (202)— New quantum phenomena in strongly correlated many-body electron systems
1. Ground-state phase diagram of the three-band d-p model
T. Yanagisawa, M. Miyazaki, K. Yamaji, EPL 134, 27004 (2021).
2.

Enhancement of superconductivity due to kinetic energy eﬀect in the strongly correlated phase in
the two-dimensional Hubbard model
T. Yanagisawa: Phys. Lett. A 403, 127382 (2021).

YASUDA, Chitoshi [ C class; 2400 (B), 0 (C) ] (262)— Numerical study of spin systems on the honeycomb lattice
YASUDA, Yusuke [ B class; 300 (B), 30 (C) ] (317)— Molecular Dynamics Simulations of Reversiblly Cross-linked Rubbers
YOKO, Akira [ B,C class; 3000 (B), 580 (C) ] (95)
— Hydrogen formation by reaction of water on reduced CeO2 (100) surface— Interaction between metallic atom and instable CeO2 (100) facet
1. Atomistic Origin of High-Concentration Ce3+ in 100-Faceted Cr-Doped CeO2 Nanocrystals
X. Hao, A. Yoko, K. Inoue, Y. Xu, M. Saito, C. Chen, G. Seong, T. Tomai, S. Takami, A.L.
Shluger, B. Xu, T. Adschiri, Y. Ikuhara, Acta Materialia. 203, 116473 (2021).
DOI:10.1016/j.actamat.2020.11.015

YOSHIDA, Tsuneya [ C class; 5200 (B), 0 (C) ] (185)— Exotic phenomena induced by strong correlations and non-Hermitian topology
1. Surface exceptional points in a topological Kondo insulator
R. Peters, K. Kimura, Y. Michishita, T. Yoshida, and N. Kawakami, Phys. Rev. B 104, 235153(2021).
DOI:10.1103/PhysRevB.104.235153
2.

Chiral edge modes in evolutionary game theory: A kagome network of rock-paper-scissors cycles
T. Yoshida, T. Mizoguchi, and Y. Hatsugai, Phys. Rev. E 104, 025003 (2021).
DOI:10.1103/PhysRevE.104.025003

3.

Topological d-wave superconductivity in two dimensions
Y. Yanase, A. Daido, K. Takasan, and T. Yoshida, Physica E: Low-dimensional Systems and390

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Nanostructures, 140, 115143 (2022).
DOI:10.1016/j.physe.2022.115143

YOSHIMOTO, Yuta [ C class; 2600 (B), 0 (C) ] (259)— Next-generation integrated engineering for developing polymer materials

391

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo◦ A classSince this class is for trial use, research reports are not required.
When other classes are also used, their publications are shown in the list of B–E classes.
Then, the pages of their reports and publications are given in ( ).
AKIYAMA, Ryota [ A class; 100 (B), 40 (C) ] ()— Band calculation of topological insulator systems
FUJINO, Tomoko [ A class; 100 (B), 40 (C) ] (194, 351)
— Electronic states of electron-rich oligomer-based conductors
GONOME, Hiroki [ A class; 100 (B), 40 (C) ] ()— Study of the principle of photothermal conversion by ab initio calculations
ISHITANI, Yoshihiro [ A class; 100 (B), 40 (C) ] ()— Phonon-property analysis for phonon control in electronic/photonic devices by wide-bandgap semiconductors
IWASE, Fumitatsu [ A class; 100 (B), 40 (C) ] ()— The ground state of cairo-fractal lattice
KITAGAWA, Kentaro [ A class; 100 (B), 40 (C) ] ()— Screening test for crystal nucleation of ﬂux method
KOTA, Yohei [ A class; 100 (B), 40 (C) ] ()— First-principles calculation of physical properties in various magnetic materials
MASAKI, Yusuke [ A class; 100 (B), 50 (C) ] (367)— Microscopic calculations of fractional vortices in topological superﬂuids
MITARAI, Yoko [ A class; 100 (B), 40 (C) ] ()— Phase stability of high-entropy alloys
NISHIGUCHI, Kazutaka [ A class; 100 (B), 50 (C) ] (314, 373)
— First-principles study of thermoelectric and magnetic properties in doped Fe2 VAl
OKUBO, Masashi [ A class; 100 (B), 50 (C) ] (157, 377)
— Development of all-solid-state capacitors using sulﬁde-based solid electrolytes
OYA, Yutaka [ A class; 100 (B), 40 (C) ] ()— Molecular dynamics simulation of matrix resin for composite materials
SATO, Shunsuke [ A class; 100 (B), 40 (C) ] ()— Theoretical investigation on THz-ﬁeld induced electron dynamics in graphene
SUZUKI, Yoshikazu [ A class; 100 (B), 40 (C) ] ()— Electronic state calculation of inorganic solid materials using Quantum Espresso
1. Reassessment of vibration spectra in alkali phosphate crystals
J. Endo, Y. Suzuki, J. Ceram. Soc. Jpn. 130, 324 (2022).
DOI:10.2109/jcersj2.21180
2.

Reassessment of vibration spectra in alkaline earth metaphosphate crystals
J. Endo, Y. Suzuki, J. Ceram. Soc. Jpn. 130, in press (2022).

392

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

DOI:10.2109/jcersj2.22034

TSUKAHARA, Noriyuki [ A class; 100 (B), 40 (C) ] ()— Adsorption states of an organic halogen molecule on semiconductor and metal surfaces
UCHIDA, Ken [ A class; 100 (B), 40 (C) ] ()— Calculation of thermal conductivity of Hexagonal Tungsten Bronze
WAKABAYASHI, Daisuke [ A class; 100 (B), 50 (C) ] (312, 387)
— Large-scale molecular-dynamics simulation of silica melt under high pressure with ANN potentials

393

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

2 SCCMS Projects
FUJITA, Takatoshi [ 4000 (B), 0 (C) ] (329)— Large-Scale GW/BSE electronic structure calculations for metal-organic hybrid materials— Developments of non-linear optical response theory based on electronic structure calculations and theirapplications to nano and biological systems
1. Fragment-Based Excited-State Calculations Using the GW Approximation and the Bethe–Salpeter
Equation
T. Fujita and Y. Noguchi J. Phys. Chem. A 125, 10580 (2021).

FUKUSHIMA, Tetsuya [ 4000 (B), 700 (C) ] (334)— Development of high-throughput calculation tools and evaluation of magnetic properties in hard magnetic materials— High-throughput calculation of magnetic anisotropy energy in permanent magnet materials
1. A novel method for generating p-type wide- and ultrawide-bandgap III-nitride by doping withmagnetic elements
A. Masago, H. Shinya, T. Fukushima, K. Sato, and H. Katayama-Yoshida, Appl. Phys. Exp.
14, 091007 (2021).
DOI:10.35848/1882-0786/ac197f
Data Repository
Automatic exhaustive calculations of large material space by Korringa-Kohn-Rostoker coherent approximation method — Applied to equiatomic quaternary high entropy alloys
https://zenodo.org/record/5606502#.Ym8-3y 3Jqs
DOI:10.5281/zenodo.5606502

GOHDA, Yoshihiro [ 2000 (B), 200 (C) ] (79)
— First-principles study of magnetic interfaces
1. Role of ferroelectricity, delocalization, and occupancy of d states in the electrical control ofinterface-induced magnetization
R. Costa-Amaral and Y. Gohda, Phys. Rev. Appl. 15, 064014 (2021).
DOI:10.1103/PhysRevApplied.15.064014
2.

Giant converse magnetoelectric eﬀect in a multiferroic heterostructure with polycrystalline Co 2 FeSi
S. Fujii, T. Usami, Y. Shiratsuchi, A.M. Kerrigan, A.M. Yatmeidhy, S. Yamada, T. Kanashima,
R. Nakatani, V.K. Lazarov, T. Oguchi, Y. Gohda, and K. Hamaya, NPG Asia Mater., in press.

3.

Intrinsic superconductivity of two-monolayer-thick indium ﬁlm
T. Ogino, I. Seo, H. Tajiri, M. Nakatake, S. Takakura, Y. Sato, Y. Hasegawa, Y. Gohda, K.
Nakatsuji, and H. Hirayama, submitted to Phys. Rev. Lett.

4.

Origin of anisotropic magnetoresistance tunable with electric ﬁeld in Co2FeSi/BaTiO3 multiferroic
inetrfaces
S. Tsuna, R. Costa-Amaral, and Y. Gohda, submitted to Phys. Rev. Mater.

IMADA, Masatoshi [ 10000 (B), 1400 (C) ] (174)— Integrated analyses on spectroscopic experiments and ab initio electronic structure calculations formechanisms of unconventional superconductors— Analysis on Superconducting Mechanism of Cuprate Superconductors
1. Unconventional dual 1D-2D quantum spin liquid revealed by ab initio studies on organic solids

394Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

familyKota Ido, Kazuyoshi Yoshimi, Takahiro Misawa, and Masatoshi Imada, npj Quantum Mater. 7,
48 (2022).
DOI:0.1038/s41535-022-00452-8
2.

Hidden self-energies as origin of cuprate superconductivity revealed by machine learning
Youhei Yamaji, Teppei Yoshida, Atsushi Fujimori, and Masatoshi Imada Phys. Rev. Research 3,043099 (2021).
DOI:10.1103/PhysRevResearch.3.043099

3.

Order-N orbital-free density-functional calculations with machine learning of functional derivatives
for semiconductors and metals
Fumihiro Imoto, Masatoshi Imada, and Atsushi Oshiyama, Phys. Rev. Research 3, 033198(2021).
DOI:10.1103/PhysRevResearch.3.033198

4.

Ab initio derivation of low-energy Hamiltonians for systems with strong spin-orbit interaction:
Application to Ca5 Ir3 O12Maxime Charlebois, Jean-Baptiste Morée, Kazuma Nakamura, Yusuke Nomura, Terumasa Tadano,
Yoshihide Yoshimoto, Youhei Yamaji, Takumi Hasegawa, Kazuyuki Matsuhira, and Masatoshi
Imada, Phys. Rev. B 104, 075153 (2021).
DOI:10.1103/PhysRevB.104.075153

5.

Dirac-type nodal spin liquid revealed by reﬁned quantum many-body solver using neural-network
wave function, correlation ratio, and level spectroscopy
Yusuke Nomura and Masatoshi Imada, Phys. Rev. X 11, 031034 (2021).
DOI:10.1103/PhysRevX.11.031034

6.

Charge Order and Superconductivity as Competing Brothers in Cuprate High-Tc Superconductors
Masatoshi Imada J. Phys. Soc. Jpn. 90, 111009 (2021).
DOI:10.7566/JPSJ.90.111009

7.

Resonant Inelastic X-Ray Scattering Spectra of Cuprate Superconductors Predicted by Model ofFractionalized Fermions
Masatoshi Imada J. Phys. Soc. Jpn. 90, 074702 (2021).
DOI:10.7566/JPSJ.90.074702

8.

High-temperature superconductivity
Xingjiang Zhou, Wei Sheng Lee, Masatoshi Imada, Nandini Trivedi, Philip Phillips, Hae Young
Kee, Päivi Törmä, Mikhail Eremets Nat. Rev. Phys. 3, 125137 (2021).
DOI:10.1038/s42254-021-00324-3

9.

Local moments versus itinerant antiferromagnetism: Magnetic phase diagram and spectral properties of the anisotropic square lattice Hubbard model
Marcin Raczkowski, Fakher F. Assaad, Masatoshi Imada Phys. Rev. B 103, 462 (2021).
DOI:10.1103/PhysRevB.103.125137

MIYAKE, Takashi [ 600 (B), 0 (C) ] (338)— Development of high-performance permanent magnets by large-scale simulation and data-driven approach
1. Evolutionary search for cobalt-rich compounds in yttrium-cobalt-boron system
Takahiro Ishikawa, Taro Fukazawa, Guangzong Xing, Terumasa Tadano and Takashi Miyake,Phys. Rev. Mater. 5, 054408 (2021).
DOI:10.1103/PhysRevMaterials.5.054408

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2.

Ordered and disordered phases in CaCu5 -type derived structures: Dumbbell cluster modeling withﬁrst-principles calculations
Fumiaki Kuroda, Taro Fukazawa and Takashi Miyake, Phys. Rev. Mater. 5, 124405 (2021).
DOI:10.1103/PhysRevMaterials.5.124405

3.

First-principles investigation of Nd(Fe,M)12 (M=K-Br) and Nd(Fe,Cr,Co,Ge,As)12 : possible enhancers of Curie temperature for NdFe12
Taro Fukazawa, Yosuke Harashima, Hisazumi Akai and Takashi Miyake, Acta Materialia, 226,
117597 (2022).
DOI:10.1016/j.actamat.2021.117597

4.

Hybrid algorithm of Bayesian optimization and evolutionary algorithm in crystal structure prediction
Tomoki Yamashita, Hiori Kino, Koji Tsuda, Takashi Miyake and Tamio Oguchi, Science andTechnology of Advanced Materials: Methods (STAM-M) 2, 67 (2022).
DOI:10.1080/27660400.2022.2055987

NAKAYAMA, Masanobu [ 1500 (B), 0 (C) ] (336)— Novel chloride solid electrolytes for all solid-state sodium metal battery (2)1. First-principles study of the morphology and surface structure of LaCoO3 and La0.5Sr0.5Fe0.5Co0.5O3
perovskites as air electrodes for solid oxide fuel cells
Masanobu Nakayama, Katsuya Nishii, Kentaro Watanabe, Naoto Tanibata, Hayami Takeda,
Takanori Itoh, and Toru Asaka, Science and Technology of Advanced Materials: Methods 1,
24 (2021).
DOI:10.1080/27660400.2021.1909871
2.

Exploring the diﬀusion mechanism of Li ions in diﬀerent modulated arrangements of La(1-X)/3LixNbO3
with ﬁtted force ﬁelds obtained via a metaheuristic algorithm
Zijian Yang, Robyn E. Word, Naoto Tanibnata, Hayami Takeda, Masanobu Nakayama, and Ryo
Kobayashi, Solid State Ionics 366–367, 115662 (2021).
DOI:10.1016/j.ssi.2021.115662

3.

Molecular Dynamics Simulation of Li-Ion Conduction at Grain Boundaries in NASICON-Type
LiZr2(PO4)3 Solid Electrolytes
Koki Nakano, Naoto Tanibnata, Hayami Takeda, Ryo Kobayashi, Masanobu Nakayama, andNaoki Watanabe, J. Phys. Chem. C 125, 23604 (2021).
DOI:10.1021/acs.jpcc.1c07314

4.

Density Functional Theory and Machine Learning-Based Analyses for Improved Surface Stabilityof a BaTiO3-Coated LiCoO2 Positive Electrode Material
Kunihiro Ishida, Naoto Tanibnata, Hayami Takeda, Masanobu Nakayama, Takashi Teranishi andNaoki Watanabe, Phys. Status Solidi B 2021, 2100526 (2021).
DOI:10.1002/pssb.202100526

5.

Chemical Composition Data-Driven Machine-Learning Prediction for Phase Stability and Materials Properties of Inorganic Crystalline Solids
Taruto Atsumi, Kosei Sato, Yudai Yamaguchi, Masato Hamaie, Risa Yasuda, Naoto Tanibnata,
Hayami Takeda, Masanobu Nakayama, Masayuki Karasuyama and Ichiro Takeuchi, Phys. Status
Solidi B 2022, 2100525 (2022).
DOI:10.1002/pssb.202100525

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OGUCHI, Tamio [ 2000 (B), 500 (C) ] (330)— Electron Theory on Secondary-Battery Materials
1. Tavorite-type orthorhombic Ax VPO4 F (A = Li, Na) for novel high-voltage cathodes in rechargeable batteries
Huu Duc Luong, Van An Dinh, Hiroyoshi Momida, Tamio Oguchi, J. Alloys Compd. 875, 159963(2021).
2.

CrySPY: a crystal structure prediction tool accelerated by machine learning
Tomoki Yamashita, Shinichi Kanehira, Nobuya Sato, Hiori Kino, Kei Terayama, Hikaru Sawahata,
Takumi Sato, Futoshi Utsuno, Koji Tsuda, Takashi Miyake, Tamio Oguchi, Sci. Technol. Adv.
Mater.: Methods 1, 87 (2021).

3.

Atomic-layer stacking dependence of the magnetocrystalline anisotropy in Fe-Co multilayer thinﬁlms at MgO(001) interface
K. Nakamura, K. Nozaki, K. Hayashi, A.-M. Pradipto, M. Weinert, T. Oguchi, J. Magn. Magn.
Mater. 537, 168175 (2021).

4.

Electric-ﬁeld tuning of magnetic properties of bilayer VI3 : A ﬁrst-principles study
Thi Phuong Thao Nguyen, Kunihiko Yamauchi, Tamio Oguchi, Danila Amoroso, Silvia Picozzi,
Phys. Rev. B 104, 014414 (2021).

5.

First-Principles Study on Cathode Properties of Li2 M TiO4 and Na2 M TiO4 (M = V, Cr, Mn, Fe,
Co, Ni)Kunihiko Yamauchi, Hiroyoshi Momida, Tamio Oguchi:, J. Phys. Soc. Jpn. 91, 034704 (2022).

6.

Understanding doping eﬀects on P2 Nax Mn1−y My O2 (M =Li, Mg, Al, Ti, V, Cr, Fe, Co, Ni)
cathode materials for Na-ion batteries
Huu Duc Luong, Hiroyoshi Momida, Van An Dinh, Tamio Oguchi, Phys. Rev. Mater. 6, 015802(2022).

7.

Performance and reaction mechanisms of tin compounds as high-capacity negative electrodes oflithium and sodium ion batteries
Hiroki Kotaka, Hiroyoshi Momida, Tamio Oguchi, Mater. Adv. 3, 2793 (2022).

8.

Spin-Polarized Band Structure in MoTe2 /Bi2 Se3 Heterostructure Designed from First Principles
Kunihiko Yamauchi, Ryoma Shimazu, Tamio Oguchi, J. Phys. Soc. Jpn. 91, 044705 (2022).

9.

Insight into anisotropic magnetocaloric eﬀect of CrI3
Hung Ba Tran, Hiroyoshi Momida, Yu-ichiro Matsushita, Koun Shirai, Tamio Oguchi,
Mater. 231, 117851 (2022).

Acta

10. Eﬀect of magnetocrystalline anisotropy on magnetocaloric properties of an AlFe2 B2 compound
Hung Ba Tran, Hiroyoshi Momida, Yu-ichiro Matsushita, Kazunori Sato, Yukihiro Makino, Koun
Shirai, Tamio Oguchi, Phys. Rev. B 105, 134402 (2022).

OSHIYAMA, Atsushi [ 10000 (B), 1400 (C) ] (42)
— Quantum-theory-based multiscale simulation for next-generation power devices
1. Gallium-gallium weak bond that incorporates nitrogen at atomic steps during GaN epitaxial
growthK. M. Bui, K. Shiraishi and A. Oshiyama, Appl. Surf. Sci. 557, 149542 (2021).
2.

Microscopic mechanism of adatom diﬀusion on stepped SiC surfaces revealed by ﬁrst-principles
calculations
K. Seino and A. Oshiyama, Appl. Surf. Sci. 561, 149927 (2021).

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3.

Defect-free interface between amorphous (Al2 O3 )1−x (SiO2 )x revealed by ﬁrst-principle molecular
dynamics simulations
K. Chokawa, K. Shiraishi and A. Oshiyama, Appl. Phys. Lett. 119, 011602 (2021).

4.

Order-N orbital-free density-functional calculations with machine learning of functional derivatives for semiconductors and metals
F. Imoto, M. Imada adn A. Oshiyama, Phys. Rev. Research 3, 033198 (2021).

SAITO, Susumu [ 2000 (B), 200 (C) ] ()— Electronic properties and materials design of stacked B-C-N atomic layers for next-generation devices
SHIBA, Hayato [ 4000 (B), 700 (C) ] (325)— Interfacial tension of dilute electrolyte liquid: large-scale molecular simulation study— Ion dissociation and association in dilute electrolyte liquid: long-time molecular dynamics study
1. Enhancing eﬃcient computation of long-wavelength relaxation dynamics in a 2D liquid involving
millions of particles
H. Shiba J. Phys: Conf. Ser. 2207, 012026 (2022).
DOI:10.1088/1742-6596/2207/1/012026
2.

グラフニューラルネットワークによる長時間分子動力学予測と性能評価
芝隼人, 下川辺隆史研究報告ハイパフォーマンスコンピューティング 2022-HPC-183, No.22 (2022).

Data Repository
PyTorch Geometric (PyG) implementation of BOnd TArgetting Network (BOTAN, 牡丹)
https://github.com/h3-Open-BDEC/pyg botan

SUGINO, Osamu [ 2000 (B), 200 (C) ] (45)— Design of oxide electrocatalyst for next-generation fuel cells
1. Machine-learning-based exchange correlation functional with physical asymptotic constraints
R Nagai, R Akashi, O Sugino, Phys. Rev. Research 4, 013106 (2022).
DOI:10.1103/PhysRevResearch.4.013106
2.

Optical representation of thermal nuclear ﬂuctuation eﬀect on band-gap renormalization
Kohei Ishii, Jun Haruyama, Osamu Sugino, Phys. Rev. B 104, 245144 (2021).
DOI:10.1103/PhysRevB.104.245144

3.

Functional-renormalization-group approach to classical liquids with short-range repulsion: A
scheme without repulsive reference system
Takeru Yokota, Jun Haruyama, Osamu Sugino, Phys. Rev. E 104, 014124 (2021).
DOI:10.1103/PhysRevE.104.014124

TAKETSUGU, Tetsuya [ 4000 (B), 700 (C) ] (332)— Ab initio study toward abundant element nanocatalysts with less precious metals
1. Catalytic Oxidative Dehydrogenation of Light Alkanes over Oxygen Functionalized Hexagonal
Boron Nitride
S. Kumar, A. Lyalin, Z. Huang, and T. Taketsugu ChemistrySelect, 7, e202103795 (2022).
DOI:10.1002/slct.202103795

WASHIZU, Hitoshi [ 2000 (B), 500 (C) ] (339)— Search for the optimum state of the ionic liquid at the solid electrolyte interface

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

YAMADA, Atsuo [ 2000 (B), 200 (C) ] (69)— Theoretical Analysis of Anion Insertion Mechanism into Conductive Carbon
1. Soft X-ray Emission Studies on Hydrate-Melt Electrolytes
T. Shimada, N. Takaneka, E. Watanabe, Y. Yamada, Y. T. Cui, Y. Harada, M. Okubo, A.
Yamada, J. Phys. Chem. B 125, 11534 (2021).
DOI:10.1021/acs.jpcb.1c07246
2.

Relationship between Electric Double-Layer Structure of MXene Electrode and Its Surface Functional Groups
T. Shimada. N. Takenaka, Y. Ando, M. Otani, M. Okubo, A. Yamada, Chem. Mater. 34, 2069
(2022).
DOI:10.1021/acs.chemmater.1c03328

YOSHIMI, Kazuyoshi [ 4000 (B), 700 (C) ] (327)— A systematic ab initio study of quasi-two-dimensional molecular conductors κ-type BEDT-TTF salts— Finite temperature dependence of ab-initio Hamiltonians and its analysis for Pd(dmit) 2 Salts
1. Ab initio derivation and exact-diagonalization analysis of low-energy eﬀective Hamiltonians for
β ′ -X[Pd(dmit)2 ]2Kazuyoshi Yoshimi, Takao Tsumuraya, Takahiro Misawa, Phys. Rev. Research 3, 043224 (2021).
DOI:10.1103/PhysRevResearch.3.043224
Data Repository
physrevresearch vol3 page043224 year2021
https://isspns-gitlab.issp.u-tokyo.ac.jp/k-yoshimi/physrevresearch vol3 page043224 year2021

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

2 Doctor Theses
1.

BAE, Soungmin
Ab initio study of electronic structure and carrier localization in two-dimensional materials
Yokohama National University, 2022-03

2.

CHINZEI, Koki
Theoretical Study on Discrete Time Crystals in Dissipative Quantum Systems
The University of Tokyo, 2022-03

3.

IINO, Shumpei
Tensor network renormalization study on surface critical behavior from boundary-CFT viewpoint
The University of Tokyo, 2022-03

4.

KAMEYAMA, Ryohei
Development of Crystalline Doped Oligomers as Single-molecular-weight Models for Conductive
Polymers
The University of Tokyo, 2021-09

5.

KIMURA, Kazuhiro
Correlation induced topological states and magnetic/electron-nematic phase transitions
Kyoto University, 2022-03

6.

MICHISHITA, Yoshihiro
Non-Hermitian Aspect of Strongly Correlated Electron Systems
Kyoto University, 2022-03

7.

NAITO, Tomoya
On isospin symmetry breaking in nuclear density functional theory
The University of Tokyo, 2022-03

8.

NAKANO, Hayate
Study of Semiclassical Periodic Orbits in Kinetically Constrained Quantum Many-Body Systems
The University of Tokyo, 2022-03

9.

NAKANO, Koki
Analysis and Exploration of NASICON-type Ion-Conductive Oxides Using Materials Simulation
Nagoya Institute of Technology, 2022-03

10. NAKASHIMA, Takeru
The fundamental studies for the exact excitation calculation; spin-orbit coupling in the all-electron
mixed basis approach and normalization in quasiparticle theory by the Ward identity
Yokohama National University, 2022-03
11. OTA, Tadashi
First-principles study on ionic and electronic transport in advanced materials
Osaka University, 2022-03
12. PUTRA, Septia Eka Marsha
Importance of van Der Waals Interaction and Hydrogen Bonding in the Adsorptions of Formic
Acid and Methane on Metal Surfaces:Density Functional Theory Study
Osaka University, 2021-09

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

13. SHIMADA, Tatau
Computational study on structure/electronic state of next-generation energy storage materials
The University of Tokyo, 2022-03
14. TAMEMOTO, Naoki
Reaction-diﬀusion systems coupled with biomembrane deformation
The University of Tokyo, 2022-03
15. WATANABE, Syunta
Formation and electronic structures of nanoscale defects in organic molecular solids
Chiba University, 2022-03
16. WONG, Yee Jie
Theoretical and Experimental Study on Dry Reforming of Methane Over Cobalt-Based Catalysts:
Insights Into Carbon Dioxide Activation and Carbon Deposition
Osaka University, 2022-03
17. YAMADA, Takuto
Ground-state phase diagram and dynamical properties of Kitaev magnets
University of Hyogo, 2022-03
18. YAMAMOTO, Tsuyoshi
Many-body eﬀect on quantum transport in superconducting circuits
The University of Tokyo, 2022-03
19. ZAHARO, Aﬂah
Atomic and electronic structures of group IV-VI two dimensional materials
Kanazawa University, 2022-03

20. SAWAHATA, Hikaru
First-principles study of topological phase transition in two dimensional materials
Kanazawa University, 2021-03
21. YAMAUCHI, Masataka
Development and Application Studies on the Generalized-Ensemble Algorithms: Stability andAggregation of Proteins
The Graduate University for Advanced Studies, 2021-03

401

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

2 Master Theses
1.

AKAZAWA, Daisuke
XAS measurements for liquid phase sugar molecules and analysis by First Principles Calculations
The University of Tokyo, 2022-03

2.

AKIYAMA, Shuhei
Catalytic eﬀect of graphene with nitrogen- and phosphorus-doped defect structures on propane
dehydrogenation
Osaka University, 2022-03

3.

AMI, Satoki
Density of states evaluated by machine learning for design of Ir-base alloys
Tokyo Institute of Technology, 2022-3

4.

ARAI, KazuakiFirst-principles study on structure change of metal oxides induced by oxygen-vacancy charging
Chiba University, 2022-03

5.

BANBA, Ryota
Theoretical study of light-element impurities at grain boundaries of α-Al2O3
Hokkaido University, 2022-03

6.

BANNO, Hirotaka
An eﬃcient method to detect collision in hard polygon systems and its applications -Diﬀusional
characteristics and local structure analyses
Nagoya Institute of Technology, 2022-03

7.

EGAWA, Noriyuki
Failure of SCAN functional for systems containing copper at diﬀerent valences
Yokohama National University, 2022-03

8.

HAMADA, Masashi
Structural analysis and tracking of phase transitions in Pb/Si(111)-√ 3 ×√ 3 using total-reﬂection
high-energy positron diﬀraction (TRHEPD) and data-driven science
Waseda University, 2022-03

9.

HYODO, Ko
Parallelization in the code of quasi-particle self-consistent GW and electronic structure in themagnetic shape memory alloy Ni2 MnGa
Kanazawa University, 2022-03

10. INOUE, Naoki
Electronic structures of the complexes of screw dislocation and Mg and H impurities in GaN
Nagoya University, 2022-03
11. ISHIKAWA, Takuto
Theoretical study of spin Hall magnetoresistance by the quantum Monte Carlo method
The University of Tokyo, 2022-03
12. IWASHITA, Wataru
Breakdown of Amontons’ Law due to precursor slip in the frictional interface of a 3d viscoelastic
objectOsaka University, 2022-03

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13. JOSHI, Ashish
Mott transition and Magnetism in a fragile topological insulator
Kyoto University, 2021-09
14. KAKIHARA, Yuito
Microscopic origin of slow relaxation in binary hard disk glassy systems - Correlation between
hopping-chain motions and quasi-voids distribution
Nagoya Institute of Technology, 2022-03
15. KASHIMOTO, Takayuki
Mixing enthalpy for phase diagram of Ti-Al-based alloys
Tokyo Institute of Technology, 2022-3
16. KATO, Jyurai
Theoretical study on impurity/defect-induced ﬂuctuation of tunneling currents at semiconductor
pn junctions
Chiba University, 2022-03
17. KITAYA, Kaito
Molecular dynamics study of a nano-scale β-type Stirling engine - Stable conditions and thermal
eﬃciency
Nagoya Institute of Technology, 2022-03
18. KOGURE, Shingo
A series expansion study for magnon spectrum of the q=0 state in the kagome-lattice Heisenberg
antiferromagnet
Tokyo University of Science, 2022-03
19. KUTSUZAWA, Taito
Large-scale sparse-matrix diagonalization study of many-body localization in disordered systems
The University of Tokyo, 2022-03
20. LORTARAPRASERT, Chayaphol
Quantitative prediction of thermoelectrics properties by machine learning
The University of Tokyo, 2022-03
21. MACHIDA, Narumi
First-principles analysis of stearic acid adsorption on calcite (104) surface
Okayama University, 20022-03
22. MASUOKA, Shino
Structural dynamics analysis of a cyanobacterial alkane-producing enzyme by molecular dynamics
simulations
The University of Tokyo, 2022-03
23. MATSUMOTO, Sairi
Rational design of neutralizing antibodies against the receptor-binding domain of the SARS-CoV2 Spike protein
The University of Tokyo, 2022-03
24. MASUMOTO, Takeyoshi
Coarse-grained Molecular Dynamics Simulations for Strain Induced Crystallization in Slide-RingGels
The University of Tokyo, 2022-03

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

25. MATSUMOTO, Yuma
Research of Kondo Eﬀect in Two-Orbital Anderson Model Dynamically Coupled with Local JahnTeller Phonons
Tokyo Metropolitan University, 2022-03
26. MATSUTANI, Kenta
Pressure-induced structural transition in GeO2 glassAnalysis by experimental data and machinelearning potential molecular dynamics
Yamagata University, 2022-03
27. MOTOHASHI, Mikio
Theoretical study for eﬀects of Dzyaloshinskii-Moriya interaction and bond randomness in thespherical kagome system W72V30
Tokyo University of Science, 2022-03
28. MUGITA, Daigo
Study on microscopic mechanism of equilibration and its eﬃciency with event-driven algorithms
Nagoya Institute of Technology, 2022-03
29. MURAKAMI, Chika
Phase separation and stress ﬁeld induced by the motility of self-propelled particles
Ibaraki University, 2022-03
30. NAKAMURA, Katsumi
Judging the phase-transition order using the non-stochastic steepest descent method
Ehime University, 2022-03
31. NGUEYN, Bao Anh Trinh
Density Functional Theory-based research on Spin ﬁltering in Electron transport through Chiral
Molecules
Osaka University, 2022-03
32. NISHIMOTO, Akira
First-principles study of Fermi-level depinning at simple metal/Ge interfaces
Chiba University, 2022-03
33. NISHIMURA, TakehiroFirst-Principles Study of Charging Eﬀect on Defects in Strained SiO2
Shimane University, 2022-03
34. OKAMOTO, Junichi
Study on Cu diﬀusion in amorphous Ta2 O5 containing H2 O using machine-learning potentials
The University of Tokyo, 2022-03
35. SATO, MasanoriFirst-principles study of atomic and molecular adsorption on the Ag-In-Yb quasicrystal surface
Kagoshima University, 2022-03
36. SERRAON, Ace Christian Feraren
Prospecting the Electrochemical Nitrogen Reduction Reaction(e-NRR) Catalysis on Alkaline Earth
Atom Doped Graphenes via Density Functional Theory Calculation
Osaka University, 2022-03

404

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

37. SHIMADA, TakanoriFirst-principles study on adsorption geometries and electronic states of phthalocyanine on theCu(100) surface
Osaka University, 2022-03
38. SHIMIZU, Kotaro
Theoretical study on control of topological spin textures based on spin moiré picture
The University of Tokyo, 2021-03
39. SHINADA, Koki
Research on nonlinear responses in strongly correlated systems
Kyoto University, 2022-03
40. SHIOTA, Tomoya
First principles calculations of dynamical phenomena on Si and Ge(001) surfaces
Kyushu University, 2022-03
41. SOFI, Nurul Ainu
Active Sites of Pt single-atom catalyst supported on N-doped Graphene
Osaka University, 2021-09
42. SUGITA, Koichiro
First principles calculation of nitride MXenes
Yokohama National University, 2022-03
43. SUZUKI, Ken
Electronic structures and modulation spectroscopic properties of LiNbO2 thin ﬁlms
University of Fukui, 2022-03
44. TAKAGI, DaichiFirst-principles evaluation on magnetic anisotropy in antiferromagnetic Mn alloys
Kanazawa University, 2022-03
45. TAKAHASHI, Kazuki
Structure and superionic conductivity in AgI-As2Se3 glasses-Molecular dynamics analysis based
on ﬁrst-principles calculations and machine learning force ﬁelds
Yamagata University, 2022-03
46. TAKAHASHI, Masahiro
Topological nematic phase transition in Kitaev magnets and Majorana zero mode trapped in
vacancies
Osaka University, 2022-03
47. TAKEHANA, Hiroki
Interaction between alkali metals and diamond and its application to diamond machining
Hokkaido University, 2022-03
48. TAMAGAKI, Yuya
First Principles eﬀective Hamiltonian of 3d / 4f Localized Electron Orbits in Nd 2 CuO4
Osaka University, 2022-03
49. TAN, Beatriz Andrea Choi
Magnetism and Semiconducting Behavior in NiS, and NiO:a Density Functional Theory-Based
Investigation
Osaka University, 2021-09405

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

50. UEHARA, Taiga
Quantum Monte Carlo study on Neel temperature in quasi-two-dimensional honeycomb lattice
antiferromagnets
University of the Ryukyus, 2022-03
51. YAMAGUCHI, Shota
Theoretical study on zinc phthalocyanines by van der Waals density functional theory
University of the Ryukyus, 2022-03
52. YAMAGUCHI, Takuma
Electronic structures and vibrational properties of YO monoxide thin ﬁlms
University of Fukui, 2022-03
53. YOKOO, Syota
First-principles exploration of permanent-magnet materials
Tokyo Institute of Technology, 2022-3
54. YOSHIKAWA, Yuki
Accuracy veriﬁcation and improvement of machine-learning potentials based on deep learningmodelsThe University of Tokyo, 2022-03
55. YOSHIMURA, Masataka
Improving Magnets photodimerizers for subcellular optogenetics by computational design
The University of Tokyo, 2022-03
56. YOSHINARI, Hiroto
Facet Dependence of Photocatalytic Activity in Anatase TiO2 by Electronic Structure Calculation
Ibaraki University, 2022-03
57. YUNITASARI, Sefty
Studies on electronic structures of nanographene using band unfolding method
Kanazawa University, 2021-09
58. ZHANG, Yaotang
First-principles study of energy-saving materials
Kanazawa University, 2022-03

406