Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

3.2

First-Principles Calculationof Material Properties

47

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Simulation of electrochemical interfaces
Osamu Sugino
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
The electrochemical interface provides a

calculated results are used then to investigate theunique environment for efficient redox reactions.

activity. So far various structures with different

The platinum-electrolyte interface has long beenstability and activity are obtained and thisfocused on the fuel-cell study because of thevariety can be recognized as the characteristics

efficient oxygen reduction reaction (ORR), butof this material. Comparison with experiment is

defective TiO2 has attracted attention for its

now underway.

enhanced reactivity and durability. It was

Through the abICS calculation, we have

explained in our previous first-principles study

constructed a machine learning model of thethat the various adsorption forms taken by theinterface, and we plan to predict the activity after

ORR intermediates, such as OH and O2H, is theobtaining sufficient number of samplings.

reason for the reactivity [1]. This contrasts to themetal electrocatalysts where the variety in the

References

adsorption is quite small and thus the ORR[1] Y. Yamamoto et al., J. Phys. Chem. C 2019,activity

123, 32, 19486–19492.

islimitedthereby[2].

Further

investigation of the oxide electrocatalyst is the[2] A. Kulkarni et al., Chem. Rev. 2018, 118,

target of this project.

2302– 2312.

Together with experimentalists, we modeled[2] abICS is a software of first-principles Montea ZrO2 surface introduced with oxygen

Carlo simulation developed by Dr. S. Kasamatsu.

vacancies and foreign dopants to study the ORR

https://github.com/issp-center-dev/abICS

reactivity. To make the model realistically mimic
the experiment, we have performed the firstprinciples Monte Carlo simulation using abICS[2] and obtained equilibrium structures for theinterface at the annealing condition. The

48

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Mechanisms of Semiconductor Interface Formation and its Electronic
Properties based on Quantum Theory
Atsushi Oshiyama
Institute of Materials and Systems for Sustainability, Nagoya University
Furo-cho, Chikusa-ku, Nagoya 464-8601
In the fiscal year of 2020, on the basis of thenanoscience and technology. We have performed

total-energy electronic-structure calculations andfirst-principles calculations that elucidate atomic

molecular

thestructures and formation energies of the surface

density-functional theory, we have studied thesteps of GaN (0001) surfaces, unveil atom-scale

epitaxial growth of power semiconductors, atomic

elementary processes of N incorporation at theand electronic structures of semiconductor-

step edges, and then provide a microscopic

insulator interfaces, and the complex of line

picture of the step-ow epitaxial growth of GaN.

dynamics simulations within

defects and impurities. The main computational
tools are our RSDFT (Real Space Density
Functional Theory) code and RS-CPMD (CarParrinello Molecular Dynamics) code. We haveclarified 1) the atom-scale mechanism of GaN
epitaxial growth [1], 2) the mechanism of theFig.1: Calculated electron densities near
the GN step (a) and the Ga2 step (b). The
densities are represented by the yellow
isovalue surfaces. The small yellow
clouds reflect the presence of the low
electron density, indicating that the GaGa weak bonds are formed at the stepedges. The Ga, Ga-ad (Ga adatom), and N
atoms are represented by the green, pink,
and blue balls, respectively.

adatom diffusion on SiC stepped surface[2], 3)
the formation of dangling-bond free interface of
GaN and a gate insulator[3,4], and 4) atomic andelectronic structures of the dislocation-impurity
complex in GaN [5].
The group identification codes for theachievements above are k0042 and m0001. The

Epitaxial growth usually takes place on Ga-

below is the explanation of the issue 1) above.

rich vicinal surfaces in which the (0001) surface

Step-flow epitaxial growth of GaN

is slightly inclined toward [1100] or [11-20]

Growth of high-quality epitaxial thin films of

direction. There are five distinct mono-bilayer

GaN is indispensable for the energy-saving power

steps on such vicinal surfaces depending on theelectronics and the clarification of the mechanism

atomic species, Ga or N, at the step edges and theof the epitaxial growth is essential to advance

inclined directions. We have performed the49Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

geometry optimization for all the possible step

We have previously shown that the NH3edges and calculated the step formation energies.

provided in Metal-Organic Vapor Phase Epitaxy

Typical structures of the step edges are shown(MOVPE) arrives at the terrace of the growing

in Fig. 1 along with the electron density. The

Ga-rich surface and is decomposed into the NH

characteristics is the presence of Ga-Ga bonds atunit [Fig. 2(c)] [6]. Now we have found this NH

the step edges. As is clear from the small electron

unit diffuses on the surface terrace with theclouds in Fig. 1, the Ga-Ga bonds are relatively

activation energy of 0.6 eV (Fig. 2).

weak and thus become hot spots for the epitaxial
growth.

Fig. 3: The GN step-edge structure with
two NH units intervening in the Ga-Ga
bonds. Burgandy, green, blue and orange
balls depict Ga adatom, Ga, N and H
atoms, respectively.

This indicates that the NH units wander on theterrace and occasionally reach the surface stepedges. We have indeed examined the energetics ofthe reaction in which two isolated NH units on theterrace diffuse toward a step edge and intervene
into the adjacent Ga-Ga bonds as in Fig. 3. We

Fig. 2: Diffusion pathway and thecorresponding energy barrier of an NH
unit on the terrace of GaN(0001)
surface. (a) The total-energy landscapealong the diffusion pathway. The left
and the right ends correspond to theinitial and the final geometries,
respectively. (b) Diffusion pathway in a
top view represented by the small redballs which denote the lateral positionsof the N atom in the NH during the
diffusion. (c) An initial geometry of the
NH unit which intervenes in the weakbond between the Ga adatom and the
top Ga atom. (d) A final geometry of the
NH unit which intervenes in theadjacent Ga-Ga weak bond. Burgandy,
green, and blue balls depict Ga adatom,
Ga and N atoms, respectively.

have found this reaction is exothermic with theenergy gain of 0.45 eV.
Then the next step is the incorporation of Ga
atom at the step edge. Since the growing surface
is Ga rich, it is highly likely that an additional Ga
atom approaches the step edge where the two NH
units are incorporated [Fig. 4(a)]. We have thenexamined a reaction in which the two H atoms aredesorbed as an H2 molecule and the arriving Ga isincorporated at the step edge [Fig. 4(b)]. We haveidentified a pathway of this reaction, andcalculated the energy profile [Fig. 4(d)]. We have50

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

free-energy gain at growth temperature and under
the typical H2 partial pressure. It is evaluated tobe 2.1 eV. This certainly compensates theobtained zero-temperature energy cost of 1.8 eV,
indicating that this reaction is favorable.
The top view of the final structure is shown in
Fig. 4(c).

The step edge before this reaction

proceeds one unit by incorporating two N atoms
from the NH units and a new Ga atom. This is theelementary process of the step-flow epitaxial
growth.

Related Publications[1] K. M. Bui, K. Shiraishi and A. Oshiyama,Appl. Surf. Sci. 557, 149542 (2021).

Fig.4: An elementary process in the stepflow growth of GaN. (a) Stable structureof the GN step edge attached with 2 NH
units and an additional Ga atom nearby.
(b) Stable structure of the GN step with
H2 desorbed from the structure (a). (c)The top view of the stable structure
shown in (b). Color code of the balls
depicting atoms are the same as in Fig. 3.
The additional Ga adatom is shown bypurple. (d) Calculated energy profile forthe reaction from (a) to (b).

[2] K. Seino and A. Oshiyama, Appl. Surf. Sci.
(2021) to be published.
[3] K. Chokawa, T. Narita, D. Kikuta, T. Kachi, K.
Shiozaki, A. Oshiyama and K. Shiraishi, Phys.
Rev. Applied 14, 014034 (2020).
[4] K. Chokawa, K. Shiraishi and A. Oshiyama,Appl. Phys. Lett. (2021) to be published.

found that the energy cost of this reaction is 1.8[5] T. Nakano, Y. Harashima, K. Chokawa, K.

eV. However, by examining the obtained energy

Shiraishi, A. Oshiyama, Y. Kangawa, S. Usami,

profile in Fig. 4(d), this is the cost to make 2H

N. Mayama, K. Toda, A. Tanaka, Y. Honda, andatoms on the surface an H2 molecule in the gas

H. Amano, Appl. Phys. Lett. 117, 012105 (2020).

phase. In the gas phase, the H2 molecule gains the[6] K. M. Bui, J.-I. Iwata, Y. Kangawa, K.

free energy owing to its translational, vibrational

Shiraishi, Y. Shigeta, and A. Oshiyama, J. Phys.

and rotational motions. We have evaluated such

Chem. C 122, 24665 (2018).

51

Activity Report 2020 / 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, Indra PARDEDE1, Daiki YOSHIKAWA2, Tomosato KANAGAWA2,
Nurul IKHSAN2, Hasan Al RASYID2, Marleni WIRMAS2, 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 studied the magnetic anisotropy and its

magnetization directions. In addition, the non-electric field (EF) effect in the thin film related

collinear spin density can estimate the shapewith spintronic devices [1]. We obtained anmagnetic anisotropy energy (SMAE) by using

qualitative agreement between theory andthe scheme developed before in our researchexperiment on magnetic anisotropy of thegroup [3]. In the present applications, themagnetic thin film including the Fe/MgO

contributions of MCAE and SAME haveinterface with Cr underlayer, by taking into

different sign in the numerical values.

account an alloying effect of Fe-Cr. Without

Therefore, an accurate numerical computation

alloying in the theoretical calculation, the total

is required for obtaining a realistic result.

magnetic anisotropy indicates an in-plane

We used the thin films in the followings;

magnetization. Such theoretical consequencevacuum/Cr(6ML)/Fe(4ML)/MgO(5ML)/vacu

had been solved in the comparison with theum(S-I) and vacuum /Cr(6ML)/Fe(1ML)/Cr

experimental result [2] that showed a(1ML)/Fe(3ML)/MgO(5ML)/vacuum(S-II).

perpendicular anisotropy. The introduction of

The magnetic anisotropy energy (MAE) was

alloying effect may be consistent with thecalculated from the total energy difference

fabrication condition in the experiment. As abetween in-plane magnetization ([100]) andresult, our first-principles approach reveals aout-of-plane magnetization ([001]), MAE =potential to describe magnetic anisotropies ofE[100]-E[001]. To apply an EF, we used themagnetic thin film.

effective screening medium (ESM) method.

In

the

computational

approach,we

employed the plane-wave basis electronicSys.

structure calculation with using a scheme ofnon-collinear

spin

relativistic

ultra-soft

VCMA MCAE SMAE MAE(fJ/Vm) (mJ/m2) (mJ/m2) (mJ/m2)

fully

S-I [1]85

0.586

pseudopotential

S-II [1]

89

1.280

densityand(including spin-orbit coupling). This scheme

Exp. [2] ~300

can provide the magnetocrystalline anisotropy−−1.336 −0.750−1.053−0.227~ 0.500

Table I. Results of VCMA, MCAE, SMAE,
MAE(=MACE+SDA) and comparisons withexperimental results.

energy (MCAE) from the difference between
the total energy calculations for the different

52

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

with those from the density functional theory
(DFT)

based

on

generalized

gradient

approximation (GGA). Half-metallicity wasobserved, where the band energy gap appears
in the majority spin state. Such property at the
Fermi level is the reason why the material has
been considered as a candidate of spintronics
application. The QSGW indicated that the gap
is larger than that of the corresponding GGA
case. The QSGW may yield more localized
3d-orbitals, compared with those from the
GGA. Based on the projected density of states(PDOS) analysis, Co atoms of the octahedral
site

negligibleacontribution

to

the

total

of tetrahedral [Co(tet)] site (high spin state).

As shown in Table 1, the alloying system

The QSGW indicated the difference of(S-II) shows a perpendicular anisotropy

octahedral crystal fields on the different cation(positive value for MAE). The most importantsites of Co(oct) and Ni(oct). The electronic

key for the perpendicular is that the MCAE

states near the Fermi level consist mainly of

increases by the alloying of Fe-Cr. As depicted

Co(tet) 3d eg-orbitals. The comparison within Fig. 1, the increase appears at the interface

the results of one-shot GW reveals that thewith MgO layer. This means that the magnetic

self-consistent treatment introduces visible

anisotropy energy at the Fe/MgO interface ischanges in the electronic structures.

sensitive to the termination of Fe layer in thethin film.

References

GW[1] I. Pardede et al., Crystals 10 (2020) 1118.

(QSGW) ele-ctronic structure calculation [4][2] T. Nozaki et al., Phys. Rev. Appl. 5 (2016)

was performed in the spinel structures of044006.

ternary magnetic compound NiCo2O4, using[3] T. Oda and M. Obata, JPSJ 87 (2018) 064803.

the software ecalj. The QSGW method iselectronicbetotal magnetization is provided by Co atoms

for MgO).

ontomagnetization. The largest contribution to thetook into account the dielectric constant (9.8

state-of-the-art

found(low spin state) among them, resulting in a

To obtain the EF inside the MgO layer, weself-consistentwere

nonmagnetic/weak magnetic configuration

Figure 1. Atom resolved MCAE in (a)S-I and(b) S-II.

Quasi-particle[Co(oct)][4] T. Kotani et al., PRL 96 (2006) 226402.

structureinvestigation without using any empiricalparameter. The results were also compared53

Activity Report 2020 / 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

4H-SiC is one of the major enabling materials for advanced high power and high temperature electronics applications. However, theperformance of the metal-oxide-semiconductor
field-effect-transistor (MOSFET) using SiC isseverely limited due to their field-effect mobility being much lower than the ideal electron
mobility. SiC based MOSFETs are usuallyfabricated on the front side of 4H-SiC(0001)
wafer (Si face) by the thermal oxidation in
dry O2 ambience. On the other hand, it isreported that MOSFETs fabricated on the C
face, which is the back side of the same wafer,by wet oxidation in H2 O ambience contain low
density of interface defects and exhibit higher
carrier mobility than that on the Si face. Electrically detected magnetic resonance (EDMR)
spectroscopy revealed that characteristic defects, which are called “C-face defects”, are observed in the wet-oxidized C face[1]. However,the details of the generation of C-face defects
are unclear.
In this project, we have conducted firstprinciples study on the formation energy ofC-face defects at SiO2 /SiC(0001) interface.
RSPACE code[2, 3, 4], which is also developedin this project is used for the first-principles
calculations. The lateral lengths of the su√
percell are chosen to be 2 3a and 4a along
the [11̄00] and [112̄0] directions of the 4HSiC(0001) surface, where a is the lattice constant of SiC, and integration over the Brillouin zone is carried out using a 2 × 2 ~k-point

mesh. The surface C atoms are connected to
OH groups to imitate oxide and the Si atoms
are terminated by H atoms. For comparison,
the formation energy of the defects in 4H-SiC
bulk is also calculated. The dimension of the√supercell is 2 3a, 4a, and c along the [11̄00],[112̄0] and [0001] directions, respectively, withc being the lattice constant of 4H-SiC bulk.
The C face defects are CSi VC c-axial,
CSi VC basal, VSi VC c-axial, and VSi VC
basal defects. It has been reported that only
CSi VC c-axial and VSi VC basal are observedat the wet-oxidized C face among them. The
CSi VC defects are generated by removing a
Si atom and moving C atom to VC site fromthe neighboring C site. We remove Si atomfrom the first or second SiC bilayer. In addition, VSi VC defects are created by removing C
atoms at the Si site from the CSi VC defects.
The computational model for the case of theCSi VC c-axial defect is shown in Fig. 1. Table 1 corrects the formation energies and magnetic moments of the defects.
When Si atom in the first SiC bilayer of theinterface is removed, CSi VC basal, VSi VC caxial, and VSi VC basal defects are hardly generated because the dangling bonds of C atom
are passivated by the O atom which comesfrom the oxide layer. As a result, the formation energy of CSi VC c-axial defect, in which
Si atom at the first bilayer is removed, is themost stable among CSi VC defects. In the caseof the VSi VC defects, the formation energy

54Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 1: Formation energies Ef and magnetic moments of C-face defects. The zero of theformation energy is set at the lowest models among CSi VC (+) at the interface, CSi VC (+) in
bulk, VSi VC at the inerface, and VSi VC in bulk.
Defects
CSi VC (+) c-axial @ 1st layer
CSi VC (+) c-axial @ 2nd layer
CSi VC (+) basal @ 2nd layer
CSi VC (+) c-axial @ bulk
CSi VC (+) basal @ bulk
VSi VC c-axial @ 2nd layer
VSi VC basal @ 2nd layer
VSi VC c-axial @ bulk
VSi VC basal @ bulk

Formation energy (eV)
0.0
+0.92
+0.49
+0.10
0.0
+0.96
+0.49
0.0
+0.09

Magnetic moment (µB )
1
1
0
1
1
1
2
2
2

of the c-axial structure is lower than that of
the basal one. Although this result is not inagreement with the experimental result, themagnetic moment of the basal defect at theinterface corresponds with that in bulk while
the magnetic moment of the c-axial does not.
This indicats that our calculated results support the experimental situation.

References[1] T. Umeda, Y. Kagoyama, K. Tomita,
Y. Abe, M. Sometani, M. Okamoto, S.
Harada, and T. Hatakeyama, Appl. Phys.
Lett. 115, 151602 (2019).
[2] K. Hirose, T. Ono, Y. Fujimoto, and S.
Tsukamoto: First Principles Calculations
in Real-Space Formalism (Imperial College, London, 2005).
[3] T. Ono, M. Heide, N. Atodiresei, P.
Baumeister, S. Tsukamoto, and S. Blügel,
Phys. Rev. B 82, 205115 (2010).
[4] Y. Egami, S. Tsukamoto, and T. Ono,
Phys. Rev. Research 3, 013038 (2021).

Figure 1: Computational model for SiC/SiO2
interface with CSi VC c-axial defect. Blue,
brown, and red balls are Si, C, and O atoms,
respectively. The supercell contains 95 Si, 96
C, 16 O, and 32 H atoms. H atoms are used fortermination of dangling bonds at the surfaces.

55

Activity Report 2020 / 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

The understanding on structures and dynamics at surfaces, interfaces and defects on
nanoscale is crucial to facilitate developmentsof novel information and energy devices. Firstprinciples calculation has sufficient accuracy of
prediction for this purpose, but its computational cost is often too high to model such devices realistically.
Keeping the above in minds, we have been
investigating atomic structures and atom dynamics in various systems via first-principles
calculations combined with multi-scale ormachine-learning approaches. In the following,some of our results in the fiscal year 2020 are
described.

2

Phase stability of Au-Li binary systems

Aiming to deepen our understanding on theoperation mechanisms of novel memory device named VolRAM [1] and all-solid-state Liion batteries, we examined Li ion distribution at the interfaces between γ-Li3 PO4 andmetal electrodes by combining first-principles
data of defect formation energies with a onedimensional continuum model [2] in the previous year. However, we have not achieved thorough understanding because of alloy formation
between Au and Li: The Au-Li binary system
is known to exhibit various alloy phases over awide range of compositional ratios. Therefore,
in the fiscal year 2020, we have explored thealloying properties of Au and Li [3].
For this purpose, we constructed ahigh-dimensional neural network potential (HDNNP) [4] based on density functional
theory (DFT) calculations. The predictions
by the constructed HDNNP on lattice parameters and phonon properties agree well withthose obtained by DFT calculations. The
predictions on the mixing energy of Au1−x Lix
also show excellent agreement with DFT
verifications. The lack of consensus on the
Au-Li stable phases in previous studies canbe understood from the existence of various
compositions with structures on and slightly
above the convex hull.
We have also examined the alloying process starting from the phase separated structure to the complete mixing phase by performing molecular dynamics simulations with theconstructed HDNNP. Our results reveal thatwhen multiple adjacent Au atoms dissolved
into Li, the alloying of the entire Au/Li interface started from the dissolved region.

3

Band alignment tuning via
thin-film insertion

Recently, interfacial resistance between the
Nb-doped SrTiO3 (STO) metal and a LiCoO2(LCO) mixed conductor has been found to de-56

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 1:
Calculated local density ofstates of (A) LiCoO2 (104)/SrTiO3 (001)and (B) LiCoO2 (104)/three unit cells of
LaAlO3 /SrTiO3 (001) along the Z-axis direction perpendicular to the interfaces [5].
crease significantly (by more than five orders ofmagnitude) upon the insertion of a 1 nm thickinsulating LaAlO3 (LAO) layer at the interface [5]. To clarify the origin of this behavior,
we have performed DFT+U calculations for
LCO/STO and LCO/LAO/STO heterostructures. In our calculation, we have adopted theundoped system for both LCO and STO, considering the fact that Nb-doping shifts only the
Fermi level, and the position of the conduction
band minimum, measured from the vacuum
level, is nearly the same between the undoped
and Nb-doped STO.
Figure 1 shows the local density of statesof the structurally optimized LCO/STO andLCO/3 unit cells of LAO/STO systems along
the Z-axis direction perpendicular to the interface. In the LCO/STO model, upward (downward) band bending of ∼0.20 eV (0.06 eV)near the interface on STO (LCO) is seen. The
difference in the valence band maximum energy of LCO and the conduction band minimum energy of STO was ∼1.8 eV. In contrast,
the energy level difference decreased to 0.28 eV
when 3 LAO unit cells were inserted at the interface. The linear change in the LAO band
level along the Z-axis shows the presence ofa built-in electric field. The electric field was
2.2 eV/nm (0.67 eV per LAO unit cell), whichis comparable to the values deduced from theexperiments [5] (0.4 eV per LAO unit cell).
The shift in the energy level via LAO insertion

suggests a reduction in the Schottky barrierheight.
We have also performed quantum mechanical calculations for electron tunneling bysolving the time-independent one-dimensional
Schrödinger equation with a simple model constructed based on the above behavior of bandalignment change due to the LAO layer insertion. The result reproduced the observed interfacial resistance change with the LAO layer
thickness: The 4 u.c. LAO case had a minimum resistance.
This study provides a proof-of-concept
demonstration of an approach to reduce theinterfacial resistance by tuning the Schottky
barrier at the interfaces of metals and mixed
conductors.

References[1] I. Sugiyama, R. Shimizu, T. Suzuki, K.
Yamamoto, H. Kawasoko, S. Shiraki, and
T. Hitosugi: APL Mater. 5 (2017) 046105.
[2] K. Shimizu, W. Liu, W. Li, S. Kasamatsu,
Y. Ando, E. Minamitani, and S. Watanabe: Phys. Rev. Mater. 4 (2020) 015402.
[3] K. Shimizu, E. F. Arguelles, W. Li, Y.
Ando, E. Minamitani, and S. Watanabe:
Phys. Rev. B 103 (2021) 094112.
[4] J. Behler and M. Parrinello: Phys. Rev.
Lett. 98 (2007) 146401.
[5] K. Nishio, T. Shirasawa, K. Shimizu, N.
Nakamura, S. Watanabe, R. Shimizu, and
T. Hitosugi: ACS Appl. Mater. Interfaces
13 (2021) 15746.

57Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical Approach to Reduce the Interface-State Density in
SiC-MOS Devices
Yu-ichiro MATSUSHITATokyo Institute of Technology, Ookayama Meguro-ku, Tokyo 152-8550
Theoretical

SiC power MOSFETs have shown

calculations

showedthat

remarkable energy-saving effects andcarbon-related defects were generated

havecommercialized.

near the interface under the temperature

However, the SiC/SiO2 interface, which

and oxygen partial pressure conditions

plays a fundamental role in SiC power

used in the actual experiments. In

MOSFETs, still has a high interfacial

particular, the residual carbon defects

defect density, and most of the inversion

distributed just at the interface werelayer carriers induced by the gate voltage

found to be stabilized and present inare trapped in the interfacial defects. In

large amounts. This calculation result

fact, only 10% of the theoretical electron

indicates that the formation of residual

mobility has been achieved in SiC-

carbonMOSFETs.

theenergetically stable and that thermal

microscopic

oxidation inevitably produces residual

already

In

been

order

interface-state

todensity,

reduceTherefore,

We have performed density-functional
toinvestigate

at

the

interfaceiscarbon defects at the interface.

identification of them is needed.

calculations

defects

wethoughtthattheformation of carbon defects due tothemicroscopic structure of interface defects.

thermal

One of the most promising candidates ofunavoidable, and we sought a way tointerface defects is the residual carbon-

overcome this problem. As a result, we

related defects at the interface. In thissucceeded in forming a high-quality

study, the stability of carbon-related

interface

defects distributed in three regions (SiC

eliminates the thermal oxidation of SiC

bulk, SiO2 film, and SiC/SiO2 justand removes the carbon defects near theinterface)on

SiC surface, followed by the formation oftemperature and oxygen partial pressure

an oxide film [2]. In the proposed process,were clarified by theoretical calculationsa Si thin film is deposited after hydrogenbased on density-functional theory [1].

etching and oxidized to SiO2 at a

and

their

dependence

58

oxidation

by

using

of

a

SiC

processwasthatActivity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

temperature where the oxidation of SiC
does not proceed. Subsequent nitridation
after the oxide film formation is effective
in reducing defects. The effectiveness ofthe proposed method was confirmed
experimentally,andahigh-quality

interfacial structure with an interfaciallevel density of (1-4) × 1010 cm-2eV-1,
which is one order of magnitude smaller
than the conventional 1011 cm-2eV-1, wasFig. 1: Successful reduction in interface-stateachieved.

density in SiC/SiO2

References[1] T. Kobayashi and Y. Matsushita, JAP,
126, 145302 (2019).

[2] T. Kobayashi, T. Okuda, K. Tachiki, K.
Ito, Y. Matsushita, T. Kimoto, APEX, 13,091003 (2020).

59

Activity Report 2020 / 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
For the investigation of the dynamic

constructed ANN potential precisely reproduces

properties of covalent liquids and glasses under

the FPMD results. The V-T relation calculatedpressure, it is important to consider the stabilityby the ANN potential trained with potentialof materials states under various conditions

energy only (E-fit) or with potential energy andfrom the viewpoint of free energy. We haveatomic forces (EF-fit) is completely different

been using the thermodynamic integration (TI)

from that by FPMD, though the E-fit method

method [1] for this purpose. The first-principles

gives almost correct V before melting. We also

molecular

simulations

found that the 128-atom system with 4k points

would be the most powerful and accurate toolfor Brillouin zone integration gives nearly

to perform TI calculations. Due to the highconverged results for the melting temperature.

dynamics(FPMD)

calculation cost, however, FPMD simulations
have been carried out only for small-sized
systems. One of the solutions to solve this costproblem is to use machine-learning interatomic
potential based on artificial neural networks(ANN) trained from the results of FPMD
simulations.
This study aims to establish the training
requirements

for

the

ANN

potential

toreproduce the phase properties of sodium as an
Fig. 1: Temperature dependence of volume V of
Na obtained by FPMD and ANN-MD
simulations.

example. Figure 1 shows the temperaturedependence of calculated volume V. The black
circles show V obtained by FPMD. It is seen

References

that, only when the virial stress tensor, as well

[1] D. Frenkel and A. J. C. Ladd, J. Chem. Phys.

as the potential energy and atomic forces, is81, 3188 (1984).

taken into account in the training (EFP-fit), the60Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Quantum Simulations on Dynamical Heterogeneous
Catalysts
J. I. ENRIQUEZ, H. H. HALIM, S. E. M. PUTRA, T. N. PHAM, Y. J. WONG,
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 2020-2021, we carried out theoretical investigation of chemical processes at surfaces
and interfaces, oxidative etching process of diamond [1], multi-scale simulation of Cu adatom
diffusion on Cu surfaces [2], formic acid adsorption in polymeric form and decomposition
on Cu(111) [3], oxygen vacancy induced metalinsulator transition of LaNiO3 thin film over
SrTiO3 [4].
In this report, we report the oxidative etching process of the diamond (100) surface [1].
Diamond possesses a unique combination ofsuperlative properties that makes it an attractive material for several novel applications. Of
all semiconductors, diamond has the highest
dielectric breakdown field, saturated electron
drift velocity, and thermal conductivity whichmake it an ideal material for next-generationelectronics that will outperform current systems in terms of operating frequency andpower handling capacity. In addition, diamond’s wide band gap, optical transparency,chemical inertness, hardness, and low thermal
expansion have led to a number of specialized photonics applications including spacecraft window, optoelectronic microlens, photodetector, high energy particle detector, UV
and infrared LED, and Raman laser. Diamondhas color centers that functions as bright single photon source (SPS) at room temperaturesand can be potentially implemented in quantum metrology and quantum information science.

At present, a theoretical study that investigates the entire oxidation process, startingfrom the adsorption of gas phase O2 up to thedesorption of CO and etching of the surface,
has never been done. This kind of study isnecessary to develop a comprehensive knowledge of diamond oxidation mechanism. For
this reason, van der Waals-corrected density
functional theory simulations of the oxidationof the C(100) surface have been performed.
Density functional theory (DFT) calculations have been performed using STATE code
package (Simulation Tool for Atom TEchnology) with generalized gradient exchangecorrelation functional (GGA) based on thework of Perdew, Burke and Ernzerhof (PBE).
Semi-empirical van der Waals correction was
implemented. Core electrons were treated using ultra-soft pseudopotentials. Wave functions were expanded using plane-wave basiswith wave function and augmentation charges
cutoff of 36 Ry and 400 Ry, respectively.
We simulated the succeeding desorption of
CO up to the complete etching of the top C
layer. The reaction paths and optimized structures are shown in Fig. 1. Following the desorption of the first CO, there are two possible
locations where the second CO could desorb,
the adjacent CObridge towards the [011̄] direction where O is on top site and the CO fromthe adjacent ether group towards the [011] direction. The former and the latter have Ebarrierof 4.53 eV and 3.62 eV, respectively. Succeed-61Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

ing CO desorptions along [011] (Fig. 1 B-E)
all have lower Ebarrier compared to [011̄], suggesting a preferred etching direction. The calculated desorption activation energies vary between 1.01 - 4.68 eV. Initial desorption of CO
along a given row in [011] direction has thehighest desorption activation energy (reaction
A→ B and E → F), while succeeding energy
barriers are lower (Fig. 1 A-E, E-I). Analysis of the reaction path geometries shows thatfor these two reactions, the initial CO desorption proceeds by the near-simultaneous breaking of two CObridge-C bond. The point defectleft by the initial desorption allows the next
CObridge to break one bond with second layer
C and form CO on top (COtop ) structure. The
non-simultaneous bond breaking reduces theheat released by the reaction and the desorption activation barrier. This suggests that the
point defect functions as nucleation point for
CO desorption along [011] direction. This nucleation function was first proposed by Johnet al. based on their observation that the surface roughness of diamond (100) did not increase even after removal of over 5300 atomic
layers, suggesting that the removal rate of rowsof atoms is more rapid than the removal rate oflayers. Our work is the first theoretical study
to support their prediction.

In summary, we performed density functional theory calculations with van der Waals
corrections to elucidate diamond oxidation
mechanism on the atomic-level which could
lead to insights that will advance the improvement of nascent nanofabrication technologies.
We developed a comprehensive theory of oxidative etching of the diamond (100) surface,from the adsorption of gas phase O2 , including
details of metastable adsorption states, intersystem crossing, and induced surface dereconstruction, to the desorption of CO and CO2 ,complete etching of the top surface layer andits subsequent stabilization.

!

Figure 1: Etching of the top-layer atoms ofC(100)-(1 × 1): Obridge surface through successive CO desorption. The heat of reactions
and activation energies in electron-volts areshown in black and blue texts, respectively.
Physisorption energies of CO are shown in orange text. Grey and red spheres correspond tocarbon and oxygen atoms, respectively, while
the dangling bonds are represented by blue
cylinder.

References[1] J. I. Enriquez, F. Muttaqien, M. Michiuchi, K. Inagaki, M. Geshi, I. Hamada,and Y. Morikawa: Carbon 174 (2021) 3651.
[2] H. H. Halim, et al., : ACS Omega 6 (2021)
5183.
[3] A. Shiotari, S. E. M. Putra, et al., : Small,in press.
[4] H. D. Nguyen, et al., : Phys. Rev. B 102(2020) 165411.

62

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development and application of ﬁrst-principles
algorithms for long-range electron transport
simulation
Yoshiyuki EGAMI
Division of Applied Physics, Faculty of Engineering, Hokkaido University
Kita 13, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-8628

In this subject, an eﬃcient computational
procedure based on the real-space ﬁnitediﬀerence formalism[1] was developed to evaluate the electron-transport properties of longsystems containing more than 105 atoms under the zero temperature and zero bias limits
in the steady state without accuracy deterioration. In the procedure, a transition region isrepresented by arranging multiple parts along
the transport direction. The Green’s function of the whole transition region extended
towards the transport direction was obtainedby recursively combining the Green’s functionsof the adjoining parts one by one. The computational cost for calculating the submatrices of
the Green’s functions required to estimate thetransport properties can be suppressed linearly
for the number of the combined parts.

To exemplify the eﬃciency of the proposed
procedure we demonstrate large-scale electrontransport calculations for BN-doped doublewalled carbon nanotubes composed of 196,608
atoms (Fig. 1), which make, to the bestof our knowledge, the largest system in theﬁrst-principles electron-transport calculation.
These works have been performed on System B
and System C of the Supercomputer Center,the Institute for Solid State Physics, the University of Tokyo.
6

Conductance (G0)

In recent years, a lot of ﬁrst-principles studies on various materials have been energetically
performed toward the development of novel
devices. First-principles calculations generally require a computational cost proportional
to the cube of the system size. In order toperform large-scale simulations, the development of O(N ) algorithms and the improvement of parallelization eﬃciency of parallel calculations have been promoted. So far, great
progress has been made in atomic structure
calculations and electronic structure calculations, but reducing the computational cost remains a major issue in electron-transport property calculations.

54

㻌 periodic doping㻌 random doping

3
2
1
0
-1.0

-0.5

0.0

0.5

1.0

Incident Energy from the Fermi level (eV)Figure 1: Conductance trace of BN-doped
double-walled carbon nanotubes consisting of
196,608 atoms.

References[1] Y. Egami, S. Tsukamoto and T. Ono:
Phys. Rev. Res. 3, 013038 (2021).

63

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo“Prediction of hydrogen function by advanced
calculation of solids containing hydrogen”“Development of data assimilation method for crystal
structure prediction and its application to hydrogencontaining compounds”
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
One of the most challenging problems in

crystal structure determination of materials

first-principles simulations of materials is tofound by high-pressure experiments where thepredict crystal structure by searching the global

range of the diffraction angle is limited or thoseminimum in multi-dimensional potential energy

containing hydrogen atoms whose positions are

surface (PES). It takes a sizeable computationaldifficult to be determined by X-ray diffraction.

cost to calculate the electronic energy of even a

The data assimilation method might accelerate

single atomic configuration from first principles.

materials exploration in combination with

It is, therefore, practically difficult to find the

combinatorial synthesis and measurement.

most stable crystal structure when the number ofThis year, we showed that the method is very

atoms in the unit cell is large and when PES has

robust against noise in the experimental data if

many local minima.

we tune the control parameter representing the

The problem is partially solved by a data

weight of the data assimilation [2].

assimilation method which we have proposed

We also extended the method to assimilate[1]. In the data assimilation method, we

multiple experimental data, such as X-ray andincorporate powder diffraction data to constrain

neutron diffraction data, at the same time. Bothsearch space based on Bayes’ theorem, by whichreflect the same interlayer distances of thewe can drastically accelerate finding a probable

crystal but with different peak intensities, giving

crystal structure. The method is valid even if theus more information. We applied this method todiffraction data is incomplete and is insufficient

Zn(OH)2 to confirm that using both sets of data

for structure determination by ordinary data

significantly improved the success rate of crystal

analysis methods. Typical applications are

structure prediction [2].

64Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Then we applied the method to two systems
containing a considerable number of atoms in aunit cell. The first one is a Li-ion conductor
LiCB9H10. The Li-ion conductivity of thismaterial is known to increase two orders ofmagnitude at around 330-360K. Still, theFig. 1 Top and side views of a theoretically
predicted structure of CaxAlyHz. Large,
middle and small spheres denote Ca, Al andH atoms.

mechanism and associated crystal-structurechange have not been clarified yet. From oursimulation, the difference in the crystal structure
below and above the transition temperature is

These works have been done in collaboration

essentially the orientation and rotative motion ofwith the experimental groups of the Grant-in-)- complex ions. Since the diffusive

Aid for Scientific Research on Innovative Areas

the (CB9H10

motion of Li ions is strongly correlated with the"Hydrogenomics:

Creationof

Innovativerotation of a nearby complex ion (CB9H10)-, it isMaterials, Devices, and Reactive Processes

greatly enhanced by its rotation in the high-using Higher-Order Hydrogen Functions" (FY

temperature phase [3].

2018-2022).

The second is a metal hydride CaxAlyHz
newly synthesized at high pressure. Although

References

powder X-ray diffraction data is available, the[1] N. Tsujimoto, D. Adachi, R. Akashi, S.

unit cell seems to be quite large, and neither its

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

accurate chemical composition nor the crystal

053801 (2018).

structure is clarified experimentally. We tried its[2] S. Yoshikawa, Ph.D. dissertation (Thestructure determination and found a plausible

University of Tokyo, 2021); S. Yoshikawa etmodel containing more than one hundred atomsal., in preparation.

in a unit cell, as shown in Fig.1 [2,4][3] R. Sato et al., in preparation.
[4] R. Sato et al., in preparation.

65

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First Principles Studies on Atomic and Electronic Structuresof Impurity-Screw Dislocation Complexes in GaN
Kenji Shiraishi
Institute for Materials and Systems for Sustainability,
Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601
Recentexperimentssuggestthat

Mg

We find that threading screw dislocations

condensation at threading screw dislocationsindeed attract Mg impurities as shown in Fig.2.

(TSD) induces current leakage, leading todegradation of GaN-based power devices. To
investigate this, we performed first-principles
total-energy calculations for various Mg anddislocation complexes. Figure 1(a) shows an
atomistic

configuration

of

a

TSD.

The
Fig. 2. (a) Binding energies of the Mg-TSD
complexes of the D<0|2>, S<0|6>, and S<0|3>
cores. dMg-dis is the distance of the Mg from thedislocation line. (b)–(d). The most stable core
structures of the Mg–TSD complexes of theD<0|2>, S<0|6>, and S<0|3> cores, respectively.
The position of the Mg atom is inindicated by theorange sphere. A red cross denotes the position ofa dislocation line.

dislocation has the Burgers vector of [0001]. To
model the TSD, the atoms are initially aligned ina helical manner along the [0001] dislocation
line.34,35 A periodic boundary condition is then
imposed on all axes of the system. The system
contains 812 Ga and N atoms in total, and avacuum layer is added on lateral planes

These findings provide a picture in which theperpendicular to the [0001] direction [Fig. 1(b)].

Mg, being a p-type impurity in GaN, diffuses
toward the TSD and then locally forms an n-type
region. The appearance of this region along the
TSD resultsin local formation of an n–n junction
and leads to an increase in the reverse leakage
current.

Fig. 1. (a) Model of a TSD. The Burgers vector is [0001],

References

and the dislocation line runs along [0001]. Green andblue spheres are Ga and N atoms, respectively. Thelarger
spheres highlight the dislocation core. (b) Schematic of
the [0001] plane of the unit cell. The green region
represents GaN, surrounding which is thefictitioushydrogen. The outermost region is vacuum. The
red cross indicates the position ofthe dislocation line.

[1] T. Nakano,Y. Harashima, K. Chokawa, K.
Shiraishi, A. Oshiyama, Y. Kangawa, S.
Usami,N. Mayama, K. Toda, A. Tanaka, Y.
Honda, and H. Amano, Appl. Phys. Lett., 117,012105 (2021).

66

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical Studies on Semiconductor MOVPE GrowthBased on Multi-Physics Simulation
Kenji Shiraishi
Institute for Materials and Systems for Sustainability,
Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601
We examined the main reaction pathway ofobtained in our study shows that when H2 isthe TMG (Ga(CH3)3) decomposition processes

sufficiently present as a carrier gas, amino

[1].

the

groups, which are responsible for the formation

decomposition rate from the Gibbs energy ofof a wide variety of polymers, are difficult toactivation and calculated the mole fraction ofform. Therefore, we were able to reduce theeach chemical species. Asa result, in B3LYP, thenumber of chemical reactions considered indecomposition pathway of TMG

is theconventional fluid simulations. GaH3 molecules

sequential reaction with NH3followed by themust be considered in the surface reaction ofreaction with H2. In M062X, the decomposition

GaN MOVPE. Furthermore, it may be effective

proceeds through repeated reactions with NH3 as

to decompose TMG at ahigh temperature ofin the previous study. Using the reaction rates weabout 1300 K for a certain period of timet oobtained, we calculated the mole fractions ofcontrol carbon contamination..

We

calculated

andcomparedeach chemical species at 1300 K. It was foundthat GaH3 was the most abundant species in
B3LYPand Ga(NH2)3 in M062X. When we
tested the difference between the two exchangecorrelation functions using the high precision
CCSD method, it was found that the results of
the CCSD method were closer to those of B3LYP.

Fig. 1: Mole fraction of each chemical species after
1s at 1300 K and main reaction pathway of TMGa
decomposition written in red obtained by the firstprinciples calculations. [Ref.1]

Moreover, the experiment also supports thereaction paths obtained byB3LYP. Therefore, themain reaction pathway of TMG decomposition

References

is shown in Fig.1: Ga(CH3)3 → Ga(CH3)2NH2 →[1] S. Sakakibara, K. Chokawa, M. Araidai, A.

Ga(CH3)2H → GaCH3HNH2 → GaCH3H2 →Kusaba, Y. Kangawa, and K. Shiraishi, Jpn. J.

GaH2NH2 → GaH3. The main reaction pathway

Appl. Phys. 60, 045507 (2021).

67

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Mechanisms of Chemical Reaction of β-diketones Moleculeswith a Metallic Nickel Surface in Thermal 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) is one

the mechanisms of decomposition ofof the key manufacturing technologies for

β−diketones molecules – such as; hexa-

nano-scale electronic devices [1] as it canfluoroacetylacetone

be used for precise and damagelessacetylacetone (tfacH), and acetylacetone

etching of metals. Thermal ALE of Ni(acacH) – on a metallic Ni surface and thewith hfacH starts with the deprotonation

effectof hfacH molecules after oxidizing the Ni

decomposition concerning thermal ALE.

surface.

By

increasing

the

of

surface(hfacH),roughnesstrifluoro-

on

the

surface

My research assistant A. H. Basher has usedtemperature in the range of 300 ~ 400 °C,

ISSP supercomputer to study the chemicalvolatile nickel complex Ni(hfac)2 andreaction of hfacH, tfacH, and acacH

water H2O molecules are formed on themolecules on flat and rough metallic Ni

surface and remove the NiO layer. In thissurfaces. In this study, we employ van derprocess, once a new metallic Ni surface

Waals (vdW) inclusive [7] periodic density

appears, no further etching occurs, whichfunctional theory (DFT) to investigate theensures the self-liming nature of theadsorption and reaction of hfacH on a metallic

thermal ALE process [2-5]. It has been

Ni surface, and clarify the surface chemistry in

known experimentally [5,6] that, when

the atomic layer etching (ALE) process of Ni.

hfacH molecules are supplied to a metallic

We

Ni surface, they decompose and form

pseudopotential code STATE [8]. In ourneither Ni(hfac)2 nor H2O molecules, andcalculation, we have used 5 nodes for eachas a result no etching of Ni takes place.

submitted jobs to run the calculations on 120

The origin of the self-limiting process inprocessors parallelly and more than 1800 hours

the thermal ALE of Ni with hfacH

has been consumed.

used

our

in-houseplane-wave

exposure was discussed in an earlier

We have investigated several adsorption sites

study[4]. The aim of this work is to clarify

to find the most stable one thermodynamically68

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

with and without vdW forces. Second, thehavedissociationwas

nature of thermal ALE for Ni withinvestigated using nudged elastic band (NEB)

β−diketone gases in general, which ismethod as well as climbing image NEB (ciNEB)

consistent

to get more accurate results. Third, theobservations [5,6].

dissociation

References

C-F

bond in

bond

of

O-H

hfacH

in

hfacH

demonstrated

with

the

earlier

self-limiting

experimental(deprotonation) was studied by two methods: a)[1] G. S. Oehrlein and S. Hamaguchi, Plasmachecking

Sources Sci. Technol. 27, 023001 (2018).

thedeprotonation

manuallybyincreasing the distance between O and H atoms.

[2] A. H. Basher, M. Krstić, T. Takeuchi, M.

b) using NEB then ciNEB methods that is still

Isobe, T. Ito, M. Kiuchi, K. Karahashi, W.

running.
Ithasphysisorption

been

found

energiesthatofWenzel, and S. Hamaguchi, J. Vac. Sci. Technol.

theA 38, 022610 (2020).

those[3] A. H. Basher, M. Krstić, F. Karin, T. Ito, K.

β−diketones are almost the same while

Karahashi, W. Wenzel, and S. Hamaguchi, J. Vac.

the chemisorption energy is higher for aSci. Technol. A 38, 052602 (2020).

β−diketone with a higher polarity and thevan der Waals forces play a decisive role[4] A. H. Basher, I. Hamada, and S. Hamaguchi,,in determining the adsorption energy. The

Jpn. J. Appl. Phys. 59, 090905 (2020).

dissociation processes of β−diketones have[5] T. Ito, K. Karahashi, and S. Hamaguchi, Proc.

been studied with a climbing imageof the 39th Int. Symp. on Dry Process (DPS2017)

nudged elastic band method, which has(Tokyo, Japan, 2017) 45, 2017.

shown the cleavage of a C-F bond of a[6] H. L. Nigg and R. I. Masel, J. Vac. Sci.

β−diketone is more likely to take place

Technol. A 17, 3477, (1999).

than the deprotonation. The surface
roughness can also help to form C-Ni

[7] I. Hamada, Phys. Rev. B 89, 121103 (2014).

bonds, which were also observed in[8] Y. Morikawa, H. Ishii and K. Seki, Phys. Rev.

experiments. In this way, our simulations

B, 69 (2004) 041403.

69

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Thermodynamic properties of icy materials
in the interior of planets and satellites
Yu Komatsu
Astrobiology Center / National Astronomical Observatory of Japan,
Osawa 2-21-1, Mitaka, Tokyo, Japan.

In this study, the equation of state (EOS) ofhydrogen sulﬁde under high pressure is investigated, which is applicable to predicting theinternal structure of icy satellites, such as Europa, and icy planets. H2 O, NH3 , CH4 andH2 S are thought to be the typical icy materials, reﬂecting conditions before establishing
the planetary system [1]. We focus on thermodynamical properties of hydrogen sulﬁde as thecomponent, whose property under high pressure and low temperature has been investigated well due to its superconductivity, butthere are no studies under a wider range oftemperature and pressure.
DFT-MD calculations of hydrogen sulﬁdesystems with a large parameter space withtemperature and density were performed using
Quantum ESPRESSO. As initial conﬁgurations, not only typical structures of hydrogensulﬁde but also the Cmca and P1 structures,
which were obtained by the structure prediction, were selected because they were suggested to be stable under higher pressure [2].
Figure 1 shows self-diﬀusion coeﬃcients
caluculated for the Cmca structure from 500
to 10,000 K, as a function of the density. Inhigh temperature ranges above 5,000K, the diffusion coeﬃcients as well as radial distributionfunctions starting from diﬀerent initial structures converged to nearly identical values atgiven temperature and density. These analyses
would be a good basis for further reﬁnement of
the new EOS for icy bodies, as the next stepof our study.

Figure 1: The self-diﬀusion coeﬃcient for thehydrogen atom (a) and the sulfur atom (b) as
function of the density of the Cmca structurewith four diﬀerent temperatures (500, 1,000,
5,000 and 10,000 K).

References[1] T. V. Johnson et al., ApJ 752, 192 (2012).
[2] Y. Li, et al., J. Chem. Phys. 140, 174712(2014).

70

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Electrochemical reaction analysis using density functional
calculation + implicit solvation model 2
Jun HARUYAMA
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
The rechargeable Li-ion battery (LIB) is a

F = EDFT + Fvib – TSconf(2)

successful energy storage device due to its highwhere F are the free energies of LIG atenergy density and long cycle life. In order tocomposition LixC6, metal Li, and AB stacked

improvequantitativegraphite C6. Free energy is represented as theunderstanding of elementary reactions in thefollowing three terms: DFT total energy EDFT,

LIB such as the reaction of Li intercalation

vibrational free energy Fvib, and configu-

from electrolyte solution into graphite andrational entropy term TSconf.

crystal structure change in graphite during theAtomic configurations and cell parameters ofreaction must be a great help. In previous

Li/6C, Li/9C, Li/12C, Li/18C, Li/24C, andstudies, we have studied charge transfer

Li/36C in-plane structures (see Fig. 1a) werereactions at electrode/solution interfaces in Li-

investigated within van-der-Waals (vdW) levelion batteries (LIB) using density functional

DFT calculations. Interlayer configurations

theory (DFT) calculations combined with

were set to AA, AB, and mix stacking (Fig. 1b).

implicit solvation model. [1–4]

Mix stacking is defined that Li-intercalated

Structure change of Li-intercalated graphite

layers were set to AA stacking and the other(LIG) during the charge/discharge processes

layers were AB stacking. We performed spin-

was recently observed by operando X-ray

unpolarized density functional theory (DFT)diffraction measurements using a synchrotron

calculations with Quantum ESPRESSO (QE)radiation at SPring-8. [5, 6] The operando XRD

package. [7]data cannot explained by conventional staging

The vibrational free energy was approximatedmodel for LIG. To compare and discuss theseby using independent harmonic oscillators

experimental

first-

representation. In this representation, phonon

principles calculations for the phase stability ofdensity of state (DOS) was obtained from

LIG.

density functional perturbation theory (DFPT)

Formation free energy ∆Ff is defined as

implemented in QE. Lattice gas model of∆Ff (LixC6) = F(LixC6) − xF(Li) − F(C6) (1)suitableits

performance,

results,

weconduct

71

constraint

wasappliedtotheActivity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

configurational entropy term.
Figure 1c shows the calculated formation freeenergies. LiC6, Li1/2C6, and Li1/3C6 stablestructures are AA-stack Li/6C stage1, stage2,
and AA stack Li/9C stage2, these structures are
consistent with experiment. [1] AB stacking isstable at the region of x < 0.05 in LixC6. Weemphasize that formation energies using only
DFT term failed to describe higher stage region(C6 – Li1/3C6) especially Li1/3C6 and AB
stacking cannot become convex hull. The
calculation also shows the existence of mix
stacking at intermediate region (0.05 < x < 0.3).
The expected AB–mix phase transition isslightly different from AA–AB phase transition

Figure 1: (a) In-plane configurations of Li/6C,

at x ≈ 0.1 suggested from X-ray diffraction

Li/9C, Li/12C, … structures. (b) Interlayer

analysis. [1] Finally, the computational AB–

configurations of AA and AB stackings. (c)mix phase transition well explained the entropy

Formation

behavior comparing with electrochemicallydiamonds, and crosses) and convex hull (blackobserved entropy. [8, 9]

solid line) obtained from eq. (1).

freeenergies(closedcircles,

References[1] J. Haruyama, T. Ikeshoji, and M. Otani, J.

[6] H. Fujimoto et al., The 59th Battery

Phys. Chem. C 122, 9804 (2018).

Symposium, 2E16 (2018).

[2] J. Haruyama, T. Ikeshoji, and M. Otani,[7] P. Giannozzi et al., J. Phys.: Condens.

Phys. Rev. Mater. 2, 095801 (2018).

Matter 21, 395502 (2009); ibid 29, 465901[3] M. Otani and O. Sugino, Phys. Rev. B 73,(2017).

115407 (2006).

[8] R. Yazami and Y. Reynier, J. Power Sources[4] S. Nishihara and M. Otani, Phys. Rev. B 96,

153, 312 (2006).

115429 (2017).

[9] J. Haruyama, S. Takagi, K. Shimoda, I.

[5] S. Takagi et al., The 60th Battery

Watanabe, K. Sodeyama, T. Ikeshoji, and M.

Symposium, 1B20 (2019).

Otani, in preparation.

72

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study of ferromagnetism in Pt(100) thin films by firstprinciples calculation
Tatsuru Yamada1, Hiroyuki Kageshima2, and Tetsuya Sato1
1Department of Applied Physics and Physico-Informatics, Keio University, 3-14-1 Hiyoshi,
Kohoku-ku, Yokohama 223-0061, Japan
2Graduate School of Natural Science and Technology, Shimane University, 1060
Nishikawatsu-cho, Matsue 690-8504, Japan

Recently,It

wasreported

thicknessthatdependence

of

the

magnetic

appears in an oscillatory

moment of Pt. As a result of the calculations

manner in the Pt(100) thin films depending onof electronic structures for the free-standing

the film thickness[1][2]. However, few studies

Pt(100) thin films from 2 monolayers(ML)have focused in the ferromagnetism in Pt(100)up to 17 ML, it was confirmed thatthin film and the mechanism for appearance offerromagnetism appeared in an oscillatory

ferromagnetism in Pt(100) thin film remains

manner with a period of 6 ML (Fig. 1). By

unclear. In this study, we performed the first-

examining the energy band structure, we

principles calculations of freestanding Pt(100)found that the flat band near the Γ point

thin films to understand the mechanism forcomposed of 5𝑑𝑥𝑧,𝑦𝑧 orbitals overlaps withappearance of ferromagnetism in Pt(100) thin

Fermi

film. We performed first-principles calculations

appears. This flat band is the quantum wellbased on the density-functional theory with theband (Fig. 2).

ferromagnetism

energy(𝐸F)whenferromagnetism

generalized gradient approximation. Projector-

From the phase model, the period at which

Augmented Wave method was adopted as thethe quantum well band in Pt(100) thin film

pseudopotential of Pt. We used 88×88×1 koverlaps with 𝐸F is 5.7 ML[1]. This ispoints (based on Monkhorst-Pack) and aconsistent with experimental result of thecutoff energy of 36 Rydberg.

previous research[2] and calculated results. So,We

calculated

latticeconstant

that

it was concluded that oscillatory magnetic

minimizes the energy. Using the obtained

behavior in Pt(100) thin film can be explained

lattice constant, we calculated the Pt layer

by quantum well states.

73

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Fig. 2: Band structure of 3ML Pt(100) thin film.

Fig. 1: Magnetic moment per Pt atom inPt(100) thin films (circles) and total energy
differences between the paramagnetic (para)

References

and ferromagnetic (ferro) states (diamonds).

[1] A. M. N. Niklasson et al.: Phys. Rev. B 75,
172402 (2007).
[2] K. Ochiai et al.: JPS2019, Gifu, 10aPS27(2019).

74

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Born-Oppenheimer MD Simulations of Excited States for
Firefly Oxyluciferin Anions in Aqueous Solutions
Yoshifumi NOGUCHI
Department of Applied Chemistry and Biochemical Engineering, Graduate School ofEngineering, Shizuoka University, Johoku 3-5-1, Hamamatsu, Shizuoka 432-8561, Japan
statesFirefly oxyluciferin anion, known as the

BOMD

simulations

showedthatlight emitter in firefly bioluminescence process,phenolate-keto was the most stable isomers,has garnered significant attention because

whose energy was 0.38 eV and 0.57 eV lower

obtaining a deep insight on oxyluciferin anions

than that of the phenolate-enol and phenol-

could be an essential first step towards

enolate, respectively [3]. We analyzed theunderstanding the mechanism of the fireflytrajectories in detail and elucidated that thebioluminescence process. However, majority ofstabilizing mechanism of the oxyluciferinstabilizingofanions in the explicit aqueous solutions is theexternaldifference between at the ground and excitedoxyluciferin

andopticalanionsproperties

in

the

states.

environments are still a mystery.

Cumulative average for BLYP total energy (eV)We have performed first-principles BornOppenheimer molecular dynamics simulations(BOMD) for three possible isomers of firefly
oxyluciferin anions (phenolate-keto, phenolateenol, and phenol-enolate) surrounded by 64
explicit water molecules and elucidated theirstabilizing mechanism in the aqueous solutions-33272.3
HO-33272.4

ENOLATE

S

N

N

S

O-

-33272.5

0.19 eV-33272.6-33272.7-33272.8-O

ENOL-33272.9

S

N

N

S

OH

0.38 eV-33273.0-33273.1-O-33273.2-33273.3

1660

KETO
1680

1700

S

N

N

S

1720

O

1740

Time (ps)

1760

1780

1800

in the excited states. To attain the equilibrium

Fig. 1. Cumulative average for BLYP

conditions, we had to run BOMD up to 1.8 ns

total energies.

(corresponding to 3.7 million MD steps).

References

Figure 1 shows the cumulative average for[1] Y. Noguchi, et al., J. Phys. Chem. B, 120,

BLYP total energies simulated for phenolate-8776 (2016).

keto,[2] Y. Noguchi, et al., J. Chem. Theor. Comput.,

phenolate-enol,

andphenol-enolate.

Unlike similar level BOMD simulations in the15, 5474 (2019).

ground state in which the phenolate-enol form

[3] Y. Noguchi, et al., J. Chem. Phys., 153,

was the most stable [1,2], the current excited

201103 (2020).

75

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analysis of Thermoelectric Properties of Clathrate Compounds with Ab
Initio Calculations
Masato OHNISHI
Department of Mechanical Engineering,
The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656

compoundsarealuminumcandidates

forenhance

Clathrate
promising

substitutions

canthermoelectric

thermoelectric materials in terms of

performancethe “electron-crystal phonon-glass”

clathrates, type-I Ba8Ga16Si30 (Fig.

concept. Clathrate compounds are

1(a)).

composedatoms

thermoelectric figure of merits (ZT)

encapsulated in cagelike structures.

with those obtained in experiment,

It is expected that electrons can

we concluded that (a) aluminumsmoothly transport in the frame

additive enhances ZT with lowering

work while phonons are scattereddopingby guest atoms. Particularly, insuppression of doping level can

type-I clathrate compounds, guest

enhance

atoms

investigate

ofvibrate

guest

in

a

strongofsilicon-based

Comparinglevel

calculated

and

ZT

(b)

furthersignificantly.

To

thermoelectricanharmonic potential because they

properties, we obtained possible

are composed of a Weaire-Phelan

structures at finite temperatures

structure, which divides a spacewith using a cluster expansion andwith the maximum volume with theMontesame cross-sectional area. While off-

thermoelectric

properties

center clathrates such as type-I

averageddifferent

Ba8Ga16Sn30, in which guest atoms

structures. As shown in Fig. 1(b),vibrate in a double-well anharmonicformationenergies

potential,

thermalstructurescansilicon-based

predicted

withclathrates are preferable for actual

expansionuse in terms of the material cost.

properties of the clathrates wereconductivity,

have

low

In this study, we show thatCarlocalculated

76

methods

for

of

be

using

and
were

possiblearbitraryaccuratelythemethod.
with[1]cluster
Phononaself-

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

consistentphonon

(SCP)

based

on

first-principles

calculations[2].

theoryconcentration, as shown in Fig. 1(c).

WhileReferences

carrier[1] M. Ångqvist, P. Erhart et al., Chem.

concentrations are around 1022 cm-3

Mater. 29, 7554 (2017) and 28, 6877

for Si-based clathrates, our analysis(2016).

shows[2] Tadano et al. Phys. Rev. Lett 120,experimentally-observed

that

thermoelectric

properties of the clathrate can be105901 (2018).

improved by suppressing carrier

Fig. 1. Enhancement of thermoelectric properties of Si-based Clathrate. (a)Crystal structure of Ba8Ga16Si30. (b) Prediction of formation energy with acluster expansion method. (c) Dimensionless thermoelectric figure-of-merit(ZT) of the clathrate at different carrier concentrations.

77

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles calculation for low-temperature oxygen
transfer in metal oxide
Akira Yoko
WPI-Advanced Institute for Materials Research,
Tohoku University, Katahira 2-1-1, Sendai, Miyagi 980-8577
relaxed within a cubic cell, and the lattice

We have studied oxygen storage and releasematerials experimentally and computationally.

parameters of perfect CeO2 and Cr-doped CeO2

This term CeO2 and Cr-doped CeO2 were

were obtained using the Murnaghan equation ofstudied with first-principles calculations.

state. Forces were converged to 0.01 eV/Å inPlane-wave basis density functional theory

all calculations.

(DFT) calculations were conducted to elucidate

Nudged elastic band (NEB) calculations

the Cr doping effects on CeO2 structure using

were performed to obtain diffusion paths andthe VASP code [1,2]. The generalized gradientbarrier energies with seven replicas, including

approximation (GGA) proposed by Perdew,

five nudged intermediate images. The spring

Burke, and Ernzerhof (PBE) [3] was employed

constant linking images was 5.0 eV/Å and theas the exchange correlation energy functional.

conversion criteria were defined that resultant

The DFT+U method introduced by Dudarev etforces, including the spring forces, were lessal. [4] was used to treat the electron

than 0.01 eV/ Å. The energy barrier was

localization. The parameter, U-J was set as 3.5

obtained by applying the climbing imageeV for Cr3d, 5.0 eV for Ce4f, and 5.5 eV for

algorithm [7], which allowed the determination

O2p states, respectively, based on the previousof the saddle point at the transition state.

studies of Cr2O3 and CeO2 [5,6]. The valence

To elucidate the mobility of oxygen for pureconfigurations of the pseudopotentials were

and Cr-doped CeO2, nudged elastic band

3s23p63d54s1 for Cr, 5s25p64f15d16s2 for Ce andcalculation was conducted. Figures 1a and 1b

2s22p4 for O. The energy cutoff for the plane-show the diffusion path of an oxygen atom towave basis was set at 500 eV for all thethe vacancy site and migration barrier.

calculations and provided the convergence ofCompared to pure CeO2 (0.41 eV), a muchthe total energy in the unit cell of CeO2 (12lower migration barrier was observed in Cr-

atoms). Defect calculations were conducted

doped CeO2 (0.28 eV). In the case of the pureusing the 2 × 2 × 2 extension (96 atoms) ofCeO2, electron polaron (Ce3+) exists at the next

CeO2 unit cell with Monkhorst–Pack k-pointnearest neighbor of the oxygen vacancy, andmesh of 4 × 4 × 4. Atomic positions werediffusion of the polaron accompanied with78

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

oxygen diffusion was observed; Rapid polarondiffusion in reduced CeO2 has been discussed

References

previously [11]. As a result of the NEB[1] Kresse, G.; Furthmuller, J., Phys. Rev. B

calculation, diffusion constants at 400 °C are

1996, 54 (16), 11169-11186.

5×10-11 m2 s-1 for CeO2 and 5×10-10 m2 s-1 for[2] Kresse, G.; Joubert, D., Phys. Rev. B 1999,

Cr-doped CeO2. The high diffusivity of oxygen

59 (3), 1758-1775.G. [3] Perdew, J. P.; Burke,

in Cr-doped CeO2 is one of the origins to cause

K.; Ernzerhof, M., Phys Rev Lett 1996, 77 (18),high oxygen mobility at low temperature

3865-3868.

observed in the experiments. This result was[4] Dudarev, S. L.; Botton, G. A.; Savrasov, S.

published in ref. [12].

Y.; Humphreys, C. J.; Sutton, A. P., Phys. Rev.

(A)

B 1998, 57 (3), 1505-1509.
[5] Wang, J.; Gong, X.-Q., Appl. Surf. Sci.
2018, 428, 377-384.
[6] Keating, P. R. L.; Scanlon, D. O.; Morgan,
B. J.; Galea, N. M.; Watson, G. W., J. Phys.
Chem. C 2012, 116, 2443-2452.
[7] Henkelman, G.; Uberuaga, B.P.; Jonsson,
H., J. Chem. Phys. 2000, 113 (22), 9901-9904.
[8] Wang, B.; Xi, X.; Cormack, A. N., Chem.
Mater. 2014, 26, 3687-3692.

(B)[9] M.V. Ganduglia-Pirovano, J.L. Da Silva, J.
Sauer, Phys. Rev. Lett., 102 (2009), Article
026101[10] Yu, M.; Trinkle, D. R., J. Chem. Phys.
2011, 134, 064111.
[11] Nakayama, M.; Ohshima, H.; Nogami, M.;
Martin, M., Phys. Chem. Chem. Phys., 2012,
Figure 1 Energy barrier of oxygen atom

14, 6079-6084.

diffusion to a vacancy site obtained by NEB[12] X. Hao, A. Yoko, K. Inoue, Y. Xu, M.

calculation for (A) CeO2 and (B) Cr-doped CeO2.

Saito, C. Chen, G. Seong, T. Tomai, S. Takami,

Light green, sky blue, dark blue, red, and

A.L. Shluger, B. Xu, T. Adschiri, Y. Ikuhara,,orange balls represent Ce4+ ion, Ce3+ ion, Cr, O,

Acta Materialia, 203, 116473 (2021)

and diffusing oxygen, respectively.

79

Activity Report 2020 / 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

reaction activities. We found that the stableand diffusion properties on light-element

Cu atoms embedded in graphene show higher

element doped graphene with the aid of theactivity than unstable Cu clusters on graphene.

first-principles calculation based on the

We investigated the oxygen absorption

density functional theory (DFT). Besides, weproperties of partially substituted Ca2AlMnO5.

investigated the oxygen absorption properties

We revealed that rotation of coordinationof heteroatom-substituted brownmillerite-type

polyhedra of cations releases the distortionoxides.

induced by heteroatom doping. In addition,

At first, we investigated the stabilities of

we investigated the effects of Pt addition on

Cu atoms embedded in light-element doped

oxygen storage properties.

graphene. We considered embedded Cu atoms

We also studied the adsorption properties

coordinated with various substituted dopants.

and catalytic activities [3] and chemical

We performed the total energy and electronicbonding states [4] of Pt sub-nano clusters on

structure calculations using The Vienna Ab

light-element element doped graphene.

initioReferences

simulation

package(VASP).

We

installed a parallelized VASP with Intel® MPI[1] J. S. Yoo, F. A.-Pedersen, J. K. Nørskov, F.

Library and Intel® Math Kernel Library. We

Studt, ACS Catal. 4 (2014) 1226.

revealed that the stabilities of Cu atoms[2] A. Sato, G. Saito, K. Abe, Y. Kunisada, N.

embedded in light-element doped graphene

Sakaguchi, T. Akiyama, T. Nomura, J.

strongly depend on the coordinated atoms. In

Alloys Compd. 851 (2021) 156817.

the cases of large coordinated atoms, The Cu[3] S. Hasegawa, Y. Kunisada, N. Sakaguchi,

atoms protrude from graphene basal planes.

Vac. Surf. Sci. 63 (2020) 413.

We also investigated the catalytic activity[4] R. Sugimoto, Y. Segawa, A. Suzuta, Y.

using a theoretical volcano plot reported inKunisada, T. Uchida, K. Yamazaki, K.

the previous study.[1] From the adsorption

Gohara, J. Phys. Chem. C 125 (2021)

energy of intermediates, we estimated the

2900.

80

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio analysis on the stability of magnetic ternary
alloysYasutomi TATETSU
Meio University, Biimata, Nago, Okinawa 905-8585
Adding a small amount of third elements in

For In-doped Fe–Pd ternary alloys, the In

binary systems not only stabilizes system but

sites were chosen by replacing Fe or Pd sites

also changes these physical properties. Recently,

with a special-quasirandom-structure method

a new ternary alloy was discovered by

implemented in the Alloy Theoretic Automate

introducing a third element of In into L12-FePd3

Toolkit [3]. The figure illustrates the formation

by Teranishi’s group in Kyoto University [1].

energies of L12-(Fe, In)Pd3 and Z3-Fe(Pd, In)3Other interesting example is Nd–Fe amorphouswhen the number of In in a system takes from 1

phases which can be crystalized after adding

to 6. By comparing these formation energies,

Ga in Nd–Fe–B sintered magnets. Although the

Z3-Fe(Pd, In)3 can be more stable than L12-(Fe,physical aspects of these added elements areIn)Pd3 only in a narrow range of the In content.

unclear and cannot be understood deeply onlyThis tendency can be seen in the experimental

through experiments.

results from XRD, EXAFS, and STEM-EDS

In this study, we conducted theoreticalanalyses.

analyses for the stability of an In-doped novel

In Ga-doped Nd–Fe ternary alloys, we

Fe–Pd and Ga-dope Nd–Fe ternary alloys using

found that Ga is a key not only to stabilizing

OpenMX. The model structures for thethe fluorite-type crystal structure but also to

calculations were based on the chemical

suppressing its Curie temperature, which might

composition ratio obtained from experiments.

be one of the reasons to explain why Ga-added
Nd–Fe–B0

Pd site in Z3
Fe site in L12

magnets

have

high

coercivity [4].

References−0.005
Eform (eV/atom)

sintered[1] K. Matsumoto, R. Sato, Y. Tatetsu, T.
−0.01

Teranishi, et al., submitted.
[2] http://www.openmx-square.org−0.015[3] A. van de Walle et al., Calphad Journal 42,
−0.02

1

2

3

4

5

13 (2013).

6

The number of In in a system

Figure: Formation energies for L12-(Fe, In)Pd3[4] Yuta Ainai et al., Jpn. J. Appl. Phys., 59,

and Z3-Fe(Pd, In)3.

06094 (2020)

81

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo!"#$%&'%(')%*+",-,$%&-.'*-,/0$-.'#)$/&)/'-&1'1-,-210$3/&'#)$/&)/'4$,5'*-##$3/.6'+-0-../.')%*+",-,$%&''!"#$%&'%()*&!!"#$%&'(#)'!*+!,$$-.#/!0%'1#(%'.23!%)/!4153.236!7*''*&.!8).9#&3.'56!
:;<=<!>*5%(%;0.)%(.6!7*''*&.!?@=;@AA=6!B%$%)C!"#$ %&#'#()$ %&*+#,)$ -.'$ ,.&&/#0$ *1)$ 2*&$&#N1/&#0$ 2*&$ )"#$ 0.).$ .(.4A'/'$ ;A$ ZL<S!$ .(0$'#3#&.4$ )*%/,'$ /($ )"#$ 21'/*($ *2$ ,*5%1).)/*(.4$-#$ 1'#0$ )"#$ '/514.)*&$ %&*J&.5$ ['/56)&"#%065.)#&/.4$',/#(,#$.(0$0.).60&/3#($',/#(,#$*($)"#$&"##0\$*&/J/(.44A$0#3#4*%#0$;A$!:$@.(.0.:$O]?QR:$

7889$ '1%#&,*5%1)#&:$ !"#$ 5./($ ,*44.;*&.)*&'$.&#$7:$<*,"/=1>/?$!:$@A*0*$BCDC67<88689EF?$!:$ @.(.0.$ B!*"*>1$ GF?$ C:$ @1>1'"/5.$ BG!*>A*F?$ C:$ H*'"/5/?$ H:$ <*)*A.5.$ B7889F?$ !:$E1+/).$B7<8F?$H:$H.5.5*)*$BGDIF?$H:$</A.).>#
BG:$!*>A*F:$!"#$ 2/&')$ )*%/,$ /'$ )"#$ 0#3#4*%5#()$ *2$ )"#$
0.).$ .(.4A'/'$ '*2)-.&#$ *2$ )*).46&#24#,)/*($ "/J"6#(#&JA$%*'/)&*($0/22&.,)/*($B!K@D9LF?$.$(*3#4$

Fig.1 (a) Schematic figure of TRHEPD
experiment. (b) The side view of 8/!T"U#$V$
Q@68/I$BWWWPF6B!X"!XF$KXW#B8/TUF$'1&2.,#$')&1,)1&#:$B,F$!K@D9L$0.).$.(.4A'/'$*2$)"#$8/TU$'1&2.,#$')&1,)1&#$OXR:$!"#$!6,**&0/(.)#$*2$)"#$'1&2.,#$.)*5$4.A#&'$/'$0#(*)#0$.'$!! " !" " # # # " !# #$!"#$,*4*&6,*0#0$/'*3.41#$%4*)'$*2$)"#$K62.,)*&?$)"#$&#'/01.4$21(,)/*($;#)-##($)"#$#M%#&/5#().4$.(0$,.4,14.)#0$0.).?$*($)"#$
4*,.4$J&/0$*2$)"#$!! $ % !" $%4.(#$$OXR:#M%#&/5#().4$ )#,"(/N1#$ 2*&$ '1&2.,#$ ')&1,)1&#$
0#)#&5/(.)/*($ OP6QR:$ DM%#&/5#()'$ .&#$ ;#/(J$,*(01,)#0$ /()#('/3#4A$ .)$ )"#$ 84*-$ 9*'/)&*($
E.,/4/)A?$7(')/)1)#$*2$<.)#&/.4'$8)&1,)1&#$8,/#(,#?$@/J"$

D(#&JA$S,,#4#&.)*&$

K#'#.&,"$

T&J.(/=.)/*(:$ E/J1&#$ P$ '"*-'$ )"#$ ')&1,)1&#$
0#)#&5/(.)/*($*2$)"#$8/!T"U#$V$Q@68/I$BWWWPF6!"#$'#,*(0$)*%/,$/'$)"#$5#)"*0$.(0$B!X"!XF$KXW#B8/TUF$'1&2.,#$')&1,)1&#$OXR:$.%%4/,.)/*($ *2$ 4.&J#6',.4#$ #4#,)&*(/,$ ')&1,)1&#$!"#$ '*2)-.&#$ 0#3#4*%5#()$ .,)/3/)A$ -.'$,.4,14.)/*('$2*&$*&J.(/,$.(0$*)"#&$5.)#&/.4'$O_6%&*5*)#0$ )*$ 9&*+#,)$ 2*&$ S03.(,#5#()$ *2$

PWR:$ !"#$ ')10A$ -.'$ ,.&&/#0$ *1)$ ;A$ *1&$ *&/J/(.4$8*2)-.&#$G'.;/4/)A$/($<.)#&/.4'$8,/#(,#$/($7889$,*0#$ D`8D8$ B$ "))%YVV---:#4'#':+%V$ F?$ .($ *&0#&6

B$ "))%'YVV---:%.'15':/''%:16)*>A*:.,:+%$ F$ /($!$ #4#,)&*(/,$ ').)#$ ,.4,14.)/*($ ,*0#$ -/)"$ .($ "#$EHZWZW$.(0$EHZWZP:$T1&$'*2)-.&#$-.'$,.44#0$%&%'%(6;.'#0$ )/J")6;/(0/(J$ 5#)"*0$ .(0$ .$[ZL<S!\$.(0$-.'$%1;4/'"#0$.'$.($*%#(6'*1&,#$

2&.J5#()65*4#,14.&6*&;/).46;.'#0$ 5#)"*0:$ 7($'*2)-.&#$ O]?^R:$ S$ !K@D9L$ '/514.)*&$ -.'$

82

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

particular,anexcited-state

theorywasconstructedfordisordered

Pentacene/C60[7]Computational

conductivity

study

properties

forelectricaloforganic

The third topic is thesemiconducting polymers and metal complex-

development of several fundamental numericalhost systems, M. Ishida, M. Arita, S. Nishino, T.

algorithms [11-12].

Hoshi, HPCI Research Report, to appear.

Interfaces [9-10].

[8] Recent progress in large-scale electronic

References

state calculations and data-driven sciences, T.

[1] Development of data-analysis software for

Hoshi, S. Ito in Handbook of Silicon Basedtotal-reflection high-energy positron diffraction

MEMS Materials and Technologies 3rd Ed.,

(TRHEPD), K. Tanaka, T. Hoshi, I. Mochizuki,

Elsevier, 2020.

T. Hanada, A. Ichimiya, T. Hyodo, Acta. Phys.

[9] Revisiting the Charge-Transfer States at

Pol. A 137, 188-192 (2020).

Pentacene/C60 Interfaces with the GW/Bethe–[2] Two-stage data-analysis method for total-

Salpeter Equation Approach, T. Fujita, Y.

reflection

Noguchi and T. Hoshi, Materials 13, 2728

high-energy

positrondiffraction(TRHEPD), K. Tanaka, I. Mochizuki, T.

(2020).

Hanada, A. Ichimiya, T. Hyodo, T. Hoshi, JJAP[10] FMO-based excited state dynamics inConf.

molecular aggregates, T. Fujita and T. Hoshi, inSeries,inpress;

Preprint:

https://arxiv.org/abs/2002.12165

Recent advances of the fragment molecular[3] Data-driven sensitivity analysis in a total-

orbital method Subtitle: Enhanced performancereflection

high-energy

positrondiffraction

and applicability, ed. Y. Mochizuki, S. Tanaka,(TRHEPD) experiment of the Si4O5N3 / 6H-SiC

and K. Fukuzawa, Springer, 2021.

(0001)-(√3×√3) R30° , T. Hoshi, D. Sakata,[11] Kω - Open-source library for the shifted

S. Oie, I. Mochizuki, S. Tanaka, T. Hyodo, K.

Krylov subspace method of the form (𝑧𝐼 −Hukushima,𝐻)𝑥 = 𝑏, T. Hoshi, M. Kawamura, K. Yoshimi,

Submitted;

Preprint:

https://arxiv.org/abs/2103.04875

Y. Motoyama, T. Misawa, Y. Yamaji, S. Todo,[4] T. Hoshi, Y. Motoyama, T. Hanada, Y.

N. Kawashima, T. Sogabe, Comp. Phys. Comm.

Konishi and K. Yoshimi, poster presentation,

258, 107536 (2021).

CCMS Workshop of the data science in[12]material science, online, 22-24. Feb. (2021).

integrator MB4 and its application to quantum-[5]

mechanical wavepacket dynamics, T. Sakai, S.

https://www.pasums.issp.u-

tokyo.ac.jp/2DMAT;

A

parallelizableenergy-preserving

Kudo, H. Imachi, Y. Miyatake, T. Hoshi, Y.

https://github.com/issp-

center-dev/2DMAT

Yamamoto, Japan J. Indust. Appl. Math. 38,[6] https://github.com/sim-trhepd-rheed/

105 (2020).

83

Activity Report 2020 / 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 catalytic properties ofactivity of Pt1 more strongly depends on thePt sub-nano clusters on light-element doped

light-element dopants in graphene lattice thangraphene and hydrogen dissolution andthose of Pt2 and Pt3. Therefore, Pt single

diffusion properties in the interfaces ofatoms on light-element doped grapheneceramic materials, with the aid of the first-

support is a promising candidate for a newprinciples calculation based on the density

catalyst which is better than the current fuelfunctional theory (DFT).

cell catalyst, i.e., bulk Pt catalyst.

At first, we investigated the adsorption

We also investigated the chemical bonding

and catalytic properties of Pt single atoms andbetween N-doped graphene and Pt single

Pt sub-nano clusters on light-element doped

atoms

graphene. We performed the total energy andtransmission electron microscopy combining

electronic structure calculations using The

with electron energy loss spectroscopy, andVienna Ab initio simulation package (VASP).

the

We installed a parallelized VASP with Intel®

properties in the interfaces of TiN

MPI Library and Intel® Math Kernel Library.

residual impurity gasses.

In this study, we focused on oxygen reduction

References

reactions (ORR). In order to evaluate the[1] J. K. Nørskov, J. Rossmeisl, A. Logadottir,

catalytic properties, we calculated the energy

L. Lindqvist, J. R. Kitchin, T. Bligaard,

diagrams of whole ORR paths. We also madeH. Jónsson, J. Phys. Chem. B, 108

a volcano-plot to show relationship between(2004) 17886.

the adsorption energy of catalytic activities
andintermediate

speciesofusinghydrogenDFT

calculations

dissolution

and

and

diffusion
with[2] S. Hasegawa, Y. Kunisada, N. Sakaguchi,

chemicalVac. Surf. Sci. 63 (2020) 413.

reactions.[1] We found that ORR activity of[3] R. Sugimoto, Y. Segawa, A. Suzuta, Y.

Pt1 is higher than those of Pt2 and Pt3. From

Kunisada, T. Uchida, K. Yamazaki, K.

the viewpoint of a support effect caused byGohara, J. Phys. Chem. C 125 (2021)

light-element doped graphene, the catalytic

2900.

84

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study on physics of gap-state control
at metal/semiconductor interfaces: II & III
Takashi NAKAYAMA

Department of Physics, Chiba University
1-33 Yayoi, Inage, Chiba 263-8522
Due to the break of atomic bonds and the lackof translational symmetry, gap states appear insemiconductor layers around metal/semiconductor
interfaces, which have the energy position in theband gap and are localized around the interface.
These states induce the electron transfer between
metal and semiconductor layers and determine avariety of physical properties at the interface, suchas Schottky barrier (SB) and carrier transport.
However, it is still unclear how to control thesegap states. In this works, we studied the SB andtunneling current at various interfaces and clarify
the origins of gap-state generation/annihilation anddeformation using the first- principles calculations.
First, we consider metal/Ge interfaces, whereFermi energies of most of simple metals arelocated around the valence-band top of Ge notdepending on the kinds of metals. This is called the
Fermi-level (FL) pinning and interrupts desirable
low-resistive metal/n-Ge contacts. Although the
breakdown of FL pinning was recently observed at
the Bi/Ge(001) interface, its origin has not beenclarified. To simulate the interfaces, we adopt (2×2)(Bi, Al)/Ge(001) repeated-slab models with various
interface structures and calculate their SBs using
local potential profiles.
Figure 1 shows calculated SBs for hole carriers
ate various interfaces. The SBs at (b) disordered
Bi/Ge and (c) plain Al/Ge interfaces are around
0.0eV corresponding to the FL pinning, while the
SB at (a) plain Bi/Ge interface has a large value
around above 0.3eV, which is in good agreementwith experiments. The origin of such SB variationis understood by observing the projected densitiesof states (PDOS) of interface Ge atoms, which are
shown in Fig.2. For (b) and (c) interfaces, theFig.1. Left: calculated Schottky barriers for holecarriers at various (Bi, Al)/Ge interfaces. Right:
schematic pictures of interface structures. (a):abrupt plain Bi/Ge interface, (b): disordered Bi/Ge
interface, and (c): plain Al/Ge interface.

continuous PDOS, thus the gap states, appear
around 0.0eV due to the orbital hybridization
between metal and Ge atoms, which induces theelectron transfer from metal to Ge and realizes theFL pinning. On the other hand, we can see thesuppression of gap states in the PDOS of interface
Ge for the (a) interface, which realizes the FLdepinning. This suppression occurs due to the weakcontact of Bi and Ge layers, which is caused by thelattice mismatch originating from the large atomic
radius of Bi and produces the Ge-Ge dimer bonds
at the interface as shown in the right of Fig. 1. In
this way, the interface Ge-Ge dimer bonds
annihilates the gap states in interface Ge layers andproduces the large change of the SB values.
Next, we consider how the gap states change inelectric fields. We consider the tunneling current at
indirect-band-gap Si and GaP, and direct-band-gap
GaAs and InP p/n junctions, in the cases without

85

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Fig.2. Calculated projected densities of statesof interface Ge atoms around (a) plain Bi/Ge,(b) disordered Bi/Ge, and (c) plain Al/Ge
interfaces, which respectively correspond tointerfaces shown in Fig.1. Orange boxes
indicate the band-gap region of Ge.

Fig.4. Calculated transmission spectra ofelectrons and local density of N-atom dopant
states at the Si p/n junction ((a) and (b)), and
the GaAs p/n junction ((c) and (d)). The casesof junctions without dopants are also shown by
red lines.

such resonance remarkably increases the tunnelingprobability across the junction as shown in Fig.4(a).
On the other hand, in the cases of direct band-gap
systems, as seen in Fig.3(b), there is no increase in
the current by the dopants. This is because thedopant gap state is strongly localized as in Fig.4(d)and the increase of tunneling is small as in Fig.4(c).
By analyzing electronic structures, we found thatthe difference in the dopant effects on tunnelingcurrents between indirect and direct band-gap
systems reflects the characters of conduction-bandstates in these systems.
All these calculations were performed using thexTAPP, VASP, and our original pspwf codes. In
order to realize the calculations for the presentinterface systems, because the system is made of alarge number of atoms (500-2000 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 onlyby the present ISSP supercomputing systems.

Fig.3. Calculated tunneling currents at (a)indirect-band-gap Si and GaP, and (b)direct-band-gap GaAs and InP p/n junctions,as a function of electric field. The cases
without and with N-atom dopants areshown.

and with N-atom dopants. Figures 3(a) and 3(b)show calculated currents for these interfaces as afunction of applied electric field. It is clearly seenthat the current is much larger for the latter
junctions, which is because the latter system havedirect band gap and have larger interband tunnelingtransitions.
When N-atom dopants are embedded in p/njunctions, the current is markedly enhanced in thecases of indirect band-gap systems, i.e., Si and GaP.
This enhancement occurs because the dopant gap
state produces the resonance states with theconduction-band states of host Si layers around thejunction in electric field as shown in Fig.4(b), and86

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles Calculations on
Magnetism in 2D Magnetic Materials
Kunihiko Yamauchi
Institute of Scientific and Industrial Research (ISIR-SANKEN), Osaka University, 8-1
Mihogaoka, Ibaraki, Osaka 567-0047
We have studied the magnetism in 2D

the ISSP ohtaka supercomputer. VI3 is a Mott

magnetic materials and discussed our current

insulator with an energy band gap is 0.34 eV. In

understanding of the mechanisms using the first-

VI3,

principles density functional theory (DFT)with D3d point group, the t2g orbital state is split

calculations.

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

under

the

trigonal

crystalfield

First, we systematically investigated thean important role in inter-layer magnetic

magnetocrystalline anisotropy energy (MAE) of

exchange interaction in a bilayer structure. By

the Co-based transition-metal thin films using

using Wannier90 code that is interfaced with the

DFT

the

VASP code, we estimated the hopping integral

ISSP seikirei supercomputer. The results show

and discussed the inter-layer magnetic exchangethat the large perpendicular MAE can beinteraction

achieved by tuning atomic-layer stacking in Ni-

mechanism. In the bilayer VI3 case, we studied

Co thin film. The MAE is decomposed into

two structures corresponding to R3 and C2/c

single-layerinter-layer

phases in bulk VI3, namely AB and AB’ stacking.

contributions to reveal the fact that not only the

The application of electric field enables toon-site SOC of 3d elements but also the strong

switch the magnetic ordering from inter-layer

hybridization between these elements play an

AFM to FM in AB’ stacking. This finding may

important role to determine the MAE. The small

pave a way to the spintronics application witheffect of electric fields on the magnetocrystalline

2D materials [2].

anisotropy also has been found in Ni-Co thin

References

film, making this system becomes the potential[1] T. P. T. Nguyen, K. Yamauchi, K. Nakamura,for future spintronics applications [1].

T. Oguchi, Journal of the Physical Society of

HiLAPWcode

contributions

and

at

Secondly, we investigated the magnetic

based

on

the

virtual-hopping

Japan, 89, 114710 (2020).

stability in 2D magnetic material VI3 making a[2] T. P. T. Nguyen, K. Yamauchi, T. Oguchi, D.

comparison with CrI3 using the VASP code at

Amoroso, S. Picozzi, arXiv:2102.04173 (2021).

87

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Band structure calculation based on the group theory

Mineo SAITO
Institute of Science and Technology, Kanazawa University
Kakuma, Kanazawa, 920-1192 Japan

In the field of spintronics, the spin-

operation

orbit coupling (SOC) is considered togenerate new functions. One of the mostCm , respectively. kjisimportant phenomena is concerning

the Bloch function for the band
index j and the wavenumber k .

topological insulators.

emphasize

The wavefunction (does not ) belongthat the group theoretical analysis isto the IR of  when Q  = 1 (Q  = 0) .

necessary to deeply understand the SOC

In this report, we focus on our resultsWe

effect on electronic structures but theon group-IV two dimensional materials.

analysis has been insufficient so far. We

In the case of graphene, the Dirac

have developed a method to identify

cone is found to belong to the two-

irreducible representations (IR) for thedimensional IR of E” in the D3h

SOC bands which are obtained by usinggroup. The SOC is found to split thefirst-principles

base

doubly degenerated level into E1/2

calculations. The identification can be

and E3/2 levels. The former level isdone by using computers and thus mis-found to be higher than the latter

identification can be avoided.

level and we clarify the reason for

plane

wave

The IR of the band having the q-

this energetical order by using adegeneracy is determined by using thetight binding model. We evaluate

following expression：

thetopologicalconfirmQ =1 p + q −1 ljj
    (Cm )*  k | Cm | k 
l j = p m=1

invariantthat the values for bothbuckled and non-buckled structuresare 1, suggesting the possibility of
topological insulators.

Where l and (C m )andare theorder of the k group and thecharacter for the m − th symmetry

88

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Effects of solvents on properties of artificial-retina molecule:
ab initio molecular dynamics simulations
Satoshi OHMURA
Research Center for Condensed Matter Physics / Department of Environmental and Civil
Engineering
Hiroshima Institute of Technology, Saeki-ku, Hiroshima, 731-5143
Molecular dyes are attractive great attention

peak at visible light region. However, the excited

because of their application for various opticalcharge dynamics after light absorption isdevices such as solar cell and artificial retina. To

influenced a great deal by H2O. Without H2O,

improve functionality of the dye molecule, it is

the generated hole by light-absorption in NK-

used to control the band gap. Therefore,

5962 transfers to counter-ion cite at less than 100

theoretical studies based on the density

fs. On the other hand, in the case of the system

functional theory tried to understand thewith H2O, the hole stays in NK-5962 site. Our

structural and photoelectrical properties such as

simulation clarified that these effects areabsorption and emission properties in the gas

attributed to interaction between H2O andphase. However, the working conditions of suchcounterion of NK5962. In addition to retina

dye molecules in nature and in the industrial

molecule, we have investigated the dissociation

applications entail their solvation. We havemechanisms from highly charged bromophenol

systematically investigated the effects of solvent,(C6H5OHBr)n+ (n≤10) by ab initio MD

H2O,

and

simulations [1]. The charge state dependence ofchlorobenzene on light-absorption properties indissociation mechanisms is observed by thisa photoelectric dye (NK-5962) which is better

simulation.

candidate for retinal prostheses by means of ab

intramolecular charge transfer time by using

initioTo

nonadiabatic quantum-mechanical molecular-

calculate absorption spectra, we adopted the

dynamics with surface hopping approach. It is

Time-Dependent

found that the hole transfer from the Br site toacetonitrile,

tetrahydrofuran,molecular-dynamics

simulations.

Density-Functional

linear-We

also

investigatedtheResponse Theory (TDDFLRT), proposed andthe molecular counterpart in ~5 fs.

formulated by Casida. The simulation reveals

Referencesthat all solvents slightly affect the light-[1] S. Ohmura, K. Nagaya, F. Shimojo and M

absorption spectrum but all systems has a main

Yao ; Z. Phys. Chem. 2021; 235(1–2): 169–187

89

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Structural and transport properties of multi-component liquid
Fe mixtures under high pressure
Satoshi OHMURA
Research Center for Condensed Matter Physics / Department of Environmental and Civil
Engineering
Hiroshima Institute of Technology, Saeki-ku, Hiroshima, 731-5143
We have investigated the effects of lightternary systems. For the transport properties, LEelements (LE) such as H, C, O, Si, and S on thein the ternary systems decrease electric

structural and transport properties of liquid Fe

conductivity of liquid Fe as same as binary

under high pressure by ab initio molecularsystems. The decreasing rates are between thosedynamics (MD) simulations. It is believed thatof binary systems as shown in Fig. 1.

Earth’s outer core consists of liquid iron (orliquid-nickel alloy) with LE impurities. LE havea strong influence on structural and transport
properties of liquid iron under high pressure.
However, there are still many uncertainties
regarding the influence of LE. For Fe-LE binary
systems, we clarified the structural properties
and interactions between LE atoms at coremantle boundary condition [1]. The simulations
clarify that H, C, and O are incorporated into
liquid Fe interstitially while Si and S are

Fig. 1: Change of electrical conductivity of liquid Fe-“substitutional” type impurities. Under these

H-O as a function of concentration of LE. Bluecircumstances, in this study, we have studied

circles show ternary systems. Red and green squares

structural and transport properties of liquidshow binary system.

ternary system consisting of liquid Fe and two
types of LE by using ab initio MD simulations.

References

From our simulations, it is found that Si and S[1] S. Ohmura, T. Tsuchiya and F. Shimojo:

atoms show “substitutional” behavior while H

Physica Status Solidi B, 257, 2000098 (2020)

and O atoms show “interstitial” behavior even in90

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Impact of the molecular quadrupole moment in themolecularly mixed ﬁlm of organic semiconductors
Susumu Yanagisawa
Faculty of Science, Department of Physics and Earth Sciences, University of the Ryukyus
Nishihara, Okinawa, 903-0213

The energy levels of organic semiconductors
are primarily determined by the molecular orbital energies of constituent molecules. Recent
studies have, however, shown that the energy
levels can be changed by the mixing ratio of
two molecules which have diﬀerent permanent
quadrupole moments. From the good correlation between the magnitude of the mixed ﬁlm’s
energy shift and the constituent molecules’
permanent quadrupole moment, it was notedthat the molecular quadrupole plays an important role in the energy shift.
In this study, I theoretically examined themixed ﬁlms of zinc phthalocyanine (ZnPc) andperﬂuorinated ZnPc (F16 ZnPc), which havepermanent quadrupole moments with opposite
directions. Here, as was successfully applied toorganic semiconductor thin ﬁlms[1, 2], a combination of the GW approximation suitable ingeneral to solid or bulk systems and a periodic
slab approach at the DFT-GGA level was employed. From the theoretical electronic polarization energy D and electrostatic energy S asa function of mixing ratio, ionization energies
and electron aﬃnities were estimated.
I performed ﬁrst-principles electronic structure calculations with the STATE programcode to determine the optimized geometriesof the pristine crystals as well as 1:1 mixed
thin ﬁlms of ZnPc and F16 ZnPc. To checkthe convergence of the electrostatic energy on
the number of the layers in the simulation
cell, one, two, and three monolayers (1−3 ML)
ﬁlms were modeled by periodic slabs. For

the pristine crystals, I ﬁxed the lattice constants to experimental values of the monoclinic
and triclinic forms for ZnPc and F16 ZnPc, respectively. The two stable facets are denotedby ”edge-on” and ”face-on” for each of thecrystals, depending on the orientation of themolecules at the surface (see Fig. 1). Since theexperimental lattice constants were not available for the mixed ﬁlm, those of the pristine
crystals were used for the mixed ﬁlms.
The 1 ML slabs for the pristine ZnPc and
F16 ZnPc ﬁlms consisted of 2 molecules, and 4
molecules comprised the 1 ML mixed ﬁlm in
the ratio 1:1. The vacuum layer with a thickness of 2.0 nm was inserted. I optimized thegeometric structures of the standing 1−3 MLslabs by taking into account the van der Waals
forces within PBE-D2. To describe the orientation dependence of the electrostatic interaction, I took the diﬀerence in the HOMO or the
LUMO energy of ZnPc and F16 ZnPc between
the slab and an isolated gas-phase molecule.
The electronic polarization energy was described by the many-body perturbation theory,
within the G0 W0 approximation with the GW
space-time code. The fundamental gaps wereobtained as the diﬀerence between the highest
occupied and lowest unoccupied band energies
averaged over the Brillouin zone. The numbersof cores used in the calculations were 256∼512.
The gaps were determined to be 2.26 eV
and 2.19 eV for the monoclinic ZnPc and thetriclinic F16 ZnPc bulks, respectively. For thegas phase fundamental gap, I estimated the91

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

electron aﬃnity (Ag ) and the ionization energy (Ig ) at the HSE06/spaug-cc-pVTZ levelof theory with the delta self-consistent ﬁeld
approach using Gaussian16 Revision B.01 installed in my own computer resources. I did
not use the gas-phase fundamental gap at theG0 W0 level, since the G0 W0 treatment tends
to over-screen the injected charge in gas-phasemolecules[3]. The electrostatic energy S wasestimated as the diﬀerence in HOMO/LUMO
energy between the surface slab and the gas
phase estimated with the GGA-PBE level oftheory[1, 2]. Based on the bulk fundamental
gap obtained with G0 W0 and the theoreticalgas phase ionization energy Ig and electronaﬃnity Ag , the electronic polarization D was
obtained.

Figure 1: Theoretical polarization energy D
and electrostatic energy S as a function of molar mixing ratio of F16 ZnPc in the mixed ﬁlm.
The calculated results are displayed by dashedlines and the experimental values are by solidlines.

on” conﬁgurations. The result implies the nature of the electronic polarization originatingfrom the stabilized injected charge surroundedby the induced polarization clouds inside thebulk, and thus does not depend on the molecular orientation at the surface of the ﬁlms.
On the other hand, the electrostatic energy changes more rapidly as a function of
the mixing ratio in the ”edge-on” conﬁguration than in ”face-on”. The diﬀerent trend
comes from the diﬀerent orientation of themolecules at the surfaces of the mixed thinﬁlm: in the ”edge-on” conﬁguration in which
the constituent molecules are standing on thesurface of the ﬁlm, the orientation angle isvery sensitive to the mixing ratio, while in the”face-on” conﬁguration, the molecular planes
are parallel to the ﬁlm surface and the orientation angle does not change signiﬁcantly withrespect to change in the mixing ratio. Thechange in the electrostatic energy in the molecular crystal ﬁlm comprised of molecules withappreciable quadrupole moment such as ZnPc
and F16 ZnPc may be elucidated in terms of
the electrostatics[5]. The present ﬁnding maylead to the insight into tuning of the charge injection energy levels at the surfaces of organic
semiconductors.

References[1] S. Yanagisawa: Jpn. J. Appl. Phys. 59(2020) 031002.
[2] K. Yamada, S. Yanagisawa, T. Koganezawa, K. Mase, N. Sato and H.
Yoshida: Phys. Rev. B 97 (2018) 245206.

Figure 1 displays the calculated D and S,
along with the experimental values[4]. Overall, the theoretical polarization energies arein good agreement with experiments. In caseof the electrostatic energies, the qualitative
trend depending on the F16 ZnPc amount in
the mixed ﬁlm is similar.

[3] S. Rafaely-Abramson et al., Phys. Rev. B
88 (2013) 081204(R).
[4] Y. Uemura, S. A. Abd-Rahman, S. Yanagisawa and H. Yoshida: Phys. Rev. B 102(2020) 125302.
[5] B. J. Topham and Z. G. Soos, Phys. Rev.
B 84 (2011) 165405.

It is found that the polarization energies arealmost the same in the ”edge-on” and ”face-92

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First principles exploration of the metastable phasesof hydrides and their superconductivity
Ryosuke AKASHI
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

Superhydrides that crystallize under extremely high pressure have attracted lots ofinterest since the discovery of high temperature superconductivity in solid hydrogen sulﬁde [1]. Recently, the domain of searchingfor new hydrides that possibly exhibit higher
transition temperatures is getting broadened
to ternary hydrides ABHx , resulting in the discovery of superconductivity in a C-S-H systemwith record of Tc = 286 K [2].
We conducted exploration of the novel(meta)stable hydrides and calculations of superconducting properties of them. In particular, we contributed to an international
theoretical-experimental study of a La-Y-H
ternary hydride system. In their pure binary
compositions LaHx and YHx , LaH10 and YH6have been discovered to form under pressure,both of which exhibit diﬀerent forms hydrogencage structures. The inverse, YH10 and LaH6 ,are metastable according to simulations. Interestingly, it is predicted that their mixtures
LaYH20 and LaYH12 can become stable at certain conditions, the origin of which may be asynergetic eﬀect of La and Y. This prediction
was veriﬁed by the experimentally observed
diﬀraction patterns. We calculated their possible values of Tc , using the density functional
theory for superconductors (SCDFT) [3, 4]
to compare them with the experimentally observed Tc .
Here we append the the scheme of calculating Tc on the basis of SCDFT. First, the KohnSham electronic and phononic structure calcu-

lations were performed using an open sourcecode package quantum espresso [5]. The
generalized gradient approximation [6] for theexchange-correlation potential was employed.
The optimized norm-conserving Vanderbilt
pseudopotentials [7] was used for the calculations. Next, the dielectric matrix and matrix elements of the eﬀective electron-electron
Coulomb interaction were calculated with an
in-house code. Finally using those data, thesuperconducting transition temperature was
evaluated by solving the following SCDFT gap
equation[3, 4, 8]∆nk = −Znk ∆nktanh[(β/2)En′ k′ ]1∑
∆n′ k′(. 1)
Knkn′ k′−2 n′ k′En′ k′
β denotes the inverse temperature.
The
exchange-correlation kernels K and Z, which
represents the eﬀects of the electron-phononand electron-electron interactions, are formulated in terms of the Kohn-Sham electronic
and phononic properties.
Solutions of the Kohn-Sham equation wasparallelized by MPI as implemented in pw.x
code of Quantum Espresso. The in-housecode for calculating the dielectric matrix has
been thread-parallelized by openmp. The
SCDFT gap equation was solved without parallelization since it was less time-consuming.
Calculations were mainly performed in System
B.
Various synthesis protocols were executedfor the La-Y-H samples and maximum Tc of ∼93

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 1: Superconducting transition temperature Tc calculated with the SCDFT gap equation Eq. (1). Coupling constant λ and typicalfrequency ωln ([9]) of the electron-phonon coupling spectra are also presented.
LaYH12 LaYH20
Tc (SCDF T ) (K)
191
252
λ
2.82
3.87
ωln
847
868

orbitals. This dependence results in correct reproduction of the Tc relation in those systems(Fig.1). This result has been published as apaper [11].

References[1] A. P. Drozdov, M. I. Eremets, and I. A.
Troyan, V. Ksenofontov, and S. I. Shylin,
Nature (London) 525, 73 (2015)[2] E. Snider et al., Nature (London) 586,
373 (2020).

250 K was observed. The calculated superconducting transition temperatures, especially in
LYH20 , show good agreement with this experiment (Table 1). This shows that the phononmediated pairing mechanism explains the superconductivity in the current ternary system.
This result is to be published [10].

[3] M. Lüders, et al., Phys. Rev. B 72, 024545(2005).
[4] M. A. L. Marques, et al., Phys. Rev. B
72, 024546 (2005).
[5] P. Giannozzi et al, J. Phys.: Condens. Matter 29,
465901 (2017);
http://www.quantum-espresso.org/.
[6] J. P. Perdew, K. Burke, and M. Ernzerhof,
Phys. Rev. Lett. 77, 3865 (1996).
[7] D. R. Hamann, Phys. Rev. B 88, 085117(2013); 95, 239906 (2017).
[8] R. Akashi, M. Kawamura, S. Tsuneyuki,
Y. Nomura, and R. Arita, Phys. Rev. B
91, 224513 (2015).

Figure 1: Impacts of the charge (plasmon) andspin ﬂuctuations on superconducting Tc in V,
Nb, and Al, taken from Ref. [11].
We also developed an extension of the
SCDFT scheme to include the spin ﬂuctuationeﬀect, which is a continuous subject since a
ISSP project in the ﬁscal year of 2018 [Project
ID: H30-Ca-0046]. We examined the eﬀects ofthe spin ﬂuctuation and charge ﬂuctuation on
Tc in elemental metals, V and Nb. We foundthat the spin ﬂuctuation strongly suppresses
Tc . Experimentally observed Tc is smaller in V
than in Nb, whereas the degree of the suppression eﬀect depends on the character of atomic[9] P.B. Allen and R.C. Dynes, Phys. Rev. B
12, 905 (1975)[10] D. V. Semenok et al., arXiv:2012.04787;
Mater. Today, in press.
[11] K. Tsutsumi, Y. Hizume, M. Kawamura,
R. Akashi, and S. Tsuneyuki: Phys. Rev.
B 102 (2020) 214515.

94

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Helical channel at twin boundaryof a boron-nitride atomic layer
Tatsuya ISHIKAWA, Yoshiyuki EGAMI and Hiroshi AKERADivision of Applied Physics, Faculty of Engineering, Hokkaido University
Sapporo, Hokkaido, 060-8628

We have made a first-principles calculationof the energy band of helical channels formed
along BNaL twin boundaries (Fig. 1). We impose the periodic boundary condition perpendicular to channels so that the unit cell contains two twin boundaries. We have foundthat polarized and unpolarized twin boundaries have quite different helical channel bands:
the distance in k space between helical channels belonging to K and K’ valleys is much
shorter in the polarized BCCB-NCCN arrangement [Fig. 1(b)] compared to that in the unpolarized NCB arrangement [Fig. 1(a)]. This result suggests a possibility of largely modifying
transport properties through a helical channel by changing the atomic arrangement in thevicinity of the channel.

using the facilities (system B and C) of theSupercomputer Center, the Institute for Solid
State Physics, the University of Tokyo.
!"#

!$#
!

!"#$%&'((

!
"
#

!

!"#$%&'((""#$)*$$%%%#$)*$$%#$&#$)*$$&#$"#$'#$)*$$)*+,"-*.
&%#( /01!"""$#$)*$$!'#$)*$$!"#$%&'(#)*!

!"#$%&'(#)*

Helical channels, which suffer little frombackscattering, have attracted much attention
in valleytronics and theoretically studied ingraphene on a boron nitride substrate [1, 2]
and in a boron-nitride atomic layer (BNaL)with a twin boundary [3]. We focus on the
BNaL twin boundary which can support a narrower helical channel. Twin boundaries of the
BNaL are classified into unpolarized and polarized boundaries such as shown in Fig. 1
in which carbon chains are inserted at eachtwin boundary to relax the repulsion between
cations and that between anions. In this work
we have studied differences in electronic properties of helical channels between polarized andunpolarized twin boundaries.

'#$

!'#$

!&#$)*$$!&#$!%#$)*$$!%#$

2%!"#$)*$$$#$$)*$$&#$$)!$'"#$$)!$'+#$$)!$',#$$)!$''#$$)*$$!""""""""""""!#$"""""""""""!#%"""""""""""!#&"""""""""""!#'""""""""""(#!"""""!! !"#$"%

!"#$%

!$#$

2%

!"#$

$#($
'#$$
!""""""""""""""""""""""""""""""""""""!#3""""""""""""""""""""""""""""""""""""(#!

$#$$!! !"#$"%

Figure 1: Helical channels at twin boundaries
with (a) unpolarized NCB arrangement (b) polarized BCCB-NCCN arrangement. The periodic boundary condition is imposed in the y
direction with periodicity of one unit cell. The
zero of energy is taken at the Fermi energy.

References[1] G.W. Semenoff, V. Semenoff, and Fei
Zhou: Phys. Rev. Lett. 101 (2008)
087204.
[2] C. Hu, V. Michaud-Rioux, W. Yao, and
H. Guo: Phys. Rev. Lett. 121 (2018)
186403.
[3] J. Jung, Z. Qiao, Q. Niu, and A. H. MacDonald: Nano Lett. 12 (2012) 2936.

The computation in this work has been done95Activity Report 2020 / 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

Theoretical investigations on transport
properties are important not only for the fundamental research of science but also for theapplications of electronics. We have developed
the nonequilibrium Green’s function (NEGF)
method, and the O(N) time dependent wavepacket diﬀusion (TD-WPD) method on thebasis of the density functional theory (DFT).
By using these methods, we have investigatedcharge, head and spin transport properties ofmaterials. [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.
We have applied the method to analyses ofthermoelectricity of magnetic semiconductors
CuFeS2 . The electronic transport properties,
Seebeck coeﬃcient, and the figures of merit are
estimated. We theoretically demonstrate theenhancement in the figure of merit by doping,which is in agreement with experimental work,and design doped systems for higher performance. [2]Figure 1: Seebeck coeﬃcient of CuFeS2 as afunction of the chemical potential.
namical simulation method. It is shown thatthe proposed methodology is an eﬀective theoretical design technique for eﬃciently developing new high-performance organic semiconductors. [3]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 proposeda prediction methodology to obtain chargetransport properties of organic single crystals from their structural formula using TDWPD method. We applied the method to C10 DNBDT molecule, and succeeded in quantitative evaluation of charge mobility of the single crystal using our quantum wave-packet dy-

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.
[2] H.Takaki, N.Kobayashi, K.Hirose,
J. Phys.: Condens. Matter. 32 325901(2020)[3] H. Ishii, S. Obata, N. Niitsu, S. Watanabe, H.
Goto, K. Hirose, N. Kobayashi, T. Okamoto,and J. Takeya,
Sci. Rep. 10, 2524 (2020)

96

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Magnetocaloric Eﬀect of Transition-Metal Alloys
Hung Ba TRAN, Hiroyoshi MOMIDA, and Tamio OGUCHI
Institute of Scientiﬁc and Industrial Research, Osaka University,
8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan(a)45

MnCoGeMn0.89Cu0.11CoGe
Mn0.85Cu0.15CoGe

40
35−∆SM (J/kg.K)

We study the magnetocaloric eﬀect oftransition-metal alloys by combining ﬁrstprinciples calculations and Monte-Carlo simulations. The parameters of the Monte-Carlosimulation are estimated from ﬁrst-principles
calculations. Several types of the magnetocaloric eﬀect such as conventional (direct)
magnetocaloric eﬀect, giant magnetocaloric effect, anisotropic magnetocaloric eﬀect, andinverse magnetocaloric eﬀect can be considered by using our original program[1, 2, 3, 4].
The isothermal magnetic entropy change of
Mn1−x Cux CoGe alloy is shown in Fig. 1(a). Stoichiometric MnCoGe has two phases,
the low-temperature phase is orthorhombic
while the high-temperature phase is hexagonal.
Both the phases are ferromagnetic below diﬀerent Curie temperatures. When there is a structural coupling between magnetic and structure
part, the isothermal magnetic entropy change
becomes gigantic as the Mn0.89 Cu0.11 CoGecase. We also perform speed-up tests for our
massively parallel Monte-Carlo program withhybrid MPI and OpenMP in new System B as
shown in Fig. 1 (b) and (c). We obtain a goodscaling in the tests of OpenMP and MPI, thatis quite important for further study such as
virtual screening of magnetocaloric materials.

30
25
20
15
10
5
0
100

(b)

200

300

400

500 600
T (K)

700

800

900

(c)

Figure 1: (a) Isothermal magnetic entropy changeof Mn1−x Cux CoGe (x = 0.00, 0.11, 0.15) [1]. (b)and (c) Speed-up tests of our Monte-Carlo programin the new System B (Ohtaka).
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).

References[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.

[1] H. B. Tran, T. Fukushima, K. Sato, Y.
Makino, and T. Oguchi, J. Alloys Compd.
854, 157063 (2021).
[2] H. B. Tran, T. Fukushima, Y. Makino,

97

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical analysis of molecular motions in protonconducting organic materials
Yuta HORI
Center for Computational Sciences,
University of Tsukuba, Tennodai, Tsukuba, Ibaraki 305-8577
Anhydrous proton conduction materials

imidazole system. The diffusion coefficients ofhave been investigated for use in electrolytes inimidazoleium cation and PVPA oligomer infuel cells. The composite materials including

PVPA-2Im further decreased and were similar

imidazolemuch

values each other. Therefore, we find that theattention because of the lack of humidity.

imidazolium cation motion was interlocked byPoly(vinylphosphonic acid)-imidazole (PVPA-

PVPA because of the strong hydron bondxIm) has shown the increase of protoninteraction between imidazolium cation andconductivity with x [1].

phosphonic acid in PVPA.

have

especiallygainedUnderstanding theproton conduction mechanism leads to theWe estimated the rotational correlation time

improvement of proton conduction materials.

of imidazole and imidazolium cation to

In this study, we discussed the proton

investigate their internal motions. The obtained

conduction mechanism in PVPA-xIm in terms

results showed the similar dynamical behaviorof the microscopic characters of the hydrogenof the translational diffusions. We compared thebond and imidazole motions as investigated by

activation

molecularTherotational motions of imidazole. The calculated

simulations were performed by the GROMACS

energies of rotational motions were lower thanpackage.

those of translational motions. Therefore, it is

dynamics

simulations.

We calculated the translational diffusion

expectedenergies

thatofprotontransrational

conduction

and

obeys

coefficients of imidazole, imidazolium cation,

Grotthuss-type mechanism.

and PVPA oligomer in PVPA-xIm to investigate

References

their[1] M. Yamada, I. Honma, Polymer, 46, 2986

translationalmotion.

Alldiffusioncoefficients increased with temperature. The(2005).

intercalation of imidazole into PVPA reduces[2] Y. Hori, et al., ACS Appl. Polym. Mater. 2,

the imidazole diffusion, because the diffusion

1561 (2020).

coefficient of imidazole significantly decreased[3] Y. Hori, et al., Chemistry Letters 50, 17

in PVPA-2Im compared to that in pure(2021).

98

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

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

We have developed a crystal structure prediction tool, CrySPY as an open source
software [1].
CrySPY is interfaced with
VASP[2], Quantum ESPRESSO[3], soiap[4],and LAMMPS code for structure optimization.
Several searching algorithms are available in
CrySPY, such as random search (RS), evolutionary algorithm (EA), Bayesian optimization(BO), and LAQA. RS is a basic algorithm andwidely used. EA[5, 6, 7] is currently very popular. Previously we have developed selectiontype algorithms with machine learning. BO
can efficiently select potential candidates froma large number of candidate structures by machine learning[8]. LAQA is one of the refinforcement learning, which can reduce the computation time[9]. CrySPY enables us to findstable structures for bulk systems. However,
CrySPY did not support molecular crystal,surface and interface structures. The original plan was to develop a method for surface
structure prediction, but we changed the planand developed a method for molecular crystal
structure prediction.
We employed the PyXtal library [10] to generate molecular crystal structure generation,and developed the interface between CrySPY
and PyXtal. We tested molecular crystal
structure prediction for Li3 PS4 using CrySPY.
The most stable structure of Li3 PS4 is knownas γ−Li3 PS4 [11], which is composed of six Li
atoms and two PS4 molecules shown in Fig.
1. Fifty molecular crystal structures of two

Figure 1: Crystal structure prediction of
Li3 PS4 . The stable structure is γ−Li3 PS4 .

formula units of Li3 PS4 were randomly generated. Structure optimizations were performed
using the density functional theory with the
projector-augmented wave [12] method as implemented in the VASP code [2]. The generalized gradient approximation by Perdew,
Burke, and Ernzerhof [13] was employed forexchange-correlation functional. A cutoff energy of 625 eV for the plane-wave expansion of
the wave function and k-point mesh density of
80 Å−3 were used.
Crystal parameters of the lowest-energy
structure perfectly agree with the experimental
ones of γ−Li3 PS4 except for the tiny amount ofdifferences in lattice constants and atomic positions. These results indicate that the molecular structure generation method is quite use-99

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

ful for stable structure predictions of molecular
crystals.

References[1] https://github.com/TomokiYAMASHITA/CrySPY.
[2] G. Kresse and J. Furthmüller, Phys. Rev.
B 54, 11169 (1996).
[3] P.
Giannozzi
J.Phys.:Condens.Matter(2009).

et
21,

al.,
395502[4] https://github.com/nbsato/soiap.
[5] A. R. Oganov and C. W. Glass, J. Chem.
Phys. 124, art. 244704 (2006).
[6] A. R. Oganov, A. O. Lyakhov and M.
Valle, Acc. Chem. Res. 44, 227 (2011).
[7] A. O. Lyakhov, A. R. Oganov, H. T.
Stokes, and Q. Zhu, Comp. Phys. Comm.
184, 1172 (2013).
[8] T. Yamashita, N. Sato, H. Kino, T.
Miyake, K. Tsuda, and T. Oguchi, Phys.
Rev. Materials 2, 013803 (2018).
[9] K. Terayama, T. Yamashita, T. Oguchi,
and K. Tsuda, Npj Comput. Mater. 4, 32(2018).
[10] S. Fredericksa, D. Sayrea, and Q. Zhua,
Comput Phys Commun. 261, 107810(2021).
[11] K. Homma et al., Solid State Ionics 182,
53 (2011).
[12] P. E. Blöchl, Phys. Rev. B 50, 17953(1994).
[13] J. P. Perdew, K. Burke, and M. Ernzerhof,
Phys Rev Lett. 77, 3865 (1996).

100

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo!"#$%&'()*#+&%,#-.(/0",1'(-#2(3,.-1%4-5."(6,#&%#**7(8,2".(9,1(!":".,;%#<(=%<0>3"19,17-#+"(3,.'7"1(?."+&1"&(!

!"#$%&'()*+,-.()%/01&(2+3.(1&4(!"50(67)789(!"#$%&'"(&)*+),"-.$(/-$0)1(2/(""%/(2)3.")4(/5"%6/&7)*+)3*87*9):*(2*9);<(87*=8<9)3*87*)>>?=@ABA)"#$%&'$&! ()! *! +($#$%&'(%! ,*&$'(*#-! ./$'$!

(2! $W0$'(,$2&)6! C/$'$43'$-! .$! (29$)&(1*&$!

&'*00$+! %/*'1$)! %*2! 1$2$'*&$! $#$%&'3)&*&(%!

%/*'1$! )&*8(#(&5! 34! ,3#$%>#$! %*2+(+*&$)!

4($#+!43'!&$2)!34!5$*')6!7(8'*&(32*#!$#$%&'$&!

.(&/!4'$$!*,(2$!4>2%&(32*#!1'3>0!./(%/!%*2!

$2$'15! /*'9$)&$'! :7"";<! %*2! %329$'&!

'$*%&! .(&/! @ADD;! $2+! 1'3>0! 34! ACL@F6!

=(2$&(%!$2$'15!(2&3!$#$%&'(%(&5!$44(%($2&#5!85!

"F! *2+! (32(K*&(32! 03&$2&(*#! :TE<! 38&*(2$+!

$#$%&'3)&*&(%!(2+>%&(326!?$%*>)$!&/$!3>&0>&!

4'3,! XIC! %*#%>#*&(32)! .(&/! 03#*'(K*8#$!

03.$'!%*2!8$!(2%'$*)$+!85!43>'!&(,$)!.(&/!

%32&(2>>,! ,3+$#! :EAN<! *'$! >)$+! &3!

8(03#*'! :2$1*&(9$! *2+! 03)(&(9$<! %/*'1(21-!

$9*#>*&$!&/$!$#$%&'32!&'*0!$2$'15!*2+!/3#$!

+$9$#30,$2&! 34! /(1/@0$'43',*2%$! $#$%&'$&!

&'*0! $2$'15! 34! 03))(8#$! %*2+(+*&$)! *4&$'!

,*&$'(*#! 43'! 83&/! 03)(&(9$! *2+! 2$1*&(9$!

+$/5+'*&(32!%32+$2)*&(32!'$)0$%&(9$#56!C/$!

%/*'1(21!()!%'>%(*#6!

*839$!)&'*&$15!()!)/3.2!(2!I(1>'$!Y6!

ABCDE!:FGA!A36!H&+6<!()!*2 *,3'0/3>)!
4#>3'(2*&$+! 03#5,$'-! .(&/! (&)! %/$,(%*#!
)&'>%&>'$)! )/3.2! (2! I(1>'$! J6! C/$'$! *'$!
&/'$$! =(2+)! 34! %3,,$'%(*#(K$+! ABCDE-!
ACL@M-!F!*2+!N6!O$%$2&#5-!M!P(,!$&!*#6!QJR!

!
!"#$%&$!A/$,(%*#!)&'>%&>'$!34!ABCDE!)$'($)6!

>&(#(K$+! S>*2&>,! %/$,(%*#! *2*#5)()! 43'!
$9*#>*&(21!%/*'1$!&'*0!34!ABCDE!$#$%&'$&)6!

3"/4+*-5(62*#&2*,-'78&29(/,+&01+&%(:"8&(;<=! .1-0#*,-"+(52,14

T&!()!)/3.2!&/*&-!*#&/3>1/!2>,8$'!34!'$0$*&!

!"#"$"%&'()*++*,-%(,.(/,+&01+&(%#210#12&%>2(&! 34! ABCDE! ()! 39$'! UVV-! &/$! &'*00$+!

F<=!
F<=!
F<=! F<=!
F<=!
F<=!
F<=!
F<=!

>? @*2#1"+(6,-A&-%"#*,-(
B&"0#*,-(C*#:(6DEFG
H? I6)F!JD(78"+1"#*,-(,.(%,+*AF%#"#&(7G(K(LI$#$%&'32! ()! #3%*#(K$+! *&! &/$! $2+! 1'3>06! T2!

%#"#*%#*0("-"+9%*%M(&S4&2#(&S4&2*&-0&M(&#0?

*++(&(32-! &/$! %3,0>&$+! $#$%&'32! *44(2(&($)!
:"F<!43'!ABCDE!.(&/!+(44$'$2&!$2+!1'3>0)!

>?(6:&/*0"+(39-#:&%*%
H?(3I!M(D3!()&"%12&/&-#
N? J,2(@77=(!&8*0&*'$! (2! S>*#(&*&(9$! *1'$$,$2&! .(&/! )>'4*%$!

FTF%1$%#210#12&
O1"-#1/(6:&/*0"+(!"#"%&#'
P6DEFGQ<&C(G/*-&M(7GM(LIR!

!"#$% '$! I'*,$.3'=! 34! )(,>#*&(32! :EAN@%/*'1$!+$2)(&5!*2+!%/*'1$!)&*8(#(&5!38&*(2$+!

XIC<!1>(+$+!,*&$'(*#!+$9$#30,$2&6!

101

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo]6! ABCDE! +*&*)$&! ()! &/$2! 8>(#&! 8*)$+!

20*'&(*##5!32!&/$)$!%*#%>#*&(32)6!!

Ionization Potential [eV]CTX-A/New Amines
4

CTX-A/AEM!!!!T2! *++(&(32! &3! >)(21! &/()! +*&*)$&! 43'!

CTX-M

6

,*%/(2$!#$*'2(21-!)&*&()&(%*#!*2*#5)()!34!&/$!
+*&*)$&! (&)$#4! $W&'*%&)! )$9$'*#! >)$4>#!

8
CTX-A

(243',*&(326! I3'! $W*,0#$-! @D@! ()! *2!

10
CTX-S
12

0

1

2
3
4
Electron Affinity (eV)5(,03'&*2&! 4*%&3'! 43'! $2/*2%(21! &/$! %/*'1$!

6)&*8(#(&5-! ./(#$! )(21#5@3%%>0($+! 3'8(&*#! ()!

!

>)>*##5!#3%*#(K$+!*&!&/$!$2+@1'3>0!43'!/(1/@!"#$% ($! EAN@XIC! "F@TE! %3,0>&*&(32! 34!

'*2=(21! ,3#$%>#$)! :I(1>'$! ^<6! N3'$!

ZVV! ACL@F[2$.! *,(2$)! .(&/! %3,0*'()32!

*2*#5)()!*2+!$W0$'(,$2&)!*'$!32@13(216!

&3!ACL@M-!F-!N-!*2+!ACL@F[F"N6!

!!!!C/()! .3'=! .*)! 0*'&(*##5! )>003'&$+! 85!
bMC!AO"MC!G'*2&!c>,8$'!bENbAOJUd]!
*2+! bENbAOJ_dJ6! C/$! %*#%>#*&(32! ()!
0$'43',$+!.(&/!MGT!TA"!LF!TMME!)5)&$,!
?!*2+!$9$'5!%*#%>#*&(32!()!/$#+!.(&/!J!23+$!
:Y^!AEe)<6!C/$!$2$'15!34!&/$!,3#$%>#$!()!

!"#$% )$! M(21#5! D%%>0($+! D'8(&*#! (2!

%3,0>&$+! ,*(2#5! 85! XIC! *&! &/$! #$9$#! 34!

2$1*&(9$#5! :#$4&<! *2+! 03)(&(9$#5! :'(1/&<!

AFN@?]HBE[Z@]JfG:+-0<-!.(&/!)3#9*&(32!

%/*'1$+!,323,$'!34!ACL@F[F"N6!

$44$%&! *++$+! 85! EAN-! 85! >)(21! S>*2&>,!

I(')&#5-!"F!*2+!TE!43'!,323,$'!ACL@M-!

%/$,(%*#!)(,>#*&(32!)34&.*'$!GFeMMTFc!

F-! N! *'$! %3,0>&$+! .(&/! EAN@XIC! *)!

QYR6!T2!*++(&(32-!+(44$'$2&!8*)()!)$&)!)>%/!*)!

43##3.)6!"F\!]6UY!$7-!^6]_!$7-!*2+!^6ZV!$7-!

MCD@]G! *2+! ]@YJG! *'$! >)$+! 43'!

'$)0$%&(9$#56! TE\! JJ6]Y! $7-! _6`]! $7-! *2+!

+$&$',(2(21! *! 133+! 8*#*2%(21! 03(2&!

Z6ZV!$7-!'$)0$%&(9$#56!EAN@XIC!"F!1*9$!

8$&.$$2!%*#%>#*&(32!%3)&!*2+!*%%>'*%56!F)!

133+! *1'$$,$2&! .(&/! 0'$9(3>)! NX@XIC!

43'! &/$! %3,0>&*&(32! %3)&-! ABCDE!

"F)\!]6^Y!$7-!]6_^!$7-!*2+!^6UZ!$76!T&!()!

/$W*,$')\! YUVV! AEe! /3>')! 0$'! ,3#$%>#$g!

*#)3! )/3.2! &/*&! "F! 34! ACL@M! ()! (2!

ABCDE!,323,$'\!]Z!/3>')!0$'!,3#$%>#$6!!

S>*2&(&*&(9$!*1'$$,$2&!.(&/!$W0$'(,$2&*##5!

*+,+-+./+0%,$*)>'$+!9*#>$!85!H"TEM!34!]6ZV!$7!QJR6!

QJR! P(,! M6-! $&! *#6-! b6! E/5)6! A/$,6! ?-! 73#6!
JY^-!c36!^Z-!006!JVUV`@JVUJ]!:YVYV<6!

a(&/(2!&/$!4'*,$.3'=!34!I(16!Y-!ZVV!"F!
*2+!TE!43'!,3#$%>#$)!34!ACL@F[F,(2$)!*'$!

QYR!N6!I'()%/!$&!*#6-!hG*>))(*2!V_-!O$96!F6!

%3,0>&$+!85!EAN@XIC-!*)!)/3.2!(2!I(16!

J-i!G*>))(*2-!T2%6!a$##(2143'+-!AC-!YVV_6

102

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo!"#$%&'#"()"'*+$&),*)-*,%".(&./&/*-.#.),#0.(&*,1+#&"(&2#1&+%)3"(4&'#.)+$$&,(2&+5)"%.(&$+*/6%#,''"(4&"(&*.762"8+($".(,*&'+#.9$:"%+$!"##$%&'"$()*$+&"#,&-./#*0)#&1"$!"#$%&'"(&)*+),-./01/2
3*4*-$'$)5$&0*($6)7(08"%/0&.2)3*4*-$'$)9:;<=>;?
!"#$%&'#"()"'*+$&),*)-*,%".(&./&/*-.#.),#0.(&*,1+#&"(&2#1&+%)3"(4&'#.)+$$!!"#$%#&'()&*+,-./0&1$./0&2"13(3,#(43/&0#$&.$&+-*&%3$+&
536*(21"&+33"&+3&#,-.*7*&$148/%&-.0-&#$5*,+&(#+.3&-3"*&,3/+#,+&9:;<=>&./&$.".,3/&3?.'*&#/'&/.+(.'*&6-.,-&.$&./'.$5*/$#4"*&23(&+-*&,1((*/+&$*%.,3/'1,+3(&./'1$+()@&A/*&32&+-*&%#./&
34$+#,"*&23(&:;<=&5(3,*$$&.$&+-*&B,-#(0*815B&

C.0& I@& ;& $,-*%#+.,& 32& +-*& '.7.'*8#/'8,3/G1*(&*22*,+&6-*(*&#,,1%1"#+*'&./,.'*/+&.3/$&./&+-*&#55(3#,-& 23(& $5".+& +-*& C=& 53")%*(& ./+3& $%#""&

C=&"#)*(&*?*(+$&*"*,+(3$+#+.,&(*51"$.3/&#/'&4*/+$&#+3%.,&,"1$+*($@&+-*&.3/&+(#D*,+3(.*$E&6-.,-&5(3%./*/+")&+6.$+$&

K/&C.01(*&IE&6*&'*$,(.4*&#&(*5(*$*/+#+.7*&(*$1"+&+-*&*+,-./0&5(32."*&32&:;<=&6.+-&1"+(#-.0-&

32& +-*& $.".,3/& *+,-./0& $.%1"#+.3/& 34+#./*'& 6.+-&#$5*,+&(#+.3@&;"+-310-&%#/)&#++*%5+$&32&5(32."*&+-*& *%5.(.,#"& (*#,+.7*& 43/'& 3('*(& 9<LMA>&$.%1"#+.3/&./&%*$3$,35.,&$,#"*&23(&(*$3"7./0&%*+-3'& #/'& +-*& '.7.'*8#/'8,3/G1*(& #55(3#,-&B,-#(0*815B&5(34"*%&-#7*&4**/&'*73+*'E&+-*&

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

5"#$%#&,3/'.+.3/&34+#./*'&4)&'*/$.+)8$*"*,+.7*")& ,1++./0& 6*#F& #/'& "3/08(#/0*&

21/,+.3/#"&,#",1"#+.3/$&,3%4./*'&6.+-&+-*&./+*(#,+.3/$& 9$3& ,#""*'& 7'Q& ./+*(#,+.3/>& #/'&(*#,+.7*&23(,*&2.*"'&$.%1"#+.3/@&HIJ",(*#+*$& %#/)& #+3%.,& ,"1$+*($& ,3%4./*'& 6.+-&103

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo,37#"*/+&./+*(#,+.3/&4*+6**/&INORNN&#+3%$@&S-*&

3,,15#+.3/&T*/$.+)&C1/,+.3/#"&S-*3()&9,8TCS>E&'.7.'*'& ,"1$+*($& #(*& ,#",1"#+*'& 4)& '*/$.+)8*"*,+(3/.,& #/'& $+(1,+1(#"& 2*#+1(*& 32& 431/'&21/,+.3/#"& +-*3()& 9TCS>& 6.+-& UMVWXT&*?,.+3/$&#(*&(*7*#"*'&#/'&(*"#+*'&31+,3%*$&$1,-&

21/,+.3/#"@& S-*& (*$1"+$& 0.7*& #,,1(#+*& #+3%.,&#$& "./*& $-#5*& 32& 4(3#'& *%.$$.3/& #/'& *?,.+3/&$+(1,+1(*$&#/'&*"*,+(3/.,&$+(1,+1(*$&23(&,#(43/&I$&+(#55./0& (#+*& 6.""& 4*& *7#"1#+*'& 23(& 5(37.'./0&

X!Y&#/'&'.*"*,+(.,&,3/$+#/+&5(*$*/+*'&./&C.01(*&

5(#,+.,#"& ,"1*$& 23(& *?5*(.%*/+#"& '*$.0/& 32&

R@&

35+3*"*,+(.,#"&#/'&5-3+373"+#.,&%#+*(.#"$@&&
S-*& *?,.+3/& $*"28+(#55./0& ,#",1"#+.3/$& 6*(*&
5*(23(%*'& 23(& +-*& =$!M."K#& 6-.,-& .$&(*5(*$*/+#+.7*&NT&

5*(37$F.+*&

1$*'&

23(&

5-3+3$*/$3($&#/'&".0-+8*%.++./0&'.3'*$&HRJ@&&
C.0& R@& S-*& $.%1"#+*'& X!Y& $5*,+(#& 4#$*'& 3/&<LMA8ZT&(*$1"+&#/'&TCS&35+.%.[*'&$+(1,+1(*$@&
S-*& X!Y& $5*,+(#& 34+#./*'& 6.+-& TCS& (*$1"+$&+)5.,#"")&$-36&

4*++*(&#0(**%*/+&

6.+-&
&

*?5*(.%*/+#"&'#+#@&!"#$%& '#"()"'*+$& ),*)-*,%".(& ./& +5)"%.(& $+*/6

C.0&R@&S-*&$.%1"#+*'&+(#55*'&*?,.+3/$&#/'&+-*.(&%#,''"(4&"(&*.762"8+($".(,*&'+#.9$:"%+$–(*"#+.7*&$+#4.".+.*$@&\368'.%*/$.3/#"& 5*(37$F.+*$& #(*& 231/'& +3&

K/&(*$1"+$E&6*&231/'&+-(**&'.22*(*/+&$*"28+(#55*'&*22.,.*/+")&*?-.4.+&6-.+*&4(3#'&*%.$$.3/&6.+-&#&*?,.+3/$&./&=$!M."K#@&Q-."*&+-*&"3,#".[*'&*?,.+3/&$./0"*&%#+*(.#"&./&,3/+(#$+&+3&,3/7*/+.3/#"&+-(**8.$&+-*&0(31/'&$+#+*&32&+-*&+(#55*'8*?,.+3/&$+#+*E&'.%*/$.3/#"& %#+*(.#"$@& Q-."*& 6-.+*& 4(3#'&

3/*8'.%*/$.3/#"& #/'& +638'.%*/$.3/#"& *?,.+3/&*%.$$.3/& .$& #++(.41+*'& +3& $*"28+(#55*'& *?,.+3/&$+#+*$& #"$3& *?.$+& 6-.,-& $-31"'& 4*& ./73"7*'& ./&9YSL>E&'*+#."*'&%*,-#/.$%&32&YSL&23(%#+.3/&.$&

4(3#'& *%.$$.3/& #/'& 5-3+373"+#.,& 4*-#7.3(& 32&(#(*")& *?5"3(*'& 4)& +-*3(*+.,#"& $+1'.*$@& K/& +-.$&=$!M."K#@&&5(3D*,+E&Q*&*?5"3(*'&431/'&*?,.+3/&23(%#+.3/&./&

References+638'.%*/$.3/#"&

HIJ&=@&C@&;4(#%$&#/'&T@&M@&](#7*$^&_@&`#,@&Y,.@&-#".'*&

5*(37$F.+*$&

23(&#,-.*7./0& -.0-")& *22.,.*/+& ".0-+8*%.++./0& '.3'*&

S*,-/3"@&;&@&!"#9RNNI>&IWa8IbI@&

9\LT>& #/'& 5-3+373"+#.,& '*7.,*$@& C(3%& +-*&

HRJ&c@&Z@&Z,=#""E&=@&=@&Y+31%53$E&Y@&Y@&c3$+./#E&$)$+*%#+.,&$+1')&32&431/'&*?,.+3/&23(%#+.3/&4)&

Z@& ]@& c#/#+[.'.$& #/'& M@& Q@& Q*$$*"$^& =-*%@&

1$./0& $*"28./+*(#,+.3/& ,3((*,+*'& ,3/$+(#./+&

Z#+*(@&&$"#9RNIW>&PIRV8PIPa@

104

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Improvement and application of
all-electron mixed basis program
Kaoru OHNO
Faculty of Engineering Science, Yokohama National University79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501
Using the all-electron mixed basis programusing TOMBO, and found out that all these

TOMBO, we performed first-principles moleculareffects are to decrease the energy gap. According

dynamics simulations of Mo and Au atom verticalto our results, the scLGW method can improvebombardments at the center of a six-membered

the one-shot G0W0 results in many cases. Thus,ring of C60 to create endohedral fullerenes. With

linearization is very powerful and effective. The

the kinetic energies of 40 eV and 80 eV, Mo andresult will be submitted soon.

Au atoms successfully penetrated inside the C60,

Lastly, we have applied our first-principle

and the endohedral fullerenes, M@C60 (M=Mo,

phase field method to Ti64 ternary alloys [2] andAu), were created. We confirmed that the createdto Ni-Ti binary alloys [3], and succeeded in

M@C60 continues to exist stably without breaking.

reproducing

This result is currently being submitted.

without introducing any empirical thermodynamic

theexperimental

microstructure

On the other hand, in the Green’s function

parameter. In the simulation of Ni-Ti alloys, we

method in many-body perturbation theory, all thenoticed an important tolerance behavior that theeffects of the Coulomb interaction between

result does not depend on the assumed atomic

electrons are incorporated in the self-energyalignment at all and found that the result does not

function. However, since the self-energy functionchange even if we used NiTi3 instead of NiTi2.

depends on the energy, the quasiparticle wave
functions,

i.e.,

the

basis functions,

Referenceswhich

diagonalize the Green’s function, are not only

[1] R. Kuwahara and K. Ohno, Phys. Rev. A 90,

effect032506;1-9 (2014).

ofrenormalization

of

the

energydependence of the self-energy has not been

[2] T. N. Pham, K. Ohno, R. Kuwahara, and S.

discussed much so far in the one-shot G0W0

Bhattacharyya, J. Phys.: Cond. Mat., 32,

approximation. Therefore, we discussed the effect

264001;1-9 (2020).

of

G0W0

[3] K. Ohno, M. Tsuchiya, R. Kuwahara, R.

approximation and the effect of linearization in

Sahara, S. Bhattacharyya, and T. N. Pham,the scGW approach (the scLGW method [1]) by

Comp. Mat. Sci. 191, 110284 (2021).

renormalization

in

the

one-shot105

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study of Efficient Training Data Generation Method forConstructing Artificial Neural Network Force Field I-II
Kohei Shimamura
Department of Physics,
Kumamoto University, 2-39-1 Kurokami, Chuo-ku, Kumamoto 860-8555
Interatomic potential using an artificial

important for MD simulations (e.g. simulations

neural network (ANN potential) can not only

under NPT ensemble), we believe that training

provide high accuracy results by training first-of pressure is indispensable and uncertainty ofprinciples molecular dynamics (FPMD) datapressure should also be added to the indicator.

but also have low computational cost, which

We recently revealed that the pressure training

allows for large scale and long-term MD

is necessary to accurately calculate thermal

simulations. In this study, we aim to finding

conductivity, which is a fundamental physicalhow to efficiently generate the training data

quantity that characterize the thermal properties

required to construct the ANN potential. Activeof materials [1]. There is a well-known method

Learning (AL) is one of the promising

using long-term equilibrium MD data andgeneration methods that we are paying attention

Green-Kubo

to. In AL, firstly, several ANN potentials with

conductivity is calculated from the timedifferent initial values of weight parameters arecorrelation function of heat flux. It was also

constructed by training with the same data.

found that a clear relation holds between the

Since an output uncertainty (e.g. standard

heat flux formula and the pressure one derived

deviation) can be defined using the ANN

from the virial theorem [1]. Since the current

potentials, the magnitude of the uncertainty

standard training method mentioned above does

provides us an indicator to identify thenotcandidate data to be trained. However, there ispotentials with inadequate pressure accuracy

still

specific

are likely to show poor thermal conductivity.

indicators. The indicators currently employedThis result further emphasizes the importancefor AL are the uncertainty of potential energy

of pressure training. We are exploring betterand atomic force. This reflects the current

indicators of AL including pressure uncertainty.

room

standardfortraining

consideration

method,ofwhereformula,guarantee

wherepressure

theaccuracy,

thermalANN

ANN

potentials learn the potential energy and force

Reference

obtained from the FPMD.

[1] K. Shimamura, et al.: J. Chem. Phys. 153,

Considering that accurate pressure is also

234301 (2020).

106

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Refined Metadynamics and Elucidation of Reaction Mechanism of Polyalcohol
Dehydration in Hot Acidic Water
Tomomi Kondo1,2， 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

Subcritical water has high solubility offrom the difference (the point where the reaction

organic molecules and is expected to be applied

occurred). However, the height of the bias

as a reaction medium. Cyclization dehydration

potential represented by the Gaussian function

reaction of polyalcohol in hot water has been

and the frequency of addition are finite, and anproven to be efficient method for utilization oferror of several kBT occurs in the free energy

biomass materials [1]. In this study we proposed

surface. Whena new method of refinement (improved

different environmental conditions such as

metadynamics method: Refined MTD),

andpressure and temperature, or when there areapplied it to cyclization dehydration of 2,5-competitive reactions, it is necessary to estimate

Hexanediol (HDO) [2].

the accurate free energy surface with an error ofcomparing

reactionswithseveral kBT or less. In this study, we used
Refined MTD, which is a method to further
refine the free energy surface obtained by MTD
Fig. 1 Reaction for 2,5-Hexanediol (HDO)

calculation. First, the W(q) deposited from theIn the metadynamics method, by adding thereactant to the product by metadynamics

bias potential according to the frequency of

calculation is added to the potential of theappearance

surfacesystem as a time-independent bias potential.

characterized by the reaction coordinates (CV),

Then, the canonical distribution ρW(q) isa chemical reaction that does not occur on thegenerated by sufficiently sampling the system bytime scale of the usual molecular dynamics

molecular dynamics calculation biased by W (q).

method is induced. From the deposited bias

A(q) can be corrected using ρW(q) as shown inpotential W(q), the free energy surface A(q) = –

the

on

the

free

energyW (q) + const is obtained, and the minimum andsaddle points of A(q) are obtained.
The activation barrier ∆A can be obtained

107

following

equation[2].

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Sampling of the biased system must bemolecules (Fig. 3). For the higher acidic system

performed sufficiently until the entire freesuch as a system containing H2SO4, metastableenergy surface in the CV space is sampled, andstructure was found in the region where protons

especially when the activation barrier is to be

are added. In addition, the proton coordination

obtained, sampling not only near the minimum

number in the transition state was n ≈ 2.0 in thereaction energy point but also near the transition

system containing acidic molecules, whereas it

state is required.

was n ≈ 1.4 in the pure water system, indicating

Calculations were conducted using softwarethat the reaction process differs depending on the

PIMD [3] working with DFTB or VASP. The

acidity. The activation barrier ∆A (kcal/mol)

calculation system consists of 1 HDO molecule,were obtained as 50.6 (pure water), 39.6

30 water molecules, and acidic molecules such

(H2CO3), 35.4 (HCl), 26.3 (H2SO4).

as HCl added under the same thermodynamic
conditions as in Experiment [1] (20 MPa, 523 K).
CV is assumed for each product. The dihedral
angle φ between the hydroxyl group and themain chain, the difference d in the O-C distancesof leaving and bonding, and the proton
coordination number n of the hydroxyl groupwere set according to the reaction path.
By using Refined MTD for the HDO system,
the free energy surface of the system containing
Fig. 2 Free energy surfaces obtained for HDO
dehydration reaction obtained by Refined MTD.
(a) HCl aqueous solution, (b) pure water.

each acidic molecule was obtained. When the
difference was taken before and after thecorrection for the minimum free energy surface

Referencesof the system containing H2CO3, the maximum[1] A. Yamaguchi et al., Green Chem., 13,

was 7.3 kcal/mol, and the average was 1.6

873 (2011).

kcal/mol (RMSE). As a result of DFTB

[2] T. Kondo et al., J. Comput. Chem., 42, 156

calculation using Refined MTD, it was(2020).

confirmed that the free energy surface of the[3]http://ccse.jaea.go.jp/ja/download/pimd/in

cyclization-dehydration reaction of HDO differsdex.jp.html.

depending on the presence and type of acidic

108

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ultimate impedance of coherent heat conduction in van der
Waals graphene-MoS2 heterostructures
Hu Shiqian
Department of Mechanical Engineering,
The University of Tokyo, Hongo, Bunkyo City, Tokyo 113-8654
Toward the ultimate goal of designing small
thermal-conductivity

materials

temperature,wehereinat

Waals (vdW) heterostructure provide an idealroom

platform for the coherent phonon transport

themanipulation. Thus, in the current work, using

investigate

controllability of coherent phonon transport inthenon-equilibrium

van der Waals graphene-MoS2 heterostructures

simulations,with different stacking orders using non-phonon transport in vdW graphene-MoS2

equilibrium molecular dynamics simulations.

heterostructure with different stacking order.

wemolecular

investigatethedynamics
coherent

Using Bayesian optimization–based materials
informatics, the optimal stacking order ofgraphene and MoS2 is efficiently identified
from tens of thousands of candidates withvarying degrees of phonon localization. The
obtained thermal conductivity of the optimized
heterostructure (0.026 W/m-K) is significantly
lower than that of its building blocks, pristine
Figure. Schematics of the machine-learning

MoS2 and graphene.

method to combine the molecular dynamics (MD)There are growing efforts to control

and Bayesian optimization.

thermal transport via coherent phonons in the
one-dimensional

superlattice.

However,Theinhistogramofthephonongeneral, the difference in the intrinsic latticetransmissions in different disordered structure

structuresmaterials

exhibits a log-normal distribution, which

inevitably generate interface disorder during

reveals the localization of the coherent phonons.

the fabrication process, greatly limiting direct

Furthermore, the optimal stacking order of theexperimental observation of the coherent

graphene and MoS2 is efficiently identified

phonon transport. The flexible integration andfrom tens of thousands of candidates byatomistic interlayer smoothness of van dermachine learning. The significantly suppressed

of

the

constituent

109

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyoof the phonon transmission in the low
frequency (<5THz) phonons of the optimized
structure lead to a significant reduction of thethermalconductancecompared

with

the

pristine graphite. Finally, the effects of thedefect effect on the thermal conductivity ofgraphite and optimized structures are also
discussed. Our work provides a deep insight
into the coherent phonons transport behavior in
the atomistically smooth vdW structure, which
is beneficial for further development ofphononics.

References[1] S. Hu, S. Ju, C. Shao, J. Guo, B. Xu, M.
Ohnishi and J. Shiomi, Mater. Today Phys. 16,
100324 (2021)

110

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development and applications of ﬁrst principles
method for light-matter interactions beyond thedipole approximation
Takeshi IWASA
Faculty of Science, Hokkaido University
N10W8, Sapporo, Hokkaido 060-0810

Near ﬁeld refers to a non-propagating lightﬁeld. The interaction between the near-ﬁeld
and molecules can overcome the diﬀraction
limit and can induce non-dipolar excitations,oﬀering a unique platform for nanoscale spectroscopy and microscopy [1], as well as photochemistry [2]. Due to the localization of thenear-ﬁeld, theoretical framework beyond thedipole approximation is required. Thus, wehave developed a ﬁrst principles method basedon the multipolar Hamiltonian, in which, theinteraction is described by coupling the electric ﬁeld and the molecular polarization ﬁeld
integrating over the space. The method has
been used to study near-ﬁeld electronic excitations [3] and vibrational excitations, i.e., thenear-ﬁeld IR combined with electrodynamics
computations [4].
In this ﬁscal year, we have developed amethod for near-ﬁeld Raman [5]. The theoretical framework we established for near-ﬁeld Raman is as follows. First, the multipolar Hamiltonian is implemented into a real-time timedependent density functional code, namely,
Octopus 9.2 [6] and calculate the near-ﬁeld excited electron dynamics to obtain the induced
dipole moment of a molecule in the time domain, which is later Fourier transformed into
the frequency domain. The induced dipole moments are calculated 6N times (N is the number of atom in a molecule) for distorted geometries where one of the x, y, and z coordinatesof an atom is shifted slightly in either the pos-

itive and negative direction to obtain a derivative of the induced dipole moment with respect
to the atomic Cartesian coordinate, which isthen transformed into the normal coordinate
derivative using the transformation matrix obtained by a normal mode analysis, performed
separately. Finally, the Raman spectrum is obtained from the square of the absolute value ofthe normal coordinate derivatives.
As a demonstration, on- and oﬀ-resonancenear-ﬁeld Raman of benzene is studied. We
showed that the obtained Raman spectra are
well understood by considering both the spatial structure of the near ﬁeld and the molecular vibration in the oﬀ-resonance condition.
For the on-resonance condition, the Raman
spectra are governed by the transition moment, in addition to the selection rule of oﬀresonance Raman. Interestingly, on-resonanceRaman can be activated even when the nearﬁeld forbids the π−π ∗ transition at equilibriumgeometry due to vibronic couplings originatingfrom structural distortions.
References [1] R. B. Jaculbia, et al., Nat.
Nanotechnol. 15, 105 (2020). [2] E. Kazuma etal., Science, 360, 521 (2018). [3] T. Iwasa and
K. Nobusada, Phys. Rev. A, 80, 043409 (2009)
and 82, 043411 (2010). [4] T. Iwasa, et al.,J. Chem. Phys., 144, 124116 (2016) and 152,
164103 (2020). [6] M. Takenaka, T. Taketsugu,
T. Iwasa, J. Chem. Phys., 154, 024104 (2021).
[5] X. Andrade, et al., Phys. Chem. Chem.
Phys. 17, 31371 (2015).

111

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical analysis of inﬂuences of phonons onmagnetism
Yoshihiro GOHDA
Department of Materials Science and Engineering, Tokyo Institute of Technology
J1-3, Nagatsuta-cho 4259, Midori-ku, Yokohama 226-8502, Japan

In addition, ﬁrst-principles computations
are performed for magnetic materials including
permanent magnets [6] and multiferroic materials [7]. We also improved formulations to
calculate Jij in OpenMX [8] by introducing theorthogonalization of localized basis sets.
Tc
959 K

−20

Tc
1522 K
1.2

−40
−60
−80

563 K

argmin[Gmag + Gph]

−100

Cmag (meV/(K・atom))eqEmag (meV/atom)

It is extremely challenging to describe
magnetism at ﬁnite temperatures by ﬁrstprinciples electron theory. There are at least
two main contributions to excitation: magnons
and phonons. Even though there are attempts to include ﬁnite tempearture eﬀects
through exchange-coupling constants Jij inthe Heisenberg model by ﬁrst-principles calculations, dependences of phonons on magnetic states has been neglected. Such an approach is also computationally challenging, because ﬁrst-principles phonon calculations andMonte Carlo simulations are required for precise evaluations in addition to the standard
total-energy minimization.

1.0
0.8

argmin[Gmag]

0.6

−120

0.4

−140

0.2

−160
0

250 500 750 1000 1250 1500 1750

0Temperature (K)In this project, we propose a new ﬁrstprinciples scheme to evaluate the Curie temperature taking the magnetism-dependent
phonons and their feedback eﬀect to magnetism into account, and apply the scheme tobcc Fe [1] and some B2 and L10 compounds [2]as examples. In our framework, we minimize the total free energy in the explicit consideration of temperature eﬀects, because themagnetic and vibrational free energies correlate with each other. Both the inﬂuences ofmagnetism on phonons and the feedback effect from phonons to magnetism are taken into
account using phonon calculations by ALAMODE [3]. The feedback eﬀect reduced theCurie temperature of bcc Fe signiﬁcantly as
shown in Fig. 1, where the magnetic energy is
calculated by the ALPS code [4] with Jij obtained by Akai-KKR [5].

112

Figure 1: The equilibrium magnetic energy (solidlines) and the magnetic speciﬁc heat (dashed lines)of bcc Fe as a function of temperature obtained by
the minimization of the total free energy and by
the minimization of the magnetic free energy [1].
[1] T. Tanaka and Y. Gohda, npj Comput. Mater.
6, 184 (2020).
[2] T. Tanaka and Y. Gohda, J. Phys. Soc. Jpn.
89, 093705 (2020).
[3] T. Tadano, Y. Gohda, and S. Tsuneyuki, J.
Phys.: Condens. Matter 26, 225402 (2014).
[4] B. Bauer, S. Todo, et al., J. Stat. Mech. 2011,
P05001 (2011).
[5] H. Akai, J. Phys.: Condens. Matter 1, 8045
(1989).
[6] Y. Ainai, S. Kou, Y. Tatetsu, and Y. Gohda,
Jpn. J. Appl. Phys. 59, 060904 (2020).
[7] R. Costa–Amaral and Y. Gohda, J. Chem.
Phys. 152, 204701 (2020).
[8] T. Ozaki, Phys. Rev. B. 67, 155108 (2003).

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Microscopic simulation for ultrafast electronic and atomic
response driven by strong and short laser pulses
Yasushi Shinohara1,2, Mizuki Tani2
1

Photon Science Center,

The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-86562
2

Department of Nuclear Engineering and Management

The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656

The development of coherent light sourcesin time-resolved reflectivity measurement [4].

allows us to realize various nonequilibrium

The semimetallic phase of TNS is realized above

material dynamics. Such processes are initiated328 K accompanied by structural phaseby electron excitation then undergoing atomic

transition. Our coauthors conduct experiments

motion via the electron-phonon interaction. A

to discover TrARPES with fine enough temporal

theoretical description of the nonequilibrium

resolution to disentangle different frequencies ofdynamics for the whole system composed ofcoherent phonon modes. By taking the Fourier

electrons and the nucleus is one of the mosttransform

challenging systems. We have investigated

FDARPES in which ARPES with a phonon

nonequilibrium

systems

frequency

directions,electron-phonon

a)

along

with

two

interaction

of

the

shows

TrARPES,electronic

weobtainstructuremodulation by the corresponding phonon. The

computation to understand the frequency-

metallic

domainphotoemission

structures coincide with 2 and 3 THz coherent

spectroscopy (FDARPES) under collaboration

phonons. To assign phonon modes to thewith experimentalists [1], and b) development of

frequencies, we perform density-functionalasemiclassicalperturbation theory (DFPT) calculation of themodeling of the optical response for simple

FDARPES. We reveal 2 THz phonon modes aremetals [2].

a motion connecting the two, semiconducting

angle-resolved

theoreticalframework of

In Ta2NiSe5 (TNS), it is reported that theandsemiconducting

electronicand semimetallic, structures.

coexistence of insulator and semimetallic

A mean-field type quantum theory hardly

electronic structures in time-resolved angle-

captures the colliding process leading toresolved

spectroscopy

relaxation or equilibrium among the electron(TrARPES) [3] and Coherent phonon generation

subsystem. A numerically efficient scheme tophotoemission

113

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

describe electron scattering is a semiclassical

TDDFT cost. We also perform systematic

equation of motion that the collision integral

benchmarking for nonlinear optical responses

added to the Vlasov equation. The Vlasov

compared with TDDFT. We are preparing theequation can be constructed from a quantum

manuscript for this work.

mechanical equation of motion, such as timedependent density-functional theory (TDDFT),by the Wigner transformation [5]. The Vlasov
equation is solved by the pseudo-particle methodthat the distribution function is described by asum of classical particles having finite spatial
and momentum width [5].

We develop atheoretical framework for a spatially periodic

References

system based on the Vlasov equation with the[1] Takeshi Suzuki, Yasushi Shinohara, et al.,pseudo-particle method and density-dependent

Phys. Rev. B 103 (2021) L121105.

functional taken from TDDFT, called Vlasov-[2] M. Tani, T. Otobe, Y. Shinohara, K.L.

LDA hereafter. A striking advantage of Vlasov-Ishikawa, in preparation.

LDA is the much lighter computational cost[3] K. Okazaki, Nature Communications volume

compared to typical time-dependent quantum

9 (2018) 4322.

mechanical simulations. We apply Vlasov-LDA[4] S. Y. Kim, et al., ACS Nano 10, 8888 (2016),

to crystalline Al and compare its results with

S. Mor, et al., Phys. Rev. B 97, 115154 (2018).

TDDFT. Optical conductivity from Vlasov-LDA[5] T. Fennel, et al., Eur. Phys. J. D 29, 367–378

perfectly(2004).

coincides

with

TDDFT,

while

computational is typically 50 times lighter than114

Activity Report 2020 / 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, Kumamoto, 860-8555
We have studied condensed matter systems,

are suitable for such test because Na has only

which are crystal, liquid, and amorphous

one valence electron and Ag2Se has manysystems. In this project, we aimed to clarify theelectrons. The calculation cost of the former isstatic structure of glass V2O5 under pressure

low, therefore, it is easy to compare the result

using our original QXMD code, which is

by ANN-MD with that by AIMD. While, theapplicable to perform ab initio molecular

cost of the latter is high, hence, the efficacy ofdynamics (AIMD) and empirical molecular

acceleration using ANN potential is checked.

dynamics (MD) simulations [1].

In this study, it was found that an optimizing

In order to investigate the static andequation including the force and virial terms,

dynamic properties of disordered materials, we

which were often ignored, was needed for theemployed one of the machine learning method,phase transition [3,4].

the artificial neural network (ANN) technic [2].
This method enables us to perform MD

References

simulations of the large scaled system with

[1] F. Shimojo, S. Fukushima, H. Kumazoe, M.

reasonably low calculation cost. However, theMisawa, S. Ohmura, P. Rajak, K. Shimamura, L.

best method to construct the interatomic

Bassman, S. Tiwari, R. K. Kalia, A. Nakano,potential of high transferability for any

and P. Vashishta: SoftwareX 10 (2019) 100307.

calculation conditions is not established. That is,[2] N. Artrith and A. Urban: Comput. Mater.

our priority mission is the establishment of

Sci. 114 (2016) 135.

construction of the ANN potential applicable[3] K. Shimamura, S. Fukushima, A. Koura, F.

for the wide range conditions based on the

Shimojo, M. Misawa, R. K. Kalia, A. Nakano, P.

result of AIMD simulations. For this purpose,

Vashishta et al. J. Chem. Phys. 151, 124303

we try to construct new ANN potentials for(2019).

different targets, liquid and crystal Na, and α-[4] A. Irie, S. Fukushima, A. Koura, K.

and β-phases of Ag2Se crystals. These targets

Shimamura, and F. Shimojo, in preparation.

115

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio calculation for thermodynamic phase
diagram
Kazuma NAKAMURA
Quantum Physics Section, Kyushu Institute of Technology
1-1 Sensui-cho, Tobata, Kitakyushu, Fukuoka, 804-8550

For the purpose of ab initio quantitativeevaluation of thermodynamic physical properties of materials, thermodynamic phase diagrams based on first-principles calculations arecalculated. Focusing on metal hydrides, which
are important as hydrogen storage alloys, wewill evaluate their phase diagram and pressurecomposition-temperature curves. The free energy model under the regular solid solution
approximation is determined from the firstprinciples calculation, and the phase diagramof this model is obtained with the CALPHAD
method.
As the benchmark, the phase diagram ofthe metal hydride Ti-H sysmtem is calculated. The calculation flow is as follows: The
starting point is the Gibbs free energy calculation. The free energy consists of threeterms, the enthalpy term, the phonon term,
and the solid-solution entropy term, all ofwhich are evaluated by first-principles calculation. The enthalpy term is evaluated fromthe density-functional calculation for pureTi and TiH systems (using xTAPP [1] andVASP [2]). The phonon term is also evaluated from the first-principles phonon calculation for Ti and TiH (using PHONOPY [3]).
The solid-solution entropy term is evaluatedusing cluster-expansion and cluster-variational
methods [4]. For these calculations, a large
amount of structural data created by inserting hydrogen or voids into the tetrahedralinterstitial site is generated, where we consider a metal having a face-centered cubic (fcc)

structure and the resulting structural data series is written as fcc-tetrahedron series. This
structural series is generated using the software ATAT [5]. In this fcc-tetrahedron series, the total number of generated structural samples was 132. In addition to the
fcc-tetrahedron series, fcc-octahedron series,
body-centered-cubic (bcc)-tetrahedron series,
bcc-octahedron series, hexagonal close-packed(hcp)-tetrahedral series, hcp-octahedron series, etc. are generated. First-principles calculations are performed for each structural series
to obtain structural and energy data.
Next, we determine parameters of the effective model based on the regular solution approximation by fitting to the above obtained
first-principles calculation data. In the firststep, we use the cluster expansion method forthe ab initio data to obtain expansion coefficients of cluster model, and then, to evaluate
temperature dependence of the cluster model,
cluster-variational method is performed for thecluster-expansion function of each structuralseries, which give the first-principles free energy surface. Finally, for the resulting free energy surface, the parameters of the regular solution model are obtained by fitting:F(x, T ) = xGTiH (T ) + (1 − x)GTi (T )+ RT [x ln x + (1 − x) ln(1 − x)]+ x(1 − x)[(1 − x) − x]0 (L0 + L00 T )+ x(1 − x)[(1 − x) − x]1 (L1 + L01 T )+ x(1 − x)[(1 − x) − x]2 (L2 + L02 T ),
(1)

116

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

where GTiH (T ) and GTi (T ) are the free energies of TiH and Ti, respectively, and x or 1 − x
is fraction of vacancy or hydrogen in Ti. The
free energy is modeled with the following function as

density-functional calculation, (ii) the phonon
anharmonicity can affect the quantitative accuracy of the phase diagram boundary, and(iii) the quantitative accuracy of the interaction term depends highly on details of the cluster expansion (the cluster shape and expansion
Gα (T ) = aα +bα T +cα T ln T +dα T 2 +eα T −1 , (2) order, etc.) for the structure and energy data.
where the subscript α specifies TiH or Ti, andaα , bα , cα , dα , eα in Eq. (2) are determined byfitting to the ab initio phonon free energy data.
The third term in Eq. (1) is the mixing entropy
term in the binary alloy system. The remaining terms in Eq. (1) are the interaction termand L0 , L00 , L1 , L01 , L2 , and L02 parameters are
determined by fitting to the ab initio cluster
variational data. Table 1 lists our determinedparameters in Eqs. (1) and (2).
Table 1: Determined parameters in Eqs. (1)and (2).

bcc-tetra

fcc-tetra

Ti

Ti

TiH6

hcp-tetra
TiH2

Ti2

Ti2 H4abcde

6413.24 60753.56
71.0177.801−14.262−1.308−0.005−0.0090.001
0.000

1978.90 −27924.55
93.111−23.512−18.495
4.362−0.007−0.0240.001
0.000−1944.38 −15163.09
87.479−18.794−16.9213.644−0.009−0.024
0.001
0.000

L0
L0 ’
L1
L1 ’
L2
L2 ’

−105733.39−2.3605−24563.95−1.0794−99788.53
0.078713618.96−0.267−9933.31
0.1296−5491.55−0.43764345.96−1.7241−11022.69−1.5862−12354.91
2.8456

From the free energy curve of the regular solution model [Eq. (1)] obtained above, a phase
diagram based on the CALPHAD method was
calculated by using the software PANDAT [6].
Figure 1 (a) shows our calculated phase diagram of Ti-H sysmtem. The panel (b) also
shows experimental phase diagram [7]. Fromthe comparison between the two, we found that
our result reasonably reproduces the experimental result. A Python Script was developed
to generate PANDAT inputs from the results ofthe present regular solution models. We foundthat (i) the entropy term can be sensitive tothe exchange-correlation functional used in the

Figure 1: Thermodynamic phase diagram of
TiH: (a) simulation and (b) experiment [7].

References[1] http://xtapp.cp.is.s.u-tokyo.ac.jp[2] https://www.vasp.at[3] https://atztogo.github.io/phonopy[4] M. Sluiter, D. de Fontaine, X. Q. Guo, R.
Podloucky, and A.J.Freeman, Phys. Rev.
B 16, 42 10460 (1990).
[5] https://www.brown.edu/Departments/
Engineering/Labs/avdw/atat/[6] https://computherm.com/[7] A. San-Martin, F.D. Manchester, Bulletinof Alloy Phase Diagrams 8, 30–42 (1987).

117

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Oxygen vacancy formation in metal-doped CeO2
nanocrystals
1

Akira YOKO1 , Kazutoshi INOUE1 , Mitsuhiro SAITO2 , and Yuichi IKUHARA1,2,∗
Advanced Institute for Materials Research, Tohoku University, Sendai, Miyagi, 980-8577
2
Institute of Engineering Innovation, The University of Tokyo, Yayoi, Tokyo, 113-8656

We studied Cr-doped cubic {100}-faceted
CeO2 nanocrystals (NCs) with an average sizeof 7.8 nm fabricated by a supercritical water reaction. A considerably large amountof Ce3+ ions was detected in the Cr-doped
CeO2 NCs by scanning transmission electron
microscopy combined with electron energy loss
spectroscopy (EELS). The Cr dopants substituted the Ce sites in the amount of approximately 3 mol%. We experimentally observedthat the oxygen-storage capacity (OSC) was
substantially improved by a low amount of Cr
doping, which can be attributed to the low oxygen vacancy formation energy and high mobility of oxygen atoms by doping Cr in CeO2 .
Plane-wave basis density functional theory(DFT) simulations were performed by using
the VASP code to understand the eﬀects of
the Cr dopant on oxygen vacancy (Vo) formation. A Ce atom was substituted by one
Cr atom in the 96-atom 2 × 2 × 2 supercellof CeO2 (Ce32 O64 ) with a Monkhorst–Pack kpoint mesh of 4 × 4 × 4, which is equivalent
to the loading amount of Cr at 3 mol%. The
incorporation of Cr in 3+ charge state canbe compensated by the formation of an extra Vo (per two Cr3+ ions) or a Vo and a
Ce3+ ion while the oxidation of Cr-doped CeO2
NCs should create Cr4+ ions. Two Ce3+ ionswere located in the next nearest neighbor positions with respect to the Vo, consistent withprevious studies of CeO2 with DFT+U. The
Bader charge of the Ce3+ and Ce4+ ions was
set +2.11|e| and +2.44|e|, respectively. The
Vo formation energy (E(Vo)) in the Cr-doped
CeO2 was calculated as 0.99 eV, which wassubstantially decreased from 2.00 eV in the
non-doped case. The high OSC performancecan be attributed to the contribution of the valence change of Cr to E(Vo), and the structuraleﬀect of Cr doping on E(Vo). Only 3 mol%doping improved the OSC, suggesting that Cr
doping aﬀects the structure of CeO2 significantly. The results of layer-by-layer EELS
analysis indicated a signiﬁcant increase in theamount of Ce3+ by Cr doping particularly in
the internal atomic layers, which is more thanthe mere compensation of Cr3+ with Vos. The
low E(Vo) of Cr-doped CeO2 NCs can lead toa signiﬁcant increase of Ce3+ ions even with a
low amount of Cr doping, as observed in theexperiments.
In summary, DFT calculations demonstrated
that the Cr dopant reduces the E(Vo), resulting in the increase of the mobility of oxygen
atoms in the nano-sized CeO2 . The high concentration of Vos as well as the high oxygen
diﬀusivity improve the OSC performance of
Cr-doped CeO2 NCs, compared with the nondoped CeO2 NCs. These eﬀects provides a fundamental understanding of the role of dopantsin formation and distribution of Vos in themetal-doped CeO2 NCs [1].

References[1] 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 Mater. 203, 116473(2021).

118

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Oxygen vacancy formation in metal-doped CeO2
nanocrystals
1

Akira YOKO1 , Kazutoshi INOUE1 , Mitsuhiro SAITO2 , and Yuichi IKUHARA1,2,∗
Advanced Institute for Materials Research, Tohoku University, Sendai, Miyagi, 980-8577
2
Institute of Engineering Innovation, The University of Tokyo, Yayoi, Tokyo, 113-8656

We studied Cr-doped cubic {100}-faceted
CeO2 nanocrystals (NCs) with an average sizeof 7.8 nm fabricated by a supercritical water reaction. A considerably large amountof Ce3+ ions was detected in the Cr-doped
CeO2 NCs by scanning transmission electron
microscopy combined with electron energy loss
spectroscopy (EELS). The Cr dopants substituted the Ce sites in the amount of approximately 3 mol%. We experimentally observedthat the oxygen-storage capacity (OSC) was
substantially improved by a low amount of Cr
doping, which can be attributed to the low oxygen vacancy formation energy and high mobility of oxygen atoms by doping Cr in CeO2 .
Plane-wave basis density functional theory(DFT) simulations were performed by using
the VASP code to understand the eﬀects of
the Cr dopant on oxygen vacancy (Vo) formation. A Ce atom was substituted by one
Cr atom in the 96-atom 2 × 2 × 2 supercellof CeO2 (Ce32 O64 ) with a Monkhorst–Pack kpoint mesh of 4 × 4 × 4, which is equivalent
to the loading amount of Cr at 3 mol%. The
incorporation of Cr in 3+ charge state canbe compensated by the formation of an extra Vo (per two Cr3+ ions) or a Vo and a
Ce3+ ion while the oxidation of Cr-doped CeO2
NCs should create Cr4+ ions. Two Ce3+ ionswere located in the next nearest neighbor positions with respect to the Vo, consistent withprevious studies of CeO2 with DFT+U. The
Bader charge of the Ce3+ and Ce4+ ions was
set +2.11|e| and +2.44|e|, respectively. The
Vo formation energy (E(Vo)) in the Cr-doped
CeO2 was calculated as 0.99 eV, which wassubstantially decreased from 2.00 eV in the
non-doped case. The high OSC performancecan be attributed to the contribution of the valence change of Cr to E(Vo), and the structuraleﬀect of Cr doping on E(Vo). Only 3 mol%doping improved the OSC, suggesting that Cr
doping aﬀects the structure of CeO2 significantly. The results of layer-by-layer EELS
analysis indicated a signiﬁcant increase in theamount of Ce3+ by Cr doping particularly in
the internal atomic layers, which is more thanthe mere compensation of Cr3+ with Vos. The
low E(Vo) of Cr-doped CeO2 NCs can lead toa signiﬁcant increase of Ce3+ ions even with a
low amount of Cr doping, as observed in theexperiments.
In summary, DFT calculations demonstrated
that the Cr dopant reduces the E(Vo), resulting in the increase of the mobility of oxygen
atoms in the nano-sized CeO2 . The high concentration of Vos as well as the high oxygen
diﬀusivity improve the OSC performance of
Cr-doped CeO2 NCs, compared with the nondoped CeO2 NCs. These eﬀects provides a fundamental understanding of the role of dopantsin formation and distribution of Vos in themetal-doped CeO2 NCs [1].

References[1] 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 Mater. 203, 116473(2021).

119

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyovan der Waals density functional study of Cu phthalocyanine
adsorbed on the Au(110) surface
Yuji HAMAMOTO
Department of Precision Engineering, Graduate School of Engineering,Osaka University, Yamada-oka, Suita, Osaka 565-0871
The lowest molecular orbital (LUMO) plays

STM measurements [1]. The van der Waals

an essential role in the electronic transport(vdW) interaction between CuPc and Au(110) is

across a metal-organic interface. Since surface

taken account of by the vdW-DF method [2].

adsorption distorts the molecular structure,

Our calculated results indicate that CuPc

influencing the properties of LUMO, it is ofprefers to adsorb on the center of the Au adatoms

particular importance to understand the interface

with an in-plane rotation as shown in Fig. 1,

structure microscopically. Here we investigate

irrespective of the number of adatoms. The

the geometric and electronic structures at a

projected density of states (PDOS) onto themetal-organic interface of Cu phthalocyanine

doubly degenerate LUMO, labeled as eg(1) and(CuPc) on the Au(110) surface [1]. The (1! 2)

eg(2), of CuPc is plotted as a function of energy*+,-!.!/0ï#

missing-row reconstructed surface of Au(110) is
modeled by removing Au atomic rows from aperiodically repeated 6! 4 unit cell of the*+,-!.!/0ï#Au(110) slab composed of six atomic layers. A
CuPc molecule is adsorbed on a missing row, inwhich n Au atoms with n = 0, 2, 4, and 6 are*+,-!.!/0ï#*+,-!.!/0

ï#

added below CuPc to reproduce the finding ofFig. 1: Schematic views of CuPc on the missingrow reconstructed Au(110) surface with n = 4.

!(
!'
!&
!%
!$
!#
!"
!( !
!'
!&
!%
!$
!#
!"
!( !
!'
!&
!%
!$
!#
!"
!( !
!'
!&
!%
!$
!#
!"
ï"4&

/12#3
/12$3

n!)!"

!

!

!

!

!

!

!

n!)!$

!
n!)!&

!
n!)!(

ï"4$

"4"

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

"4(

"45

#4"

"4$
"4&
E!ï!E6!.!/0

The blue (red) balloons show the isosurfaces ofFig. 2: Density of states projected onto the eg(1)absolute square of eg(1) [eg(2)].

[eg(2)] orbitals of CuPc.

120

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

in Fig. 2, where the center of the peaks for thestates is enhanced for large n. Our results reveal

LUMO-derived states is lowered roughlythat the LUMO of CuPc is sensitive to themonotonically as n is increased, in gooddetailed structures of the reconstructed Au(110)agreement with the results of STS measurements.

surfaces.

The lowering of the peaks is qualitatively

References

consistent with lowering of the effective[1] H. Koshida, H. Okuyama, S. Hatta, T.

potential of the bare surfaces as a function of n.

Aruga, Y. Hamamoto, I. Hamada, and Y.

The splitting of the peaks suggests that the

Morikawa, J. Phys. Chem. C 124, 17696

hybridization between CuPc LUMO and surface(2020).

[2] M. Dion, H. Rydberg, E. Schröder, D. C.
Langreth, and B. I. Lundqvist, Phys.
Rev. Lett. 92, 246401 (2004).

121

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study of molecule/metal interfaces
Ikutaro Hamada
Department of Precision Science and Technology, Graduate School of Engineering,Osaka University, 2-1 Yamada-Oka, Suita, Osaka 565-0871
Carbon-basedasExperimentally, the DAPh molecule isgraphene and nanographene have attracted

thermally reacted into a cyclodehydrogenatedenormous attention, owing to their fascinating

diazulenopyrene (DAPy), but the reaction

electronic, optical, and magnetic properties. Forintermediate has not been determined. We

precise fabrication of nanographene, on-surface

performed extensive DFT calculations andsynthesis has been developed, in which

successfully identified the intermediate asprecursor molecules are thermally induced tohydro-diazulenopyrenyl (hDAPyr). By using areact on a surface, and the technique has been

Cu-terminal

proven to be powerful to fabricate graphene

cyclodehydrogenation of hDAPyr to form

based nanostructures. In this work, we propose

DAPyr. To understand the reaction mechanism,

an alternative method, in which a tip of scanning

we used a 10-atom pyramidal model Cu tip overtunneling microscopy/non-contact-atomic-force

hDAPyr and could reproduce the tip-induced

microscopy is utilized as a manipulable metal

cyclodehydrogenation reaction. Furthermore,catalyst, which activates cyclodehydrogenation

we clarified the detailed potential energy surfaceof hydrocarbons [1].

and by the electronic structure analysis, we

we

used

nanomaterials,

suchdiazuleno[1,2-c:2′,1′-

tip,

we

inducedtherevealed the electronic origin of the tip-inducedg]phenanthrene (DAPh), as well as 10,10′-

catalytic dehydrogenation reaction.

dibromo-9,9′-bianthracene (DBBA) adsorbed

References

on a Cu(100) surface, to demonstrate the tip-

[1] A. Shiotari et al: Nano Lett 20 (2020) 8339.

induced cyclodehydrogenation reaction. To[2] M. Dion et al.: Phys. Rev Lett. 92 (2014)

investigate the mechanism of the tip-induced

246401.

reaction, we performed atomistic simulations[3] https://statedoc.readthedocs.io/

based on density functional theory (DFT) with

[4] J. Wu and F. Gygi: J. Chem. Phys 136 (2012)

the van der Waals (vdW) density functional

224107.

(vdW-DF) [2] as implemented in our in-house[5] Y. Hamamoto, I. Hamada, K. Inagaki, and Y.

DFT code STATE [3-6], to describe theMorikawa: Phys. Rev. B 93 (2016) 245440.

interaction between organic molecule and metal[6] I. Hamada: Phys. Rev. B 89 (2014)

accurately.

121103(R).

122

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical study of oxygen-redox chemistry in spinel oxides
Atsuo YAMADA
Department of Chemical System Engineering,
The University of Tokyo, Bunkyo-ku, Hongo, Tokyo 113-8656
Oxygen-redox chemistry has recently paved

program and molecular orbitals were built witha path to develop large-capacity cathodemaximally localized Wannier functions usingmaterials for rechargeable batteries. Despite

Wannier90 code.

oxygen-redox

The presence of ionic Mg2+ in spinelcathodes, few studies have been reported for

LiMg0.5Mn1.5O4 brings labile O 2p states forthe oxygen-redox reaction in spinel oxides. In

oxygen-redox activity. However, in contrast

this work, we theoretically uncover the oxygen-with the dominant Mn-O interactions that could

redox behavior in the stable spinel framework

stabilize oxidized oxide ions in a typicalusing the density functional theory calculations.

lithium-rich layered oxide Li2MnO3, the spinel

We performed all calculations using Vienna

structure is dominated by O-O interactions near

Ab-initio Simulation Package. The projector-

the Fermi level, which are less able to stabilize

augmented wave method with a plane-wave

holes. Consequently, the spinel oxide isbasis set was used. We applied the U values ofpredicted to undergo structural degradation

4.84 eV and 3.90 eV for Mn in the spinel andmore easily during the oxygen-redox reactions.

vasteffortson

exploringlayered structures, respectively. The HSE06
hybrid functional was employed for calculating

References

electronic structures. The crystal orbital overlap[1] X.-M. Shi, E. Watanabe, M. Okubo, A.

population was computed with the Lobster

Yamada, Chem. Mater., 32 (2020) 7181.

Fig. 1 (a) Spinel LiMg0.5Mn1.5O4. Electronic structures of (b) spinel and (c) layered oxides.

123Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Order-disorder transition in ultrahigh-pressure phase of the
Na-Mg-F system
Koichiro Umemoto
Earth-Life Science Institute,Tokyo Institute of Technology, 2-12-1 Meguro-ku, Ookayama, Tokyo 152-8550
MgSiO3 bridgmanite with the orthorhombic

order-disorder transition has been predicted in I-

perovskite structure is a major constituent of the

42d-type Mg2GeO4 [6], a low-pressure analog oflower mantle of the Earth. It takes the post-

Mg2SiO4.

perovskite (PPV) structure near the core-mantle

In this study, we investigated the order-

boundary pressure (~125 GPa). The PPV phase

disorder transition in NaMg2F5 by firstis the final form of MgSiO3 in the Earth.

principles [7]. To deal with the order-disorder

However, at much higher pressures in “super-transition, we prepared as many configurations

Earths” which are exoplanets expected to be

as possible in a supercell of 64 atoms andterrestrial with masses much larger than thecalculated a partition function. Then, the order-

Earth, MgSiO3 PPV should undergo “post-PPV”

disorder transition temperature (Tc) can betransitions. So far, first principles studies haveobtained by locating the peak temperature ofpredicted the three-stage dissociation of MgSiO3

heat capacity calculated from the partition

PPV: MgSiO3 PPV → I-42d-type Mg2SiO4 +function. Our calculations showed that Tc is

P21/c-type MgSi2O5 → Mg2SiO4 + Fe2P-type

1500~2000 K over 20~100 GPa. The order-

SiO2 → CsCl-type MgO + SiO2 [1-3].

disorder transition was not taken into account in

NaMg2F5 is a low-pressure analog ofthe experiment [5]. We expect the disordered

MgSi2O5. Theoretically NaMgF3 PPV wasphase may show a better explanation of the XRD

predicted to dissociate into NaF and NaMg2F5

pattern in the experiment.

[4] and this prediction has been confirmed by aSince NaMg2F5 is the low-pressure analog ofrecent experiment [5]. There are two kinds of the

MgSi2O5, the order-disorder transition predicted

Mg sites. One of them is very similar to the Na

in this study is expected to occur also insite; both Na and Mg atoms are surrounded by 9

MgSi2O5 and will play an important role in

F atoms which form tricapped triangular prisms.

modeling interiors of super-Earths.

This similarity leads us to an idea of order-

The first principles calculations in this study

disorder transition at high temperature over thewere performed using the Quantum-Espresso

cation sublattice of Na and Mg atoms. A similar

package on the supercomputer (system B) at the124

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Umemoto and R. M. Wentzcovitch, JPS Conf.

Institute for Solid State Physics.

Proc. 4, 011002 (2015).

References[5] R. Dutta, et al.: Proc. Nat. Acad. Sci, 116,

[1] S. Q. Wu, et al.: J. Phys.: Condens. Matter 26

19324 (2019).

(2014) 035402.

[6] K. Umemoto and R. M. Wentzcovtich:[2] H. Niu et al.: Sci. Rep. 5 (2015) 18347.

arXiv:2012.08056.

[3] K. Umemoto et al.: Earth Planet. Sci. Lett.

[7] K. Umemoto and R. M. Wentzcovitch, in

478 (2017) 40.

preparation.

[4] K. Umemoto and R. M. Wentzcovitch: K.

125

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First principles study of effect of Al impurity on the post-postperovskite transitions
Koichiro Umemoto
Earth-Life Science Institute,Tokyo Institute of Technology, 2-12-1 Meguro-ku, Ookayama, Tokyo 152-8550
MgSiO3 bridgmanite with the orthorhombic

The presence of Al atoms decreases theperovskite structure is a major constituent oftransition pressure of the first dissociation.

the lower mantle of the Earth. It takes the post-

Considering effects of configuration entropy atperovskite (PPV) structure near the core-mantle

high temperature, Al atoms start to exist also inboundary pressure (~125 GPa). The PPV phase

MgSi2O5.

is the final form of MgSiO3 in the Earth.

Recently, we predicted a new temperature-

However, at much higher pressures in “super-induced order-disorder transition in I-42d-type

Earths” which are exoplanets expected to be

Mg2GeO4, a low-pressure analog of Mg2SiO4terrestrial with masses much larger than the[4]. The knowledge obtained in this study will

Earth, MgSiO3 PPV should undergo “post-PPV”

be utilized for the study in the post-PPVtransitions. So far, first principles studies havetransition at high temperature, which ispredicted

expected to occur in super-Earths.

thethree-stage

dissociationof

MgSiO3 PPV: MgSiO3 PPV → I-42d-type

The first principles calculations in this study

Mg2SiO4 + P21/c-type MgSi2O5 → Mg2SiO4 +were performed using the Quantum-Espresso

Fe2P-type SiO2 → CsCl-type MgO + SiO2 [1-3].

package on the supercomputer (system B) at

In real super-Earths, impurities may play animportant

role

in

the

above

the Institute for Solid State Physics.

post-PPVtransitions. In this study, we investigated theReferences

effect of Al atoms, one of major candidates of[1] S. Q. Wu, et al.: J. Phys.: Condens. Matter

impurities, on the post-PPV transitions. To do it,

26 (2014) 035402.

we prepared supercells of (Mg1-xAlx)(Si1-[2] H. Niu et al.: Sci. Rep. 5 (2015) 18347.

xAlx)O3,[3] K. Umemoto et al.: Earth Planet. Sci. Lett.

(Mg2-xAlx)(Si1-xAlx)O4, and (Mg1-

xAlx)(Si2-xAlx)O5, for x=0.25, 0.125, and 0.0625.

478 (2017) 40.

We found that Al atoms prefer to exist in[4] K. Umemoto and R. M. Wentzcovtich:

Mg2SiO4 after the fist post-PPV dissociation.

arXiv:2012.08056.

126

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles molecular dynamics study of water/TiO2
interfaces using hybrid functionals
Tatsuhiko OHTO
Graduate School of Engineering Science,
Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531
Density functional theory-based molecular

We employed the CP2K code [2], which is

dynamics simulations are increasingly being

based on the mixed Gaussian and plane wave

usedbasis sets. The simulation of the water/TiO2

forsimulating

aqueousinterfaces.

Nonetheless, the choice of the appropriate

interface is on-going.

density functional, critically affecting theoutcome of the simulation, has remained
arbitrary. Here, we assess the performance ofvarious exchange-correlation (XC) functionals,
based on the metrics relevant to sum-frequency
generation spectroscopy. The structure anddynamics of water at the water-air interface aregoverned by heterogeneous intermolecularinteractions, therefore providing a criticalbenchmark for XC functionals. We find that the
revPBE and revPBE0 with the dispersion

Fig. 1: The ability of different functionals tocorrection show excellent performance. The

accurately predict water properties is directly

poor performance of the empirically optimized

compared. The smaller (larger) score 𝜅density-functionalcorresponds to better (worse) predictive power(M06-L)

manifests

theimportance of satisfying exact functionalof the functional [1].

condition. Understanding the performance ofdifferent XC functionals can aid resolving theReferences

controversial interpretation of the interfacial[1] T. Ohto et al. J. Phys. Chem. Lett. 10, 4914

water structure and direct the design of novel,(2019).

improved XC functionals better suited to[2]

describe the heterogeneous interactions in

http://cp2k.berlios.de/condensed phases. [1]

127

The

CP2K

developersgroup,

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab Initio Band Structure Calculation of InAsSb
Using VASP Based on Hybrid Density Functional Theory
Hiroki I. FUJISHIRO, Yoshitaka MATSUMOTO, and Akira ENDOH
Department of Applied Electronics,
Tokyo University of Science, Niijuku, Katsushika, Tokyo 125-8585
In 2019, we carried out ab initio band

The terahertz band (0.1 to 10 THz) is the

structure

capacity communications and sensing systems.

compressively strained InSb using Vienna Ab

Sb-based high electron mobility transistors

initio Simulation Package (VASP) based on the(HEMTs) are one of the most promising

method in the local density approximation todevices that can operate in the terahertz band.

obtain band parameters [5]. We used the hybrid

In our previous works, we developed InSb [1,coefficient of the density functional [6]. The

2] and GaInSb [3] channel HEMTs. In order tohybridachieve higher speed operation of HEMTs, it ismodification

desirable that the electron effective mass in the

Ernzerhof 0). The functional is constructed bychannel semiconductor is lighter and thethe mixing of a fraction 𝛼 of the Fock exchange

electron concentration in the channel layer iswith a fraction 1 − 𝛼 of the PBE exchange. The

higher. InAsSb is a semiconductor that satisfies

exchange-correlation

the above conditions [4].

expressed by the following equation:

Bandgap energy, Eg [eV]main radio resource for future high-speed large-

calculations

functional
of

of

used

unstrained

in

PBE0

energy0.4
Eg = 0.7191x2 - 0.5257x + 0.159

0.3
0.2
0.1
0.0
0.0

0.2

0.4
0.6
InAs content, x

0.8

Fig. 1: InAs content x dependence of bandgap energy 𝐸 .

128

1.0

[6]

was

and

a

(Perdew-Burke-

𝐸

can

be

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo(1)

mass in the  valley 𝑚∗. The x-dependence ofis the𝑚∗shows a tendency similar to that of 𝐸 . The

PBE𝑚∗ values of InAsxSb1-x at x = 0.25 and 0.50 are

correlation [6]. We obtained the bandgap

lighter than that of InSb. It is well known thatenergy 𝐸 closest to the literature value by

the 𝑚∗ in InSb is the lightest among group III-using 𝛼 = 0.21 for InSb. In this work, we

V compound semiconductors. According to theapplied this method to InAsSb to explore thecalculations in this study, the 𝑚∗ in InAsSb ispotential of InAsSb channel HEMTs.

lighter than that in InSb depending on the InAs

𝐸

= 𝛼𝐸 + (1 − 𝛼)𝐸+𝐸

where 𝐸 is the Fock exchange, 𝐸
PBE

exchange,

and 𝐸

is

the

First, we applied this method to InAs. We

content. Therefore, InAsSb channel HEMTs

obtained the 𝐸 closest to the literature one byhave a potential to be the fastest of all HEMTs

using 𝛼 = 0.24 . We carried out the bandusing group III-V compound semiconductors.

structure calculations of InAsxSb1-x at x = 0.25,

Referencesused linearly interpolated values. Figure 1[1] K. Isono et al.: Proc. CSW2016, WeD1-5.

shows the InAs content x dependence of[2] N. Oka et al.: Abst. TWHM2017, p. 83.

bandgap energy 𝐸 . The x-dependence of 𝐸 is[3] K. Osawa et al.: Abst. TWHM2019, p. 53.

not linear and shows a downwardly convex[4] O. Berolo et al.: Phys. Rev. B 8 (1973) 3794.

dependency. We obtained the electron effective[5] H. I. Fujishiro et al.: Activity Report 2019,

masses 𝑚∗’s in the  valley of InAsSb from thep. 153.

calculated band structures. Figure 2 shows the[6] T. Garwood et al.: Infrared Physics &InAs content x dependence of electron effective

Technology, 2017.

Electron effective mass,
m*/m00.50, and 0.75. For the 𝛼 values of InAsSb, we

0.020
m* = 0.0309x2 - 0.0217x + 0.0091

0.015
0.010
0.005
0.000
0.0

0.2

0.4
0.6
InAs content, x

0.8

1.0

Fig. 2: InAs content x dependence of electron effective mass in  valley 𝑚∗. 𝑚 is electron rest
mass.

129

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

DFT calculation of atomic displacement captured by energy
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
3AdvanceSoft Corporation, Tokyo 101-0062

IMaSS, Nagoya University, Nagoya, Aichi 464-8601

In the last two decades the conservative andbond formation in an alternative atomic

non-conservative (dissipative) force interactions

configuration of the Si surface atoms, including

between a tip and a sample in proximity have

the Si atom at the apex of AFM tip. In this study,

been intensively examined by non-contact

to elucidate the phenomena, the surface

atomicIndiffusion potentials of a Si adatom wereparticular, the channel of nc-AFM to measurecalculated using real-space density functional

the energy dissipation through the non-theory (RSDFT) [2] when the Si tip was brought

conservative

beencloser to the Si(111)-(7×7) surface. RSDFT is aregarded to have great potential to explore nano-first-principles program developed by Oshiyama

mechanical phenomena; the dissipation channel

and Iwata, which uses a real-space difference

gives the change in the amount of mechanicalmethod and a pseudopotential method.

force

microscopy

force(nc-AFM).

interactions

hasenergy to maintain the constant oscillation

First, we optimized the structures of aamplitude of an AFM cantilever. We had

Si(111)-(7×7) reconstructed surface consisting

experimentally found that, when the nc-AFM

of 298 Si atoms and 49 H atoms and a [001]image showed the high resolution for theoriented Si tip by RSDFT. Then, while the tip

individual adatoms on a Si(111)-(7×7) surface,

was placed over the hollow site and brought

the simultaneously obtained energy dissipation

closer from 5.0 Å to 3.0 Å, the surface diffusion

signal increased in close proximity over the

potentials for a corner Si adatom were calculated

hollow sites surrounded by a Si adatom and a Si

from the original position of the Si adaom to therest atom with a dangling bond per each [1].

neighboring hollow site. It is known that theBased on the experimental results, the dynamic

hollow site is a meta stable site for the adatom,

atomic processes responsible for the dissipationand there is a diffusion barrier between the

had been discussed in regard to breaking of theoriginal adatom site and the hollow site. Our

backbonds of the Si adatom and subsequentcalculations indicated that the diffusion barrier

130

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyoheight was lowered as the tip was approached.
However, we did not obtain the evidence forpromotion of the adatom diffusion from theadatom site to the hollow site only by bringing
the tip closer. Next, we calculated the structurechanges and the forces for two cases: the Si atomon the original adatom site or on the hollow sitewith the tip approaching over the hollow site, as
shown in Fig. 1. Even for the Si atom on the moststable adatom site, when the tip approaches thehollow site, the Si atom was lifted up (Fig. 1(a–e)). But the Si atom did not move to the hollow
site even when the tip was closer from a heightof 3.0 Å (Fig. 1(e)). For the Si atom on thehollow site, it was found that the strong force
acted between the tip Si atom and the Si atom on
the hollow site (Fig. 1(f–j)), as a result ofbonding formation between them. The paper ofthis study is under preparation.
Fig. 1 Calculated structures of Si(111)-(7×7)
reconstructed surface and [001] oriented Si
tip. (a–e) For the Si on the adatom site,
denoted by the red circles. (f–j) For the Si on
the hollow site. The number shown with theunit of Å shows the vertical separation
between the tip atom and the Si atom on thesite.

References[1] T. Arai, R. Inamura, D. Kura, and M.
Tomitori, Phys. Rev. B 97, 115428 (2018).
[2] J.-I. Iwata, D. Takahashi, A. Oshiyama et al.,J. Comput. Phys. 229, 2339 (2010).

131

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Construction of magnetic materials database by
KKR Green’s function method
Tetsuya FUKUSHIMA
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

We have developed an automatic exhaustive calculation tool which is based on the
Korriga-Kohn-Rostoker coherent potential approximation (KKR-CPA) method. Our tool
can explore the huge materials space consisting of disordered systems and construct largescale materials databases. In this year, we implemented a new feature in our tool, where
electronic structures, magnetic properties, andtransport properties at finite temperature canbe calculated [1].
In order to calculate electronic structuresat finite temperature, we incorporate the effects of local phonon excitations and spin-wave(magnon) excitations in the framework of the
KKR-CPA method. In the KKR Green’s function method, the single-site t-matrix is the sumof the coefficients of partial wave expansion ateach atomic position and contains informationof the single-site scattering effect. We can thus
replace the multiple scattering effect by an effective medium potential using CPA. We treat
local phonon excitation and magnon excitation
as the configuration average with respect to the
local phonon displacements and local moment
disorder (LMD) states, respectively.
For CPA calculation of the local phonon excitation, the probabilities of the atomic displacements must be known. Here, we employ an alloy-analogy model. The single-sitet-matrix changes responding to the atomic displacements and has to be determined selfconsistently. In this case, it is convenient toexpand each single-site t-matrix centered on

the displaced position for self-consistent calculation. However, later, we must re-expand thedisplaced single-site t-matrix to partial waves
centered on the undisplaced atomic position,and transform the scattering matrix for the
displaced potential into that defined with respect to the regular lattice position. Thisis possible because the effect of atomic displacement on the electronic structure is local.
Accordingly, the backscattering term of theGreen’s function referring to the regular latticeis also obtained. In the present calculations,
we take six directions (i.e., {0,0,1} cubic directions) into consideration for the local phonon
displacements of each atom.
To handle the magnon excitation, we use the
LMD model. When the temperature increases,
the spin tilts slightly away from the directionof the magnetization, and its effect propagatesto surrounding spins, namely, spin-wave excitation. We consider the configuration average of the linear combination of the spin flips
at every site. This model is called the LMD
state. We estimate it from the decrease in the
spontaneous magnetization observed in the experimental data. For Co2 MnSi, for simplicity,
we assume that the decrease in the magnetization originates solely from the spin-flip in
the Mn atoms, and construct the LMD modelas Co2 Mn↑1−x/2 Mn↓x/2 Si, where Mn↑ and Mn↓denote the up and down magnetic moments,
respectively. For instance, the magnetization
ratio between 0 K and 300 K is 0.983. We
thus assume that 0.85% of the spins are re-132

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

verse while the others are unchanged at 300 K(Co2 Mn↑0.9915 Mn↓0.0085 Si random alloys).
Moreover, we calculate the conductivity using the Kubo-Greenwood formula including
vertex correction, in which the vertex functions
are expressed using the ladder-like approximation. The conductivity tensor is defined as follows:σµν1
lim [σ̃µν (ε + iη, ε + iη)
4 η→0+ σ̃µν (ε − iη, ε − iη)=− σ̃µν (ε + iη, ε − iη)− σ̃µν (ε − iη, ε + iη)].

(1)Here, ε is energy and iη is an infinitesimal
imaginary part. Note that σµν depends on ε.
Moreover, σ̃ is calculated byh̄
Trhjµ G(z1 )jν G(z2 )iCPA ,πN Ω(2)
where N is the number of unit cells, Ω is theunit cell volume, and jµ(ν) is the current operator. The bracket indicates the configuration
average for the disordered systems by CPA.
Figure 1 shows the the temperaturedependent electrical resistivity of Co2 MnSi using the Kubo-Greenwood formula. The resistivity of Co2 MnSi derived from a local phononis proportional to the temperature except in
the low-temperature region. The resistivity
originating from the magnon scattering reflects the experimentally observed magnetization curve. We determined that either local
phonon displacement or LMD alone was insufficient to reproduce the experimental data.
This is expected because at low temperatures,
scattering due to lattice vibration and spin
fluctuation is suppressed, and impurity scattering becomes dominant. It is known that
there are considerable native defects in Heusler
alloys, such as vacancies, interstitials, and antisite defects. For Co2 MnSi, previous works suggest the presence of antisite disorders between
Co and Mn. Scattering effects from these antisite defects may be the main source of theσ̃µν (z1 , z2 ) = −Figure 1: Temperature dependent electricalresistivity estimated by the Kubo-Greenwood
formula.
finite resistivity at low temperature. Therefore, we attempted to calculate the resistivities
considering the Mn-Co antisite disorders. Antisite effects can be easily added to the calculation in the framework of CPA. If we assume
that 1.0% of the Mn-Co antisite disorders (i.e.,(Co0.995 ,Mn0.005 )2 (Mn0.990 ,Co0.010 )Si) is introduced, the calculated residual resistivity is 6.47µΩcm. This value is consistent with the experimental results at extremely low temperature. The pink stars in Fig. 1 represent the calculated temperature-dependent resistivity of
Co2 MnSi when the Mn-Co disorders are included in addition to local phonon and magnon
disorders. The result is in reasonable agreement with the experimental results. Therefore,
it can be concluded that to accurately calculate the finite-temperature transport properties of Co2 MnSi, three disorders (local phonon,
magnon, and Mn-Co antisite disorders) should
be considered in the comprehensive procedureon the basis of CPA.

References[1] H. Shinya, S. Kou, T. Fukushima, A.
Masago, K. Sato, H. Katayama-Yoshida,and H. Akai, Appl. Phys. Lett. 117 (2020)
042402.

133

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Hybrid Ab-Initio/Machine-Learning Optimization of Nano Interfaces
and Molecular Structures
Kenji TSURUTA, Md. Abdullah Al ASAD, Kyosuke SATO,
Masaaki MISAWA, 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
Designing and developing functional
materials/molecules often require vast searchingof target properties from extra-large data set,
which is far out of the capability of conventional
computing algorithms. In recent years, theDeep-Learning (DL)-based molecular design
methods have been extensively studied.
Recently, we have reported [1] a machinelearning method for predicting molecularproperties by mapping a graph representation ofa molecule to a latent variable space and bylinking the variable to physical property of themolecule. Representing molecules in the latent
space enables an efficient property search within
existing data, because the DL model transforms
the discrete representation of a molecular graphinto a continuous variable space suitable forvarious numerical algorithms.
In the present study, we further improve theoutput rate of valid SMILES of decoder byintroducing a discriminator attached to the VAE
stream. Adopting a molecular-mechanics
method to calculate 3D structure from SMILES,
we can optimize physical properties of themolecule by other simulation methods such as
density-functional-theory calculations evenwhen there is not enough data set. The range ofphysical property space covered by the SMILES
representation is thereby expanded and the datadriven optimization using Kernel Ridge
Regression method can be performed within the
search space. We have demonstrated theeffectiveness of this method for optimizing amolecular HOMO-LUMO gap as an example.
Another effort is taken to perform efficient
search for insertion/reaction path of anmolecules on the surface of a functional
materials. We computationally investigate aninsertion process of water into themethylammonium lead halide perovskite(MAPbI3). The rapid decomposition of MAPbI3

reaction with water has been recognized to be amajor obstacle to its solar-cell applications. To
overcome this drawback process, it is important
to identify the initial stage of water insertion into
the MAPbI3. The first-principles calculation
based on the density-functional theory is
performed to investigate the water insertion
process on outer surface layer of MAPbI3 slab
model. Using the Nudged Elastic Band method,
we find that the initial insertion process follows
the three steps: approaching, re-orienting andfinally sinking into the perovskite layer. This
process requires approximately 0.60 eV toovercome an energy barrier, which agrees withan in-situ X-ray diffraction (XRD) measurementof the reaction threshold of water molecules with
the MAPbI3 crystal at room temperature [2].
These computations have been done in part byusing the Super-computing System at SCC-ISSP

Fig. 1 Insertion path of water molecules in the MAPbI3
surfaces and barrier energy variation along the path.

References[1] K. Sato and K. Tsuruta, Mater. Sci. Forum
1016, 1492 (2021).
[2] M. Hada, M. A. A. Asad, M. Misawa, Y.
Hasegawa, R. Nagaoka, H. Suzuki, R.
Mishima, H. Ota, T. Nishikawa, Y. Yamashita,
Y. Hayashi, and K. Tsuruta, Appl. Phys. Lett.
117, 253304 (2020).

134

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Investigation on the electronic structure ofphoto-catalytic double-perovskite
Kazume NISHIDATE
Faculty of Science and Engineering, Iwate University
Ueda 4-3-5, Morioka, Iwate 020-8551

In recent experiments, a signiﬁcant band
gap widening was observed when Sb was
substituted for Bi in the double-perovskite
Ba2 PrBiO6 .
In this work, we study aseries of double-perovskites, Ba2 BiIII BiV O6 ,Ba2 PrBiO6 , and Ba2 PrSbO6 using the ﬁrstprinciples density functional theory with the
Heyd-Scuseria-Ernzerhof hybrid functional toinvestigate the substitution eﬀect on the structural and electronic properties [1].
We use the density functional theory (DFT)
as implemented in the Vienna ab-initio Simulation Package (VASP) and the projector augmented wave (PAW) potentials to study the
structural and electronic properties of the double perovskite. We use the Heyd-ScuseriaErnzerhof hybrid functional (HSE06) to account for the strong correlation eﬀects of thesystem. We use an energy cutoﬀ of 500 eV for
plane wave basis set together with a 6×6×6
k-point grid. The rather high energy cutoﬀ
and dense k-point grid are necessary to predict
correctly the crystal structures in the HSE06
computations. Equilibrium crystal structures
were achieved so that the maximum force component was smaller than 1 meV/Å3 , and the
maximum stress component smaller than 1
meV/Å3 .
In a monoclinic system, the shape of theBrillouin zone depends non-trivially on the lattice vectors. In fact, there are ﬁve possible
shapes of Brillouin zones for the monoclinic
crystal structure depending on the choice oflattice vectors. Where we choose the C2/m

which corresponds to the MCLC1 lattice. To
generate the set of k-points along the edges of
the Brillouin zone, we use the code pymatgen. We show the obtained band structure in
the Figure 1.

Figure 1: Band structure and density of states
curve of Ba2 BiIII BiV O6 . Fermi level is at 0 eV.
We ﬁnd that the BiIII 6s states at the top ofvalence band of Ba2 BiIII BiV O6 vanish on the
Pr substitution for Bi at B ′ III -site. When Sb
is substituted for Bi at B ′′ V -site, the BiV 6s
states at the bottom of the conduction band
vanish causing additional widening of the band
gap.

References[1] K. Nishidate, A. Adiko, M. Matsukawa,
H. Taniguchi, A. Sato, A. Matsushita,
S. Tanibayashi and M. Hasegawa, Mater.
Res. Express 7 (2020) 065505.

135

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Studies on electronic structures and optical properties internary oxide crystals
Takayuki Makino
Research Center for Development of Far-Infrared Region,
University of Fukui, Bunkyo Fukui, Fukui 910-8557
Lithium niobate ternary compound is
known

to

exhibitseveralupward convex in the 1.5－4-eV range (notinteresting

shown in a figure). This feature is in good

properties such as superconducting behavior
underdelithiatedunderstandingsforphase.
thisagreement with the experiment [3].

Deepercompoundareimportant from both technological and basic
viewpoints [1]. In this research, we intend tocompare calculation results on the complex
dielectric function and experimental data.
We

used

the

Quantum-ESPRESSO

package to optimize the crystal structure andperform the band structure calculations. In
this work, we used a set of the optimized
norm-conserving

pseudopotentials.

The

corresponding activity diagram is shown at
the right hand side.

We confirmed that

evaluated bandgap energy (BGE in the figure)is similar to that evaluated by Ylvisaker etal[１].

References

We then moved into study on opticalproperties. For the optical spectra calculations[1] Erik R. Ylvisaker and Warren E. Pickett:such as dielectric functions, we used Respack

Phys. Rev. B 74 075104 (2006).

ab-initio[2] K. Nakamura et al., arXiv:2001.02351

package[2].

Neglecting

contributions from the optical anomalies,(2020).

overall ε1(ω) in the calculated spectrum is a[3] T. Kurachi et al., J. Appl. Phys., submitted.

monotonicallydecreasing

function

with

136

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Vacancy cluster stabilization by impurities and theirmigration property in tungsten
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 binding energies of impurities to vacancy

candidates for plasma facing materials (PFMs)

and stabilization of di-vacancy by the impurities

used in fusion reactors because of their excellent

were calculated in terms of first-principle

properties, e.g. high melting point, low hydrogencalculations based on density functional theory.

(H) solubility, and toughness for irradiation.

We used the Vienna ab-initio simulation package

However, a large amount of H and H isotopes(VASP). A large simulation cell, composed ofare retained in vacancy (V) and vacancy type6x6x6 bcc lattice (432 atoms), were used inlattice defects in W specimen nucleated underorder to reduce the effects of periodic boundary

the irradiation circumstance. In particular,

condition imposed on the simulation cell. The

tritium (T) retention in the PFMs is a serious

cut-off energy of plane wave was 520eV.

problem for safety operation of fusion reactors.

The binding energy of impurity (X) to

So, the control of the vacancy type lattice defects

vacancy (V) was defined as

is important subject in the field of PFMs.

Eb(VX)=E[V]+E[X]-{E[VX]+Eref},Vacancy clusters and their interaction with

where E is cohesive energy of the supercell

impurities included in W are investigated bycontaining V, X and vacancy-impurity complex

experimental

methods.

XV, and Eref indicates energy of perfect lattice.

According to first-principle calculations, di-Similarly, the binding energy between VX and V,

vacancy (V2) in W are unstable compared withstabilization of di-vacancy by impurity, wasisolated vacancies. However, the di-vacancy anddefined as

andcomputational

growth of vacancy clusters in W materials were

Eb(V2X)=E[VX]+E[V]-{E[V2X]+Eref}.

observed in positron annihilation lifetime

Positivebinding

spectroscopy.

attractive

interaction.

In

the

presentwork,

weenergycorresponds

Besides,tomigration

investigated the stabilization of di-vacancy byenergies (Em) of impurities and vacancy were

impurities contained in the W specimen.

estimated by nudged elastic band (NEB) method.

137

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Results

Discussion

We investigated interaction of vacancy with

Let’s consider the stabilization of di-vacancy

interstitial type impurities, i.e. hydrogen (H),by the interstitial impurities. W specimen for the

carbon (C), nitrogen (N), and oxygen (O). As

positron annihilation lifetime spectroscopy werelisted in Table I, the four impurities can beprepared in water coolant circumstance, so

accommodated in a W vacancy, because theimpurities of low migration energy (H and O)

binding energies Eb(XV) are positive. While, thewere possible to migrate in the specimen andinteraction between two vacancies is repulsive,

trapped in W vacancy to form vacancy-impurity

that is, Eb(V2)= -0.13eV. According to Eb(V2X),

complex VX. On the other hand, vacancy

all impurities stabilize di-vacancy in W.

diffusion was observed at about 623K, which

However, the stabilization effect of H is quite

corresponds to migration energy for W vacancy

small compared with those of other impurities.

(1.69 eV). The binging energies of H and O to

Fig. 1 shows barrier height of the impurities

vacancy were estimated to be 1.22 and 3.04 eV,and vacancy along the migration paths. The

respectively. Therefore, we infer that VO

migration energies for H and O are quite small

complex is stable at the vacancy diffusioncompared with those of C and N. The reason istemperature, while VH complex may bethat H and O are located at tetrahedral interstitialdissociated at the temperature. Therefore, O is

sites, while C and N are located at octahedral

still accommodated in W vacancy at the vacancy

interstitial sites. Therefore, the migration paths

diffusion temperature. O is the most plausible

between neighboring interstitial sites of H and O

candidate for di-vacancy stabilization among theare shorter than those of C and N.

interstitial impurities contained in W specimen.

Table I: Binding energy of impurity tovacancy Eb(VX), stabilization of di-vacancy
by impurities Eb(V2X), and migrationenergy of impurities and vacancy Em.

Fig. 1: Barrier height of each impurity andvacancy along migration path.

138

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Optical gaps of metastable Ga2O3 and GaN
with impurity doping effectKen-ichi SHUDO
Fac. of Eng/Sci, Yokohama Nat’l Univ.
Tokiwadai 79-5, Hodogaya-ku Yokohama 240-8501
Electronic state of Mg-doped GaN was
calculated using VASP package based on local
density approximation. In contrast to the moststable phase of a well-studied wurtzite GaN,
thin films of haekelite phase (4|8-GaN) aresuggested to show stable p-type semiconductor
even with the dope.
At the same time, we calculated spindependent

electronic

structure

of

two-

dimensional spin network of organic molecule
array,
(MOF)

made

of

metal-organic−framework

fromCl[5,10,15,20-tetra(4-carboxyphenyl)-porphyrin] TCPP with Mn(II)and Fe(III) at the center hole. Spin-resolved

Fig 1．Calculated electronic states

density of states for several spin-polymorph areof an isolated molecule (top), andobtained, as in Fig.1, and photo-absorption

MOF structures of Fe-TCPP forspectra were calculated. These results suggests

ferro-magnetic

that several spin states would coexist because

antiferromagnetic structures, andthe eigenenergies were mutually very close, andthethat ferrimeagnetic phase could be discernible

ferrimagnetic states.

latterandconvergesatwhen the system is cooled. The optical results
are consistent with our experimental findings

photo-transition in the intramolecular spinby means of magnetic circular dichroism

states, and some signals do from Cu-ions that

(MCD) of optical transmission spectroscopy.

link the molecules in MOF formation.

The observed MCD signals originate from the139

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Optical gaps of metastable Ga2O3 structuresmodulated by impurity dope
Ken-ichi SHUDO
Fac. of Eng/Sci, Yokohama Nat’l Univ.
Tokiwadai 79-5, Hodogaya-ku Yokohama 240-8501
Ga2O3 has good electrical conductivity, andits wide bandgap of 4.8 eV offers great
potential for various applications. The most ofresearches of this oxide material are limited
within the most stable βphase. We previously
reported optical spectra [1] of κ- and εGa2O3 , which is widened by Co-doping. Thechange in the electronic states due to this Co
impurity was calculated (Fig.1) to clarify theexperimental photo-absorption.
The photo-absorption in Ga2O3:Co isFig.1: The density of state of Ga2O3:Co.

difficult to be simply associated to theBlue thin curve is the density projected tobandgap of oxide material. But the adjustable

Co impurity.

shift of the cutoff in the photo-absorption is
accounted by the theoretical calculation in thisstudy.

The change of the experimental

workfunction due to the Co doping was also
explained with a band diagram ofε-phase in
Fig. 2. In this phase n-type pinning occurs due
to unintentional impurities such as Si and Ge,
as is intrinsic especially ε-phase, and Ovacancy less contributes.

Fig.2:

Calculated

photoabsorption[1] K. Mukai, A. Tsuno, K. Shudo, and H.

modulated by the Co-impurity dope.

Otani, Jpn. J. Appl. Phys. 58, SBBK05 (2019).

This accounts for the experimental
optical spectra.

140

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Eﬀects of electron–phonon and electron–magnon
scattering on ﬁnite temperature magnetic properties
H. Akai
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

The eﬀects of phonons are taken into account through random displacements of atoms
around their equilibrium positions. The average displacements are estimated from either
the Debye model or ﬁrst-principles phonon calculations: no notable diﬀerences between thetwo was found. The eﬀects of magnongs,
on the other hand, are calculated by randomly ﬂipping the local magnetic momentswith probability determined self-consistently
at each temperature. All the calculations were
performed in the framework of ﬁrst-principles
calculation using KKR-CPA [1].

becomes remarkable in the case of Nd2 Fe14 B
permanent magnet materials. Some examples
of calculated TC are given in Table 1. The ﬁrst
column indicates the temperature in which theaverage displacement due to phonons is calculated. The experimental value of TC is 585K.
Figure 1 shows the calculated magnetizations of Nd2 Fe14 B. Both the eﬀects of phonsand magnons are included. The theoreticalcurve shows a weak ﬁrst-order transition at themagnetic transition temperature, which occurs
as a result of electron–phonon coupling. The
temperature is scaled so that TC reproduces
the experimental value of 585K although thescaling factor is close to 1. The calculated results are fairly consistent with experiments is
concluded.
40
Nd2Fe14B M(T)M (T) (µB/f.u.)

There are several kinds of excitations thathave to be taken into account when discussing
ﬁnite temperature magnetic properties of magnetic materials. Among them are phononsand magnons. Usually, single electron excitations at Fermi surfaces do not contributesigniﬁcantly to the magnetic properties at
the assumed temperature range of 0 ∼1500K.
We have studied the eﬀects of phonons andmagnons on ﬁnite temperature magnetism,targeting at permanent magnet materials.

30

20
thoeryexperiment
Kuz'min

10

00

In the case of bcc Fe, there is a signiﬁcant effect of electron–phonon scattering on the Curie
temperature TC , while that of magnons is notprominent. The eﬀect of magnons, however,Table 1: Calculated TC
phonons only plus magnons
0K
500K

1062K
1198K

100

200

300

400

500

600

Temperature (K)Figure 1: Calculated and experimental magnetizations vs. temperature of Nd2 Fe14 B

References

561K
548K

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

141

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Magnetic properties of(Sm1−xZrx)(Fe0.75Co0.25)11+y Ti1−y rare-earth magnetic
materials
H. Akai
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

Figure 1 shows the calculated magnetizations as functions of temperature where theCurie temperatures are scaled so as to fit theexperimental ones. More precisely, first theCurie temperatures, which are not necessarily known experimentally, are estimated by fitting the temperature dependence of magnetic
moment by Kuz’min’s empirical formula. On
the other hand, the theoretical Curie temperatures are obtained by first-principles calculation using KKR–CPA[1]. Theoretical temperature dependence of magnetization is then obtained again using Kuz’min’s formula. Finally,
the temperatures are scaled using experimentally estimated Curie temperatures.
The crystalline magnetic anisotropy constant K1 of (Sm1−x Zrx )(Fe1−y Coy )11.5 Ti0.5 isalso calculated. Since the treatment for 4f
states of Sm is still rather controversial, we

142neglect the contribution of 4f to magnetic
anisotropy through hybridization, adopting an
open core treatment. These results indicatethat adding Co improves the magnetization although it degrades the magnetic anisotropy. Zrslightly contributes to improve the magnetization but not much to the anisotropy. Main
contribution of Zr must be that to structural
stabilization.
2.0(R1-xZrx)(Fe0.75Co0.25)11+yTi1-y

1.5

JS (T)

Rare-earth permanent magnet materials of
SmFe12 family attract much attention because
expected performance using NdFe12 family asa main phase of permanent magnets has beenrecognized as hardly reached. Much work has
been done to seek better intrinsic magnetic
properties for SmFe12 by adding some elements
as ingredients. In this study, we have tried several SmFe12 family cases, which are implied
from experiments to be possible candidates
for permanent magnet materials. Finite temperature properties, including the magnetizations, Curie temperatures, and magnetocrystalline anisotropy, were examined.

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
0

200

400
600
Temperature (K)

800

1000

Figure 1: Temperature dependence of magnetization of various systems of SmFe12 family.

References[1] H. Akai, AkaiKKR, http://kkr.issp.
u-tokyo.ac.jp/ (2002).

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical Analysis of Photocatalytic Reaction Mechanism atTitanium Dioxide Interfaces
Tatsuya JOUTSUKA
Institute of Quantum Beam Science,
Graduate School of Science and Engineering, Ibaraki University, Hitachi, 316-8511 Ibaraki,Japan
We have studied the reaction mechanism ofphotocatalytic

TiO2bare surface but at the hydroxylated surface,surfaces [1] using cp2k program package

especially at the hydroxyl group of the(MPI parallelization with multiple threads). We

hydroxylated (112) and (001) surfaces. The

focused on the energetics and structure duringexperimental

the hole migration. This is a collaborative work

consistently elucidate the high photocatalytic

withactivity at the anatase TiO2(112) surface.

theYamauchioxidationatexperimentalistat

Ibarakianatasephotogenerated hole is stably trapped not at the(Prof.

Satoshi

University),

who

and

theoreticalfindings

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
by low-pressure chemical vapor deposition.
The deposition rate is three times higher thanthat of the multi-orientation layer on the Pylex

Fig. 1: Molecular mechanism of hole migration.

glass. The photocatalytic activity induced byultraviolet (UV) irradiation around 365 nm in

References

methylene

is[1] T. Joutsuka, H. Yoshinari, and S. Yamauchi:

significantly high. The density functional

Bull. Chem. Soc. Jpn., 94 (2021) 106–111.

theory (DFT) calculations using the constrained(Selected Paper, Inside Cover, Open Access).

DFT method [2] and the hybrid functionals[2] T. Joutsuka and K. Ando: J. Phys. Chem. B,

show that the (112) surface stabilizes the

124 (2020) 8323–8330.

blue

aqueoussolutionsadsorbed water molecule most strongly. The

143

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab Initio Calculation of High-Rate Deposition of Metal Films
by LowPressure Chemical Vapor Deposition
Tatsuya JOUTSUKA
Institute of Quantum Beam Science,
Graduate School of Science and Engineering, Ibaraki University, Hitachi, 316-8511 Ibaraki,Japan
We have studied low-pressure chemical

our calculations to analyze the dynamical

vapor deposition of Cu on Ru substrate using

properties by the constrained DFT[3] and the

CuI [1] using cp2k program package (MPI

dynamical reaction path analysis.[4]parallelization with multiple threads). This year,
we focused on the ab initio calculation ofdesorptionofby-products.

This

is

a

collaborative work with the experimentalist [2](Prof. Satoshi Yamauchi at Ibaraki University),
who conducted the LPCVD experiment.
In this study, we elucidated the molecularmechanism of Cu deposition using copper(I)iodide (CuI) on Ru substrate by low-pressurechemical vapor deposition through electronic

Fig. 1: Molecular mechanism of LPCVD of Cu.

structure calculations. Figure 1 shows themolecular mechanism of Cu deposition by the

References

LPCVD method. Using density functional[1] T. Joutsuka, S. Yamauchi: Chem. Phys. Lett.

theory (DFT) molecular dynamics (MD)741 (2020) 137108.

simulations, we show that CuI molecules[2] T. Nishikawa, K. Horiuchi, T. Joutsuka andadsorb and decompose exothermically due to a

S. Yamauchi: J. Cryst. Growth, 549 (2020)strong adsorption of iodine atoms onto the125849.

Ru(001) surface. The rate-limiting step of the[3] T. Joutsuka and K. Ando: J. Phys. Chem. B,

Cu deposition is found to be the desorption of

124 (2020) 8323–8330.

iodine atoms or molecules from the Cu(111)[4] T. Joutsuka and K. Ando: J. Phys. Chem. A,

surface by molecular dynamics simulations.

115 (2011) 678–684.

Based on this study, we are now extending144

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Dynamical stability of two-dimensional simple metals
and ordered alloys
Shota ONO
Department of Electrical, Electronic and Computer Engineering, Gifu University
Gifu 501-1193

The family of two-dimensional (2D) materials has been expanded signiﬁcantly in recent years. However, the dynamical stability
as well as the synthesizability of 2D metals
have not been explored in detail irrespective of
the presence of the interrelationship between
the energetic stability in the 2D and threedimensional (3D) structures. In this study, we
have performed high-throughput density functional theory (DFT) and density functional
perturbation theory (DFPT) calculations toconstruct the metastability database for simple metals and ordered alloys. The databasecurrently includes (I) the phonon dispersionsof 46 simple metals from Li to Pb in the three
2D structures, including the planar hexagonal,
the buckled honeycomb (BHC), and the buckled square (BSQ) lattices [1]; (II) the phonon
dispersions of 2D Po, named poloniumene, inthe planar square structure [2]; and (III) theformation energies of 1081 binary compounds
in the 2D structures (BHC and BSQ as shownin Fig. 1) and the 3D structures (B2, L10 , andBh corresponding to bcc, fcc, and hcp in simple metals, respectively) and the phonon dispersions of more than 50 ordered alloys in the
BHC structure [3].
In Ref. [1], we have demonstrated that thetrend in the dynamical stability of 2D metals
is correlated with that of 3D metals. This provides design principles of ordered alloys: 2D
metals are building blocks for constructing 3D
alloys, where the similarity regarding the dynamical stability of diﬀerent 2D metals is important for creating dynamically stable alloys.
In Ref. [2], we have shown that the 2D polonium has the planar square lattice structure
as its ground state and demonstrated that the

!" #

!$#

!"

!"

Figure 1: Schematic illustration of binary ordered alloys in the BHC and BSQ structures.
After Ref. [3].
spin-orbit coupling (beyond the scalar relativistic approximation) suppresses the Peierls
instability and is necessary to obtain no imaginary phonon frequencies over the Brillouinzone.
In Ref. [3], by analyzing of the formationenergy and the dynamical stability of binary
alloys, we have demonstrated that (i) a negative formation energy is neither a suﬃcient nor
necessary condition for producing the dynamical stability of 2D ordered alloys; and (ii) if anordered alloy in the Bh structure is synthesizable, that in the BHC structure is dynamicallystable. In addition, the stability of ordered AuCu alloys has been studied in Ref. [4].

References[1] S. Ono: Phys. Rev. B 102 (2020) 165424.
[2] S. Ono: Sci. Rep. 10 (2020) 11810.
[3] S. Ono and H. Satomi: Phys. Rev. B 103(2021) L121403.
[4] S. Ono and D. Kobayashi: Phys. Rev. B
103 (2021) 094114.

145

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Boltzmann equation solver for nonequilibrium
electrons and phonons in solids (BENEP). II.
Application to experiments
Shota ONO
Department of Electrical, Electronic and Computer Engineering, Gifu University
Gifu 501-1193

Understanding the ultrafast electron dynamics of laser-excited solids, where theelectron-electron (e-e) and electron-phonon (eph) scatterings occur simultaneously within apicosecond time scale, is important to analyze the pump-probe experimental data. The
author has developed the Boltzmann equation solver for nonequilibrium electrons andphonons which enables us to study the ultrafast electron and phonon dynamics [1]. We
have applied our code to the calculation of the
femtosecond infrared photoluminescence (PL)of silver (see Fig. 1). The preliminary results
have been reported in Activity Report 2019.

Figure 2 shows an application to the timeevolution of PL spectra and the transient PL
at 0.9 eV in silver. The agreement between
the theory and experiments is good, indicatingthat the eﬀect of electron nonequilibrium is important in the PL dynamics. The disagreement
may be attributed to the nanoscale roughness
at metal surfaces and the e-e umklapp scattering on the ultrafast electron dynamics [2].
The author thank Prof. Tohru Suemoto for
useful discussions.
3

1.2

30x10

0.0 ps0.2 ps
0.5 ps1.0 ps

(a)
25

1.0

! "#$%&' #"( )"' *+$,)- *). *- %"/ ( $,0+1213,4 ! 56
7 *+)%#/ ( ,4 8 9 ,!"#$: ; / ( / ( ,4 8 9 ,%"&$
7 *"- $; <+#2 =. ( )%"/ ( ,'! ("&$

,*"&$
,*
.
,,- #$%"
5"> +&+?/ *. %"/ ( ,/ =,) # - ( @,*"&$3,+" - ( @,+#$3,- ( @,%
; +,
/' %
")- *,$' +)%#- ,0+1213,: A6

0.6

10

0.4

5

0.2

0.6

0.8

1.0

Photon energy (eV)

,)"#$
,)
,)
,)
.
/
H,
,,- "%",- "%#$,- &'("): - #- > +%+#$,0* - ( @,1*0"( ,%; +,' #+$+( %
,$%
. @C6

15

0
0.4

D( %
+2#- %"/ ( ,/ =,%; +,E/ *%F> - ( ( ,+G. - %"/ ( ,

0.8
PL (0.9 eV)

Photons/sec

20

B#C$%
- *,$%#. )%. #+

Calc.
Exp.

(b)

0.0
-0.5 0.0

0.5

1.0

1.5

Decay time (ps)Figure 2: (a) The evolution of PL in silver:
The experimental PL (circle) and the calculated PL (solid). (b) Comparison of the transient PL at 0.9 eV. After Ref. [2].

References
Figure 1: Flow chart describing the timeevolution calculation of the distribution functions in metals. After Ref. [2].

[1] S. Ono: Phys. Rev. B 97 (2018) 054310.
[2] S. Ono and T. Suemoto: Phys. Rev. B 102(2020) 024308.

146

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Noisy simulations of first-principles calculations using
quantum classical hybrid algorithms
Wataru Mizukami
Center for Quantum Information and Quantum Biology, Institute for Open andTransdisciplinary Research Initiatives, Osaka University, Osaka 560-8531, Japan,

affected by noises.

In recent years, quantum computers withdozens of qubits have been built; we now expect

In this work, we have investigated theto see quantum devices with hundreds of qubits

influence of this noise on the VQE by using a

in the near future. Such quantum computers arequantum circuit simulator. There are many types

often called noisy-intermediate scale quantumof noises in quantum computers, such as read-devices (NISQs) since they do not have quantumout error and amplitude damping. Since it iserror correction functionality. Nonetheless, indifficult to model all kinds of errors, we have

2019, Google showed that a NISQ with as few

only dealt with depolarizing noise, which is aasoutperform

typical error model for quantum computers, insupercomputers when limited to a specific task.

this study. This noise can be described as Pauli

Many research projects have been currently

operators probabilistically acting on each gate ofunderway to exploit the computational potential

aof NISQs.

depolarizing noise, we can effectively say that53

qubitscould

alreadyquantum

circuit.

In

thepresenceof

One promising algorithm for NISQs is thethe noise probabilistically changes the quantum

quantum-classical hybrid algorithm, which cancircuit at each sampling. It means that theoperate even in the short coherence time of anumerical simulations with depolarizing noise

NISQ. Among them, the variational quantum

using classical computers, are required toeigensolver (VQE) can be applied to first-

simulateprinciples calculations of materials or molecules.

simulation with depolarizing noise is much moreAn advantage of the VQE is that it can

expensive than the simulation without it.

parametrize some wave functions ansatzes such

Besides, because such a simulation is a sampling

as unitary coupled clusters (UCC)in polynomial

problem, the individual circuits changed by thetime,

exponentiallynoise are independent. Hence, the VQE withonclassical

depolarizing noise can be highly parallelizable.

computers. However, if a NISQ is used for theThis year, we have realized the simulation

VQE, the computational results are unavoidablywith depolarizing noise up to 1 million samples

while

the

computationallyUCC
expensiveis147

variousquantum

circuits:theActivity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

by using the MPI parallelization and thechemical accuracy with the error rates of today's

supercomputer of the ISSP. In addition, by using

quantum computers. This implies that ana many-body expansion, we have studied theefficient way to suppress the effect ofeffect of depolarizing errors on up-to a 100-depolarizing noise is vital for the practicalqubits problem. We have chosen the most basic

application of first-principles calculations using

molecule, the hydrogen molecule, as the

NISQs.

benchmark system. In our program, the PySCF
quantum chemistry program library [1] is used

References

to prepare the second quantized electronic[1] Q. Sun et al., WIREs Comput. Mol. Sci. 8,

Hamiltonian; Qulacs is employed as a quantum

e1340 (2017).

circuit simulator [2]. The obtained numerical[2] Y. Suzuki et al., arXiv:2011.13524

results illustrate that it is impractical to achieve148

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First principles calculations of crystals with quantum classicalhybrid algorithms
Wataru Mizukami
Center for Quantum Information and Quantum Biology, Institute for Open andTransdisciplinary Research Initiatives, Osaka University, Osaka 560-8531, Japan,

quantum circuit parameters.

First-principles calculations of solids or solid
surfaces are routinely performed in materials

This year, we have extended the VQE toscience. They have become an indispensable

solid-state systems [1]. Specifically, we prepare

tool in the fields of condensed matter physics

a second quantized Hamiltonian in the crystal

and inorganic chemistry. The workhorse of theseorbital representation, and make a one-to-one

ab initio calculations is currently density

correspondence between crystal orbitals andfunctional theory (DFT). An approach beyond

qubits. The UCC ansatz in the crystal orbital

DFT is the introduction of quantum chemical

representations has also been converted into themethods such as the coupled-cluster theory (CC).

qubit representation. These mapping allows us

The problem of CC is that it works well only

to describe the electronic structure of acrystalline system on a quantum computer.

for weakly correlated systems. It is known to
break down in systems with strong electron

We have applied the developed VQE-UCC tocorrelation. This issue comes from the fact that

one-dimensional hydrogen chains and calculate

CC is not variational. Although there is atheir potential energy surface, confirming thatvariational CC method, such a method is

the VQE-UCC works in the regime where theexponentiallyofelectron correlation becomes strong so that thecomputational costs. However, in 2014, it wasconventional CC does not work. We have also

shown that a kind of variational CC, the unitarydeveloped an algorithm to calculate the quasi-

CC (UCC), can be solved in polynomial time

particle band structure from the VQE wave

using a quantum computer.

function based on the extended Koopman's

expensive

in

terms

theorem [1].

This method is called the variational
quantum eigensolver (VQE). In the VQE, thewavefunction ansatz is represented by aReferences

quantum circuit. Then, a classical computer[1] N. Yoshioka, Y.O. Nakagawa, Y.-y. Ohnishi,

updates the VQE's wavefunction parameters as

W. Mizukami, arXiv:2008.09492

149

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles Calculation of Electric Field Eﬀects
in Spin-to-charge Conversion Materials
Naoya YAMAGUCHI
Nanomaterials Research Institute, Kanazawa University
Kakuma-machi, Kanazawa, Ishikawa 920-1192
We have studied materials possessing the
Rashba eﬀect that induces spin splitting,which is applicable to spin-to-charge conversion [1]. The Rashba eﬀect originates fromspin-orbit interaction and spatial inversion
symmetry breaking, and is controlled by electric ﬁelds. Based on the modern theory ofelectric polarization, one can apply uniform
electric ﬁelds even for bulk insulators in calculations with density functional theory (DFT)
codes with the periodic boundary condition[2]. We have developed a linear-combinationof-pseudo-atomic-orbital (LCPAO) version ofsuch a function making k-dependent potentials
and implemented it to the OpenMX code. This
year, we tried to focus on electric ﬁeld eﬀects insuch Rashba systems with Berry phases by using the OpenMX code. Under an electric ﬁeld,
cations or anions are expected to shift theirpositions slightly, but shifts of ions’ positions
induce such a large electric polarization thatRashba spin splitting occurs. During structural relaxation, such ions move by following
forces on themselves, but the forces are often smaller than a usual criterion of calculated
forces (e.g. 10−4 Ha/Bohr) when we consider
the realistic strength of electric ﬁelds. However, for nonorthogonal cells such as hexagonal cells, in the case of generalized gradient approximation (GGA), the “egg box effect” appeared as a diﬃculty because OpenMX
uses PAOs expanded in the real space grid tocompute physical quantities, but descriptionof PAOs depends on the origin of the grid,that is, introducing the grid causes numericalerrors. To overcome the diﬃculty, we addedfunctions of calculations of a total energy andforces with several grid origins. Once calculations of electronic systems converge, one canget density matrices (DMs) and taking anotherreal space grid with a diﬀerent origin, one canevaluate an energy and forces again with thefrozen DMs. In the way, we succeeded in evaluating forces under electric ﬁelds with a moderate number of grids (i.e. cutoﬀ energy). We
also added a function to change the order ofthe Lagrange interpolation to estimate density
gradients, and it improved evaluation of forces.
These two functions enabled us to predict not
only relaxed structures under electric ﬁelds but
also static dielectric constants and Born eﬀective charges in any cell shape. Indeed, we conﬁrmed that our calculated values of dielectric
constants and Born eﬀective charges for typicalinsulators are consistent with the prior theoretical and experimental studies. Since we encountered the problems of the ”egg box eﬀect”,
we have not done calculations of applications,but we have suggested a simple model of surface alloys, such as Bi/Ag surface alloys inducing giant spin splitting, based on DFT calculations [3]. This year, we also succeeded in
reducing half of computational time for Berryphases averagely through tuning, and running
our implemented code with up to 323 k-points
for zinc blende primitive cells through eﬃcienttransfer of arrays of k-dependent potentials in
the message passing interface (MPI).

References[1] J. C. Rojas Sánchez et al., Nat. Commun. 4, 2944
(2013).
[2] I. Souza, J. Íñiguez, and D. Vanderbilt, Phys. Rev.
Lett. 89, 117602 (2002).
[3] M. Nur, N. Yamaguchi, and F. Ishii, Materials 13,4444 (2020).

150

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study of atomic and electronic
structures of intermetallic compound catalysts
Kazuki NOZAWA
Department of Physics and Astronomy, Kagoshima University
1-21-35, Korimoto, Kagoshima 890-0065

This ﬁscal year, we carried out the following
studies using the VASP code with the PAW
method and the PBE exchange-correlation
functional.
Quasicrystals (QCs) are long-range orderedmaterials with no translational symmetry.
Partly because the atomic structure of mostQCs have not been solved completely, DFT
studies have usually been carried out using thesurface of a crystalline phase having a closecomposition and common structural building
unit to the quasicrystalline phase. Recently,
however, single-element quasiperiodic ultrathin ﬁlms have been obtained using the AgIn-Yb QC as a template. The Ag-In-Yb
QC belongs to the only QC family whose
atomic structure has been solved unambiguously. Thus, DFT studies using the actual
quasiperiodic surface atomic arrangement are
required to elucidate the atomic structure of
the ultra-thin ﬁlms. Although a straightforward way to approximate the QC surface is touse an atomic cluster extracted from the structural data of the QC, the cluster size dependence of the adsorption energy for the aperiodic surfaces has not been well studied. Therefore, this time we studied the convergence behavior of the adsorption energy of a single Bi
atom concerning the cluster size [1]. Two typesof clusters, the cylindrical and hemisphericalclusters, are tested. Unnaturally rippled potential energy surfaces were obtained for clusters with smaller radius regardless of the cluster thickness. It was revealed that the ripples
are disappeared when clusters with a suﬃcient

cluster radius of 1.4 nm or larger are used.
This trend is also conﬁrmed in their root meansquare errors. Consequently, it was concluded
that both cluster models tested with a speciﬁc
size are expected to give relative adsorptionenergy within an error of 0.15 eV. It was also
pointed out that the cylindrical cluster modelis relatively economical in terms of the calculation cost than the hemispherical cluster model.
We also investigated the surface atomic
structure of the antiferromagnetic 1/1 Au-Al
Tb approximant crystal using DFT calculation[2]. Experimentally observed stable surface atomic structure showing a linear row
structure of Au/Al atoms, which is an example of a surface reconstruction in this family of
QC-related systems, was found stable by thecalculation.
We studied the inﬂuence of the adsorbed
oxygen atoms on the surface atomic structureand electronic structure of PdZn(111) surface
using DFT calculation[3].

References[1] M. Sato, T. Hiroto, Y. Matsushita, and
K. Nozawa, Mat. Trans. 62 (2021) 350.
[2] S. Coates, K. Nozawa, M. Fukami, K. Inagaki, M. Shimoda, R. McGrath, H. R.
Sharma, and R. Tamura, Phys. Rev. B
102 (2020) 235419.
[3] Y. Otani, Master Thesis (Kagoshima University, 2021).

151

Activity Report 2020 / 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, Kiyoto KAYAO, Kouji INAGAKI, Yoshitada MORIKAWA
Graduate School of Engineering,Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871
There is a growing demand on ultra-smooth surface with sub-Angstrom root-mean-

precision optical components for scientific andsquare roughness is achieved on the Si

industrial applications, especially in extreme

substrate.

ultraviolet (EUV) and X-ray regimes. Using the

Our recent studies indicated that the

short-wavelength light, scientific imaging ofremoval mechanism of SiC and SiO2 etching

cutting-edge materials/biological samples andvia CARE is hydrolysis reaction, in which thenanoscale lithography have become possible

catalyst

thanksopticalstabilization of hypervalent state, increasing

components. Low thermal expansion materials

rate of the reaction [3]. Thus, the purpose of thesuch as glass and Si are still the main materials

proposed research is to clarify the removal

used for fabricating these optical components.

mechanism of Si etching via CARE using first-

Compared to glass, Si possesses more attractive

principles calculation. Additionally, in Si

properties,

cleanliness,polishing, the effect of self-oxidation bymachinability, and workability. Accordingly,

oxygen and water is still not well understoodultra-precisionSi

due to the instability of Si under ambient

surfaces has been achieved significant advancescondition. Thus, the oxidation effects of oxygenin accuracy and smoothness. A highly ordered

and water are also taken into account.

to

the

such

ultra-precisionassurfacehighermachiningforassistswater

dissociation

andsurface with a root mean square roughness at

The mechanistic removal pathway of CARE

the level of several tens of picometer is greatly

for Si(111) has been clarified and shown in Fig.

desired for the highest reflectivity and the

1. In the pathway with the Pt catalyst, at first, alowest unwanted scattering [1].

water molecule is dissociatively adsorbed on Pt.

In this study, we apply catalyst-referred

In the next step, the adsorbed OH is transferredetching (CARE), an abrasive-free polishing

to the targeted Si, forming the five-foldmethod, to planarization of a crystalline Si

coordinated state in the metastable state (MS).

surface, using Pt as the catalyst and pure water

At this state, the Si-Si back-bond is elongatedas the etching solution [2]. An atomicallyand weekend. Finally, the Si─Si back-bond is152

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

broken by a proton transfer at the final stateoxidation by oxygen at a terrace site might be(FS). The activation barrier is reduced from 1.0

difficult. The obtained results are quiteeV (without the Pt) to 0.6 eV (with the Pt). We

consistent with the previous study [4]. The

expected that similar results would be observed

obtained results could also explained why theon a Si(100).

wettability of Si(111) surface could be lasted
for several hour in the ambient conditions in theprevious experimental study [5].

Fig. 1: A mechanistic reaction pathway of
the Pt-catalyzed water etching of the Si(111)
surface in comparison with the pathway

Fig. 3: Atomic configurations and energy

without the Pt catalyst.

diagrams of oxidation by an oxygen molecule
at a step-edge and a terrace site.

We consider oxidation effects by an oxygen
molecule at terrace and step-edge sites on a

The study has clarified the mechanistic

Si(111) surface, as illustrated in Fig. 2.

removal pathway of CARE for Si in pure waterand oxidation effect of a Si(111) surface byoxygen or water. Oxygen plays an main role in
the oxidation of a Si(111) surface. Moreover,combined oxidation effects of oxygen andwater might be an important factor to beconsidered in the future.

Fig. 2: Illustration of oxidation effects by an

References

oxygen at terrace and step-edge sites on a[1] R. J. Noll: Opt. Eng. 19 (1980) 249.

Si(111) surface (top-view).

[2] H. Hara et al.: J. Electron Mater. 35 (2006) L11.

The activation barriers of the oxidation by[3] P.V. Bui at al.: Jpn. J. Appl. Phys. 57 (2018)

an oxygen molecule are 0.46 and 0.15 eV,055703.

respectively (Fig. 3). The obtained results[4] F. A. Soria, E. M. Patrito, and P. Paredes-Olivera:

indicated that the oxidation might occur readily

J. Phys. Chem. C 116 (2012) 24607.

in the air at a step-edge site. However, the[5] M. Niwano at al.: J. Appl. Phys. 76 (1994) 2157.

153

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Doping and molecular adsorption of graphene
Yoshitaka FUJIMOTO
Depertment of Physics, Tokyo Institute of Technology
Ohokayama, Meguro, Tokyo 152-8551

Graphene is one of candidate device materials for molecular sensors using field-eﬀect transistors due to their high charge mobility andchemical reactivity to adsorbates. Recently, we
have reported the adsorption properties of environmentally polluting and/or toxic molecules(NO and NO2 moleucles) onto boron andnitrogen-doped graphenes, and only NO andNO2 molecules in air are strongly adsorbed on
the B-doped graphenes.
We here report the adsorption property
of a toxic CO molecule on the boron-doped
graphene and (8,0) CNT to reveal the curvature eﬀects of the graphene using a firstprinciples density-functional calculation [1, 2,
3].
Table 1 shows the adsorption energies andthe binding distances between the B atom andthe adsorbed molecule for the CO molecule on
the B-doped monolayer and bilayer graphenes,
and B-doped (8,0) CNT. The CO molecule isfound to be adsorbed not strongly but weakly
with short distance and small adsorption energy on the B-doped monolayer graphene. In
the case of the B-doped bilayer graphene, theadsorption energy and the binding distance forthe adsorption of the CO molecule show similar

Table 1: Adsorption energy Ea (eV) and binding distance d (Å) between adsorbed moleculeand B atom for CO molecules adsorbed on Bdoped monolayer and bilayer graphenes, andB-doped (8,0) CNT.

Monolayer
Bilayer
CNT

Ea
-0.12
-0.12
-0.62

d
2.89
2.89
1.53

154

to those of the B-doped monolayer graphene,
respectively.
We also study the adsorption energy and thebinding distance of the CO molecule on the
B-doped (8,0) carbon nanotube (CNT). Unlike monolayer and bilayer graphenes, the COmolecule is found to strongly bind on the Bdoped (8,0) CNT with the large adsorptionenergy and the short binding distance. Thus,
the adsorption properties of the CO moleculeon the B-doped (8,0) CNT is found to be enhanced, compared with those on the B-dopedmonolayer and the B-doped bilayer graphenes
due to the curvature eﬀects.
In summary, we have studied the adsorption properties of the toxic CO molecule on
the B-doped monolayer and bilayer graphenes,
and B-doped (8,0) CNT, using first-principles
density-functional calculations. The B-dopedmonolayer as well as bilayer graphenes does
not strongly but weakly bind with the COmolecule, while the B-doped (8,0) CNT canstrongly bind with the CO molecule. The Bdoped (8,0) CNT may be useful for sensor applications to detect CO molecules.

References[1] Y. Fujimoto and S. Saito, Chem. Phys.
478, 55 (2016).
[2] Y. Fujimoto and S. Saito, Jpn. J. Appl.
Phys. 58, 015005 (2019).
[3] Y. Fujimoto and S. Saito, Appl. Surf. Sci.
Adv. 1, 100028 (2020).

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Stability and electronic structures of MoS2 nanowires
Toshihiro SHIMADADivision of Applied Chemistry, Faculty of Engineering,
Hokkaido University, Kita-ku, Sapporo, Hokkaido 060-8628
Nanotubes of layered materials started withthe discovery of variety of helicities in carbon
nanotubes.

Since then, various layeredmaterials are found to form nanotube structures.
These structures show important functions suchas catalytic activities, lithium ion storage,transistor

actionandchemicalsensing.

Recently, we discovered that FeO nanoparticles

Fig. 1: Strain energy of MoS2 nanotubes withwork as catalyst to make MoS2 nanowires[1].

square or cylindrical cross sections.

We found that the cross section of the MoS2
nanowires show rectangular shapes. In order toinvestigate the mechanism of the formation andpossible new functions of these nanotubes, weused VASP to calculate the stability of

MoS2

nanotubes with cylindrical and square shaped
cross sections with armchair and zigzag
helicities[2]. The calculation result shows that

Fig. 2: 2D deformation charge density map of

this structure has lower strain energy in the low-square-shaped nanotube.

diameter region (~30 Å) than the conventional

References

cylindrical nanotubes (Fig.1). The electronic[1] M. Weng, T. Yanase, F. Uehara, S. Watanabe,

structure and the surface energy per length of theT.

square nanotubes showed unique properties

CrystEngComm 19, 3915 (2017).

because of ﬁve coordinated Mo atoms at the[2] M. Zhang, M. Weng, T. Tamura, M. Goto, I.

corner. Catalytic activities and unique sensing

Yamane, T. Yanase, T. Nagahama, T. Shimada:functions are expected.

Physica E 130, 114693 (2021).

155

Miura,

T.

Nagahama,

T.

Shimada,Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles derivation of a many-body effective model based on PMT
basis
Hirofumi SAKAKIBARA
Advanced Mechanical and Electronic System Research Center (AMES),
Tottori University, Tottori, Tottori 680-8525
To establish a construction method to[2]. The PMT basis function is a hybrid

obtain a model which captures the low-basis between the plain wave basis andenergythe muffin-tin basis. In the new model

part

of

electronic

structures

obtained in first-principles calculation isconstruction

an urgent problem. The model is often

described in the plane waves basis set

used to calculate physical quantities suchare taken into account in the model

as

and

Hamiltonian expressed on the muffin-tintransition temperatures of magnetism ororbital basis. Namely, we obtain asuperconductivity.

Maximally

projection operator from full-space (PMT

localized Wannier function (MLWF [1]) is

space) to the (reduced) model space,often used to derive a tight-binding

which is spanned by muffin-tin orbital.

model reproducing the first-principles

In the operator, we introduced weightband

However,function so as to reproduce the band

MLWF has a problem that it requires

structure of low energy region. Note thatseveral optimization parameters. This

the new method does not require any

requirement inhibits the automation ofhandful parameters, so this can be usedmodel construction. If the automation isin the automation of model constructions.

achieved, we can search the materials

We have applied MLO to Si crystal.

self-energy,

structure

conductivity,

The

very

well.

method,effects

only

from

The figure 1 shows the comparison of thematerial databases. In addition, MLWF

energy eigenvalues between the first-

has a difficulty in the model construction

principles calculation and MLO. We canfor slabs and surfaces.

see MLO nicely reproduce the first-

havingdesirable

properties

To overcome the problems of MLWF,

principles eigenvalues. Even in other

we propose a construction method assemiconductors such as GaAs and GaN,

Muffin-tin

the eigenvalues are well reproduced.

based

Localized

Orbital(MLO) based on the PMT basis function

In summary, MLO basis function can

156

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

accurately reproduce the eigenvalues
calculated

in

the

first-principles

References

calculations. In the next step, we apply[1] N. Marzari and D. Vanderbilt, Phys. Rev.

MLO to more difficult systems such as

B 56, 12847 (1997).

interfaces or slabs.

[2] T. Kotani, H. Kino, and H. Akai, J. Phys.

Soc. Jpn. 84, 034720 (2015).

Figure 1: Result of MLO in a simple Si crystal.
Solid line shows the eigenvalues obtained infirst-principles calculations and circles shows
the MLO results. The triangles show the result
considering only the MTO basis.

157

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-Principles Analysis of Melt Structure andProperty in Na Flux GaN Growth
Takahiro KAWAMURA
Graduate School of Engineering, Mie University
1577 Kurimamachiya-cho, Tsu, Mie 514-8507

At first, graphite was used as a C source.
After that Murakami et al. used methane(CH4 ) gases and found they were more effective than graphite [3]. In this study, weinvestigated activation free energies for C–C
and C–H bond dissociation in Na–Ga melts
using first-principles calculations and clarified
the reason why CH4 gases are more eﬀective
than graphite.
We used the first-principles molecular dynamics (MD) simulation program STATESenri (Simulation Tool for Atom TEchnology),
which is based on density functional theory
with norm-conserving/ultrasoft pseudopotentials and plane-wave basis sets [4]. We used thegeneralized gradient approximation of Perdew
et al. for the exchange-correlation function [5].
The cutoﬀ energies for the wave functions andcharge densities were 25 and 225 Ry, respectively. The number of k-points for Brillouinzone sampling was 1×1×1.
We modeled Na–Ga (Na:Ga ≈ 4:1) melt

models composed of about 54 atoms. A setof C and C or C and H atoms was includedin the models. Periodic boundary conditions
were used in all directions. We performed constrained MD simulations for 10 ps at 1073 K
and at constant volume. The C–C and C–H
interatomic distances were constrained to therange of 1.0–3.5 Å. By using data from the latter half of the 10 ps period, free energy profiles
were calculated with the blue-moon ensemble
method [6, 7].
Figures 1 show plots of the free energy profiles for C–C and C–H bond in Na–Ga melt.
The horizontal axis is the constrained interatomic distance. The interatomic distance atwhich the free energies reach a local minimum
indicates a stable bond length. The dissociation activation energies were determined from
3
C-C

Change of free energy [eV]To produce high-quality III-V nitride semiconductor devices at low cost, large bulk
GaN crystals for freestanding substrate aredemanded. The Na-flux method is one of
the most promising crystal growth techniquefor bulk GaN. It is known that C additives
improve the growth rate and suppresses thegeneration of polycrystals [1]. Using firstprinciples calculations, we previously foundthat formation and dissociation of the C–Nbond in the Na–Ga melt strongly aﬀects themechanism for enhanced GaN growth [2].

C-H

2

E

1

C-H

=1.34 eV

0

-1

E

C-C

=2.71 eV

-2

-3
1.0

1.5

2.0

2.5

3.0

3.5

Interatomic distance [Å]Figure 1: Free energy profiles for the C–H bondin the Na and Na–Ga melts.

158

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

the energy diﬀerence between a local maximum and a local minimum. From the result,
we found that the activation free energies for
C–C and C–H bond dissociation are 2.71 and1.34 eV, respectively [8]. Because the dissociation energy of the C–H bond is lower than thatfor the C–C bond, CH4 gas decomposes moreeasily than graphite; that is, CH4 gas is more
eﬀective as a C additive than graphite.

References[1] M. Imade, Y. Hirabayashi, Y. Konishi, H.
Ukegawa, N. Miyoshi, M. Yoshimura, T.
Sasaki, Y. Kitaoka, and Y. Mori: Appl.
Phys. Express 3 (2010) 075501.
[2] T. Kawamura, H. Imabayashi, M.
Maruyama, M. Imade, M. Yoshimura,Y. Mori, and Y. Morikawa: Appl. Phys.
Express 9 (2016) 015601.

[3] K. Murakami, S. Ogawa, M. Imanishi, M.
Imade, M. Maruyama, M. Yoshimura, and
Y. Mori: Jpn. J. Appl. Phys. 56 (2017)055502.
[4] Y. Morikawa: Phys. Rev. B 51 (1995)
14802.
[5] J. P. Perdew, K. Burke, and M. Ernzerhof:
Phys. Rev. Lett. 77 (1996) 3865.
[6] E. A. Carter, G. Ciccotti, J. T. Hynes,
and R. Kapral: Chem. Phys. Lett. 156,
(1989) 472.
[7] M. Sprik and G. Ciccotti: J. Chem. Phys.
109 (1998) 7737.
[8] T. Kawamura,
M. Imanishi,
M.
Yoshimura, Y. Mori, and Y. Morikawa:Comp. Mater. Sci. 194 (2021) 110366.

159

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analysis on atomic and magnetic structure in magnetic
molecular complex, crystal and interface and investigation of
external electromagnetic field effectMasao 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 andHowever, some differences should be pointed

magnetic structure of ferrimagnetic spinel ofout, e.g., the size of the energy gap on the

NiCo2O4 by using the beyond generalized

majority spin. Remarkably, QSGW predicts thegradient approximation (GGA) approach suchunoccupied energy of Ni eg orbitals to be more

as GGA+U or quasi-particle self-consistentthan 1 eV higher than those calculated by GGA.

GW (QSGW). The NiCo2O4 spinel has drawn a

It may affect the estimation of electric andlot of attention for its material application due

optical properties such as reflectance orto its low cost with excellent electronictransmittance.

high

We also extended the QSGW calculation byelectrochemical activity. However, some of the

combining it with the effective screened

latest reports of its first-principles calculation

medium method [3]. It allows us to estimate theresult have some discrepancies with thefinite electric field effect of slab systems on

experimental one. One of the reasons may

GW level without relying on perturbation

come from the poor electron correlation

theory. We have succeeded in evaluating thedescription of GGA calculation. For this study,

dielectric constant in high accuracy [4].

the first-principles calculation package ecalj [1],References

which adopts the mixed-based set between[1] https://github.com/tkotani/ecalj/

local orbital and plane waves, is used. We[2] H. Al Rasyid, M. Obata, T. Kotani, T.

mainly focused on the inverse spinel structure

Oda, The Science Reports of Kanazawa

containing 14 atoms, namely, eight oxygen andUniversity, in press.

six cation atoms, in the primitive cell.

[3] M. Otani and O. Sugino, Phys. Rev. B,

conductivity,

redox

reaction,and73, 115407 (2006).

The results show that both GGA and QSGW
gave the ferrimagnetic magnetic structure with

[4] H. Sakakibara, T. Kotani, M. Obata, T.

a half-metallic electronic configuration[2].

Oda, Phys. Rev. B, 101, 205120(2020).

160

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Molecular dynamics study on non-equilibrium processes ofsilica and silicates using first-principles calculation andmachine leaning
Masaaki MISAWA
Graduate School of Natural Science and Technology, Okayama University
In this project, we studied (1) pressure-

fayalite during compression and decompression

induced amorphization behavior of fayalite andprocesses were obtained. We elucidated that the(2) shock-compression behavior of quartz

high-fold coordinated Si atoms exist in thebased on molecular dynamics simulations.

amorphous phase even after decompression toan ambient conditions. Additionally, it wasFirst-principles molecular dynamics

found that the Si atoms play a role of network-

simulation

former in the amorphous phase at high-pressure,ofpressure-induced

amorphization of fayalite

but change into network-modifier at an ambientconditions. Furthermore, it is expected that the

Fayalite (Fe2SiO4), an end-member of thecrystal-to-amorphous

medium- or long-range order of Fe atoms aretransformation at high-pressure and room-

partially remained in the amorphous phase,temperature conditions [1]. It was reported that

resulting in the appearance of its unique

thismagnetic ordering structure.

olivine,undergoespressure-induced

amorphizedfayalite

exhibits different features from olivine glasses
synthesized by heat-and-quench processes [2].

Molecular

However there are no theoretical investigations

shock-compression behavior of quartz

aboutusing ANN potential

thephenomenonpressure-induced
and

the

amorphizationpressure-induced

dynamics

simulationofArtificial neural network (ANN) potential,

amorphized phase yet.

which is an interatomic potential constructed by

In this study, we perform first-principles

machine-leaning,

attracts

attentionasamolecular dynamics study of fayalite topromising method to achieve extra-large-scale

investigate energetic and structural properties

molecular dynamics (MD) simulation withof the pressure-induced amorphized fayalite.

first-principles accuracy [3,4]. Application of

The volume-and-energy relations, partial pairthis

distribution functions, and coordination number

phenomena, such as fracture and pressure-changes of crystalline and amorphous phases of

induced161

ANN-MDtotransformation,

far-from-equilibriumisimportanttoActivity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

understand structural properties of materials

reference data [7]. Using this improved ANN-

under extreme conditions. For this purpose, wepotential, it was succeeded that reproducing thehave tried to perform ANN-MD simulation ofelastic-to-plastic transition behavior and plastic

shock-induced structural transformation of

deformation of α-quartz with an accuracy close

silica.

to FPMD simulation. Thus, the ANN-potential

To compute shock-compression behaviors

trained with energy, force, and pressure is awithin the framework of MD method, thepotentially powerful tool to investigate wide

multiscale-shock technique [5] was employedrange of far-from-equilibrium phenomena andin our simulations. Potential energy of shock-will also provide useful information for solid

compressed

earth physics field in future.

α-quartz

obtainedbyfirst-

principles MD (FPMD) method is used as areference data for training of ANN-potential.

References

As a result of ANN-MD simulation for elastic[1] Q. Williams et al.: J. Geophys. Res. 95

shock-wave
behaviorsofregion,elastic-deformation(1990) 21549.

α-quartz

was[2] S. Kohara et al.: Science 303 (2004) 1649.

successfully

reproduced with high-accuracy [6]. On the[3] J. Behler and M. Parrinello: Phys. Rev. Lett.

other hand, for plastic shock-wave region, the98 (2007) 146401.

ANN-potential[4] N. Artrith and A. Urban: Comput. Mater.

hascompletely

failedon

prediction of both structure and energy, because

Sci. 114 (2016) 135.

of that irregular structure appears and rapid[5] E. Reed et al., Phys. Rev. Lett. 90 (2003)

movement of atoms occurs during the elastic-

235503.

to-plastic transition process.

[6] M. Misawa et al.: J. Phys. Chem. Lett. 11

In order to improve the predicting ability of(2020) 4536.

ANN-potential, we introduce a more accurate[7] K. Shimamura et al.: J. Chem. Phys. 153

training method that uses not only potential(2020) 234301.

energy but also atomic force and pressure as

162

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Search and realization of novel electronic properties ofsolid surfaces and interfaces and of small particles
Takeshi INAOKA

Department of Physics and Earth Sciences, Faculty of Science,
University of the Ryukyus, 1 Senbaru, Nishihara, Okinawa 903-0213
We mention two subjects which we
addressed this year.
The Ni(110)-(2x1)O surface is known tohave a missing-row reconstruction
structure, as is shown in Fig. 1 [1]. Oxygen(O) atoms are adsorbed at bridge sites toform Ni-O-Ni atomic chains in the y,namely, [001] direction. The O-derived
bands exist near the upper and lower
edges of the substrate Ni bands. The
bands around the lower edge have alreadybeen studied well by means of firstprinciples calculations using small-scaled
slabs and some experimental studies.
This year, using a large-scaled slab
composed of 21 Ni atomic layers andadsorbed O atoms at both surfaces, weinvestigated the upper O-derived bands,
and identify them with surface states
when separated up from the upper edge ofthe substrate bands.
We employed the program package‘Vienna Ab initio Simulation Package’(VASP) [2,3] on systems B and C.

Fig. 1 Missing- row
reconstruction
structure at theNi(110)-(2x1)O
surfaceyNanoribbons with zigzag edges have
localized edge states, while those witharmchair edges possess no edge states.
We consider the electronic structure ofgraphene systems of finite area. By meansof the tight-binding method, we examined if
edge-localized states can be formed in
finite graphene systems, and how theelectronic structure of these systems
depends on system shapes or areas.
(1) Identification of surface states at theNi(110)-(2x1) O surface [4]Assuming a slab of 21 Ni-atom layerswith O atoms adsorbed at each surface
and using the generalized gradient approximation, we obtained the optimized groundstate structure. Figure 2 (a) shows theband dispersion on the  - Y line formajority spin. As is displayed by an arrow,
there exist a pair of nearly degeneratebands that lie above the densely
distributed substrate bands due to Ni dorbitals. Figure 2 (b) exhibits electrondensity isosurfaces of the higher energy
one of the above paired states at the

E-EF (eV)(a)

x [ 1 10]

0

-0.5

[001]

Graphene is a very popular single-layer
structure of carbon (C) atoms arranged ina hexagonal lattice. The band structure ofthis material is characterized by aso-called Dirac cone, and predicts an
extremely high electron mobility. When thismaterial takes a form of nanoribbons, theband structure due to  orbitals around the
Fermi level depends on edge shapes.

163

-1



Y

y

x

Fig. 2 (a) Band dispersion on the  - Y line
for majority spin and (b) electron density
isosurfaces of the state on the midpoint ofthe  - Y line, as is arrowed in (a).

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

middle point of the  - Y line. Isosurfacesof the lower one are almost the same. This
isosurface map clearly indicates that thisstate is localized near the surface, and thatthe px orbital of an O atom, which extends
in the x, namely, [ 1 10] direction, plays amajor role, and it bonds to dxy orbitals of asurface Ni atom. We can recognize thistailed localization at the surface only insuch a large-scaled slab as ours. However,
we still have to verify that these surface
states really exist even in a semi-infinite
substrate. We consider that bulk which canbe obtained in the limit of increasing theslab thickness, and evaluate the upperedges of those bands which correspond to
the substrate bands of the slab. We findthat these upper bulk-band edges are
below the paired nearly degenerate bands.
Through this analysis, we concluded thatthe surface states are really present in thesemi-infinite substrate.
We made the same analysis of the
O-derived bands around the upper edge ofthe substrate bands on the  - X line aswell. We identified the surface states inwhich the py orbital of an O atom bonds tothe dyz orbitals of a surface Ni atom.
(2) -band structure of finite graphenesystems [5]We examined the electronic structure offinite graphene systems for various shapes
and areas. Each eigenstate is expressed ina form of a linear combination of pz orbitalsof C atoms extending in a plane-normal
direction, and each component of its
eigenvector represents the pz orbital
coefficient of the corresponding C atom.
As an example of the results, figure 3
displays the pz-orbital coefficients in color
scale of (a) the lowest-energy state (n=1),(b) the highest-occupied state (n=23) and(c) the highest energy state (N=46) for aparallelogram graphene with 46 C atoms.
This parallelogram is quite special in having
only zigzag edges.
As is shown in Fig. 3 (a), the pz orbital
coefficients in the lowest-energy state arecoherent in sign. On the other hand, figure
3 (c) indicates that, in the highest-energy
state, the coefficient alternates in signalong each hexagonal atom ring. In either of164

these states (a) and (c), the coefficient
amplitude tends to decrease as we movefrom the center to the edge. Thesefeatures are common to various shapes offinite graphene.
Figure 3 (b) shows that the highest
occupied state has edge localization. Red
and blue circles indicate atoms with large
positive and low negative coefficients,
respectively. These coefficients with large
amplitudes alternate in sign along the edgeline. The electron density distribution is
localized around the acute-angle vertices,namely, at those edges farther away fromthe center. Generally, edge localization
occurs at zigzag edges in specific statesat or just near the Fermi level.
(a)

(b)

0.4

(c)

0.3
0.2
0.1
0
0.1
0.2
0.3
0.4

Fig. 3 pz-orbital coefficients in color scale fora parallelogram graphene. (a) Lowest- energy
state, (b) Highest-occupied state, (c)Highest-energy state.

References[1] G. Kleinle et al., Surf. Sci. 225 (1990)
171-183.
[2] G. Kresse and J. Hafner: Phys. Rev. B 47
(1993) 558-561.
[3] G. Kresse and J. Furthmüller: Comput. Mat.
Sci. 6 (1996) 15-50.
[4] T. Inaoka and Y. Uehara: Identification of
surface states formed above the substrate
bands of the Ni(110)-(2x1)O surface, to besubmitted.
[5] T. Ohshiro and T. Inaoka: unpublished.

Activity Report 2020 / 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

Mirror-symmetrical two states with respect
to each other in a two-dimensional Brillouinzone form a mirror-symmetrical state by making the system ﬁnite along the direction perpendicular to a mirror symmetrical line. All
states become mirror symmetrical in onedimensional systems and all photoelectrons excited with linearly polarized light are spinpolarized. However, the wave functions areeither symmetrical or anti-symmetrical, andthe spin orientation of photoelectrons is determined by the symmetry of wave functions.
The spinor in strong spin-orbit systems containboth type of wave functions and the magnitudeof these components vary.
To investigate the spin polarization in onedimensional Rashba systems we used a simple
Rashba Hamiltonian and numerically solved it.
We used both plane-wave expansion and ﬁnite
diﬀerence methods, and veriﬁed that the diﬀerence between results by these methods is small.
Figure 1 shows an example of calculated re-165

sults. The electron spin is positively and negatively polarized for kx < 0 and kx > 0, respectively, where kx is the wave number along
the one-dimensional direction. The polarization decreases with decreasing |kx |. However,spin polarization is not necessarily low evennear kx ∼ 0. This is due to the propertiesof the Rashba Hamiltonian for the states withenergy E < 0.
Weighted spin expectation value

In 2020 we theoretically studied onedimensional Rashba systems. Perfect spinpolarization and spin-orientation reversal ofphotoelectrons have been observed in spinand angle-resolved photoelectron spectroscopy(SARPES) of strong spin-orbit systems [1, 2].
These phenomena have theoretically been explained in terms of mirror symmetry of thesystems [2, 3]. A problem, however, is thatthe states having mirror symmetry are restricted to lines in two-dimensional Brillouinzones. Only a small amount of photoelectrons
are fully spin polarized. To improve the efﬁciency of spin polarization we considered a
one-dimensional Rashba system and theoretically investigated it.

kx

Figure 1: Spin expectation values calculated asa function of kx for a ﬁxed energy E < 0. Red
and green circles show symmetrical and antisymmetrical components of wave functions.
Expectation values are weighted with the normof each component.

References[1] C. Jozwiak et al.: Nat. Phys. 9 (2013) 293.
[2] K. Yaji et al.: Nat. Commun. 8 (2017) 14588.
[3] K. Kobayashi et al.: Phys. Rev. B 95 (2017)205436.

Activity Report 2020 / 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

Our project has been focused on physicalproperties of structural elementary excitationsof semiconductor surfaces and interfaces. We
have performed one topic in this year. It is thephysical properties of oxygen vacancies (VO ) in
SiO2 at interface with Si. [1] The calculations
were performed based on the ﬁrst-principles
calculation. Program package PHASE/0 was
employed.
Because of recent progress of integrated
circuits,
three-dimensional
metal-oxidesemiconductor ﬁeld-eﬀect transistors (MOSFETs) have been attracting attention. The
vertical body-channel-MOSFET has a gateinsulating thermally oxide Si ﬁlm around a Si
pillar with a diameter of several tens of nm,
but it is considered that a large stress distributes in the oxide ﬁlm. When a Si nanowire
with a width of 50 nm and a thickness of
30 nm is processed by dry oxidation at 1000◦ C
for 80 min, it is known that a compressive
strain of about 3% is accumulated near theinterface and a tensile strain of about 3% isaccumulated near the outer surface.
The strain induced in the oxide ﬁlm musthave an unconventional eﬀect on the ﬁlm reliability such as dielectric breakdown. It is known
that the dielectric breakdown of the oxide ﬁlm
is triggered by VO -related defects in the ﬁlm.
The VO -related defects trap holes, and transform into 3-coordinated Si’s with +1 charge.
These 3-coordinated Si’s diﬀuse and aggregate
under a gate-channel electric ﬁeld of MOSFET
operation to create a one-dimensional conduc-tive chain from the Si interface to the gate interface in the oxide ﬁlm. Then, a gate leak current ﬂows through this chain, and leads to thedielectric breakdown. Since the oxide ﬁlm of
the three-dimensional MOSFETs is subjectedby the strain, it is considered that these processes are also aﬀected by the strain.
We focused on the fundamental properties of
VO in the oxide ﬁlm, and investigated the effect of strain on them using the ﬁrst-principles
calculation. We found that the stability of VO
increases under compression. We also foundthat the height of the diﬀusion barrier increases under compression. In addition, we
found that the diﬀusion barrier height is determined by the Si-Si bond length of the VO .
Considering the gate oxide ﬁlm in the vertical body-channel-MOSFET, the VO density
increases because the interfacial oxide ﬁlm issubjected to compressive strain. This suggeststhat interfacial traps are more likely to occur
and performance may be slightly degraded. On
the other hand, tensile strain is applied to thesurface oxide ﬁlm to reduce the density of VO ,but diﬀusion of VO is promoted. This meansthat the reliability of the oxide ﬁlm is aﬀectedby the stain because VO can diﬀuse from theinterface of the oxide ﬁlm to the surface.

References[1] K. Yata and H. Kageshima, Jpn. J. Appl.
Phys. 60 (2020) 035504 (6 pages).

166

Activity Report 2020 / 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 305-8565

Organic small-molecular crystals show a variety of crystal structures and electronic properties. Among them, there is a class of compounds called “hydrogen-bonded systems”, inwhich proton transfer causes π-bond dipole
switching. Some of them show ferroelectricity
or antiferroelectricity [1]. First-principles calculations toghther with the Berry phase theory
successfullty predict spontaneous polarization
values of such ferroelectrics [2, 3, 4, 5, 6]. Antiferroelectrics consist of polar subunits. By applying a strong electric ﬁeld, some of them canbe converted into ferroelectric phases. Evaluating polarization of the subunit, the total
polarization can be predicted in such induced
ferroelectric phases [7, 8].
In 2020, we have applied this approachin predicting electric-ﬁeld-induced polarization of bis-(1H-benzimidazol-2-yl)-methane(BI2C), in which non-polar and/or polar subunits exist depending on temperture, andthe obtained polarization values are in good
agreemet with experimetally obtained results[9]. In addition, similarly to our previous workon antiferroelectric squaric acid [10], calculations with a computationally-applied electricﬁeld are ongoing for several hydorogen-bonded
ferroelectrics and anitiferroelectics.

[2] S. Horiuchi, K. Kobayashi, R. Kumai,
and S. Ishibashi, Nat. Commun. 8, 14426(2017).
[3] F. Kagawa, S. Horiuchi, N. Minami, S.
Ishibashi, K. Kobayashi, R. Kumai, Y.
Murakami, and Y. Tokura, Nano Lett. 14,
239 (2014).
[4] K. Kobayashi, S. Horiuchi, S. Ishibashi,
F. Kagawa, Y. Murakami, and R. Kumai,
Chem. Eur. J. 20, 17515 (2014).
[5] S. Horiuchi, Y. Noda, T. Hasegawa, F.
Kagawa, and S. Ishibashi, Chem. Mater.
27, 6193 (2015).
[6] S. Horiuchi, S. Ishibashi, K. Kobayashi,
and R. Kumai, RSC Adv. 9, 39662 (2019).
[7] S. Horiuchi, R. Kumai, and S. Ishibashi,
Chem. Sci. 9, 425 (2018).
[8] K. Kobayashi, S. Horiuchi, S. Ishibashi,
Y. Murakami, and R. Kumai, J. Am.
Chem. Soc. 140, 3842 (2018).
[9] S. Horiuchi, S. Ishibashi, R. Haruki, R.
Kumai, S. Inada, and S. Aoyagi, Chem.
Sci. 11, 6183 (2020).
[10] S. Ishibashi, S. Horiuchi, and R. Kumai,
Phys. Rev. B 97, 184102 (2018).

References[1] S. Horiuchi and S. Ishibashi, J. Phys. Soc.
Jpn. 89, 051009 (2020).

167

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Search of accessible surfaces for catalyst informatics
Yoyo HINUMA
Institute of Innovative Research
Tokyo Institute of Technology
4259 Nagatsuta-cho, Midori, Yokohama, Kanagawa 226-8502
High catalytic reactivity in oxides is

topmost and bottommost surfaces need to be

expected in high index surfaces and at surface

reconstructed, which is the case in the normal

defects, such as corners and step edges, sincespinel surfaces in this study [3]. Surfaces which

there are cations and anions with more

do not have the lowest energy for a given

unfavorable

environmentsorientation, including terminations found byincluding low coordination number. Theoreticalgenetic algorithm calculations (obtained using

studies are leading experimental investigations

the USPEX code [4]), or its surface energy canon irregular sites because of the difficulty of thebe reduced by forming macroscopic facets [5],latter.

were removed.

coordination

To increase the volume and variety of the

The following orientations were found to bedata without compromising veracity, surfaces

experimentally accessible in β-Ga2O3, in orderthat are appropriately reconstructed need to beof increasing surface energy: (100), (20-1),

added. From another viewpoint, terminations(310), (101), (11-2), (11-3), (11-1). This methodthat are likely to be experimentally accessible

can be used for other materials, and will be aneed to be distinguished from those that are not

powerful tool to find overlooked high-energy

becausesurfaces.

only

surfaces

that

can

be

experimentally synthesized, preferably withless effort, can be used industrially andReferences

therefore contribute to improvement of our[1] Y. Hinuma et al.: Comp. Mater. Sci. 113

society.

(2016) 221.

This study considered 67 terminations (34[2] Y. Hinuma et al.: Phys. Rev. Mater. 2 (2018)

orientations) of β-Ga2O3. The automated124603.

nonstoichiometric and nonpolar slab-and-model[3] Y. Hinuma et al.: Mater. Trans. 61 (2020) 78.

generation algorithm already developed by[4] A.R. Oganov et al.: J. Chem. Phys. 124,

Hinuma et al. [1,2] was expanded to allow(2006) 244704.

automatic derivation of models where the[5] Y. Hinuma et al.: Mater Trans.61 (2020) 143.

168

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Calculation of multication oxide surface properties forcatalyst informatics
Yoyo HINUMA
Institute of Innovative Research
Tokyo Institute of Technology
4259 Nagatsuta-cho, Midori, Yokohama, Kanagawa 226-8502
Surface point defects of metal oxides, fornonstoichiometric and nonpolar slab-and-model

instance O vacancies, have a dominant effectgeneration algorithm already developed byon heterogeneous catalysis. The Mars-Van

Hinuma et al. [1,2] was expanded to allow

Krevelen mechanism is one of the mostautomatic derivation of models where thefrequently encountered catalytic process. In one

topmost and bottommost surfaces need to be

example, O vacancies on a metal oxide catalyst

reconstructed, which is the case in the normal

surface act as reaction sites. The energy

spinel surfaces in this study [3]. A large

minimum required to remove O from a surface,variation of up to 3.6 eV in the smallest EOvac ofwhich is denoted as the surface O vacancyaformation energy (EOvac), can be used toorientations of same material. EOvac wasrationalize and predict catalytic performance intypically higher in a more stable surface withinsuch a catalytic process. Calculation of EOvac

the same compound, which is in line withrequireswithchemical intuition. A good correlation between

sufficient spacing between O vacancies, hence

EOvac and Ebulk, band gap, and electron affinity

some estimation of EOvac from less costly

was obtained between the same orientation for

calculations, such as slab-and-vacuum model(100) and (110) surfaces, although the trend for

calculations with minimum cell size and eventhe (111) surface was contradictory.

bulk calculations, will be effective in screening

Referencesmaterials for a given purpose.

[1] Y. Hinuma et al.: Comp. Mater. Sci. 113aslab-and-vacuum

model

The EOvac of ZnM2O4, where M is one of Al,

surfacewasobservedfordifferent(2016) 221.

Ga, In, V, Cr, Mn, Fe, or Co, was calculated.

[2] Y. Hinuma et al.: Phys. Rev. Mater. 2 (2018)

These compounds take the normal spinel

124603.

structure, and the (100), (110), and (111)[3] Y. Hinuma et al.: Mater. Trans. 61 (2020) 78.

surfaces

wereevaluated.

The

automated

169

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study on complexes of impurity anddislocation in GaN p-n diodes
Yosuke HARASHIMA1,2
1
Institute of Materials and Systems for Sustainability, Nagoya University
Furo-cho, Chikusa, Nagoya, Aichi 464-8601
2
Center for Computational Sciences, University of Tsukuba
Tennodai, Tsukuba, Ibaraki, 305-8577

The development of power semiconductor
devices is one of the key issues for the realization of a sustainable society. GaN has properties suitable for power devices, such as a large
band gap, and is expected to be a candidate
for next-generation power semiconductor materials. On the other hand, the threading dislocations generated during the synthesis of GaN
become a source of leakage current, which impairs the rectifying eﬀect, an important characteristic of the device. It has been reported
that the leakage current is related to the typeof threading dislocation and the condensationof impurities around the dislocation, but the
microscopic mechanism of leakage current generation has not been clariﬁed.
Power semiconductor devices consist of a
combination of p-type and n-type layers, with
impurities such as Si and Mg doped to eachlayer. To understand the mechanism of leakage current generation, it is necessary to understand the electronic state in each layer. The
electronic structure of the complex of Mg andscrew dislocations doped to make the p-layer
has been clariﬁed by our previous studies usingﬁrst-principles calculations and atom probe tomography. [1] The purpose of this study is toanalyze the interaction between Si impurities
doped to make the n-layer and dislocations,and to clarify the properties of the complex
consisting of Si and dislocations.
The eﬀective mass of electrons is smaller

than that of holes in GaN, and the eﬀective
Bohr radius, which indicates the width of the
impurity states, is larger. Therefore, it is necessary to consider larger systems. For larger
system size calculations, we use RSDFT[2, 3], ahighly parallelized and eﬃcient ﬁrst-principles
code. In this study, we consider a screw dislocation with the Burgers vector [0001]. The dislocations break the periodic structure and weuse a supercell. In order to avoid these strainsaﬀecting each other at the periodic boundary,a vacuum layer is inserted in the lateral directions of c-axis.
We consider a 21 Å × 27 Å × 30 Å supercell, which includes about 800 atoms. An
Si atom is substituted at a Ga site. In orderto analyze the binding energy of Si, we performed calculations for several substitutionalsites. We optimized the atomic positions andobtained the stable structures of the complex.
We are analyzing the results for the binding
energy of Si to the screw dislocation.

References[1] T. Nakano, Y. Harahsima, et al.: Appl.
Phys. Lett. 117 (2020) 012105.
[2] J.-I. Iwata, et al.: J. Comput. Phys. 229(2010) 2339.
[3] Y. Hasegawa, et al.: Int. J. High Perform.
Comput. Appl. 28 (2014) 335.

170

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Simulation of scanning tunneling microscopy images ofgraphene ribbons with edges
Junhuan LI, Kenta ARIMA
Department of Precision Engineering, Graduate School of Engineering
Osaka University, Yamada-oka, Suita, Osaka 565-0871
We are aiming at elucidating local electronic

local density of states, an electron density was

structures of finite-size graphene sheets andintegrated over a specific energy window, or atheir impact on scanning tunneling microscopyeV,(STM) images. For this purpose, we have

Molecular Orbital). At each (x, y) coordinate, astarted first-principles calculations of single-

z-height possessing the same electron density

layer graphene ribbons possessing either zigzag(6.72×10-4 /Å3) was investigated and its contour

or armchair edges by the use of a simulation

map was depicted. This approximates a

package named STATE (Simulation Tool for

simulated STM image at the sample bias of a V.

Atom TEchnology). STATE is based on the

We used the module (intel/18.0.5) for thedensity functional theory. The exchange andcompilers and mpt/2.16 for MPI library. The set

correlation potential is described by theof calculation was usually executed on F4cpu

generalized gradient approximation by Perdew-

or F36cpu with suitable nodes in ISSP.

below

HOMO

(Highest

Occupied

To check the performance of our calculation,

Burke-Ernzerhof (GGA-PBE). We also usedand

we modeled a graphene nanoribbon with zigzag

pseudopotentials. When running STATE, weedges terminated by H atoms. Figure 1(a)first defined the atomic structure of a finite-sizeshows a simulated STM image of a zigzag-

graphene. This model as well as otheredged ribbon named C28 at the sample bias of -parameters were placed as an input file on a

1.0 V. C28 indicates the ribbon width

supercomputer.

field

possessing 28 dimer lines across the width. In

method was employed, which is an iterative

Fig. 1(b), a hexagonal carbon network is

method that involves selecting a Hamiltonian,superimposed in the image in Fig. 1(a). Figure

solving the Kohn-Sham equation to obtain a

1 shows that either a hexagonal or a triangularmore accurate set of orbitals, constructing thepattern is formed in the interior of the ribbon

potential for each wave function, and solving

whereas isolated bright spots are formed at boththe Kohn-Sham equation again with these until

edges of the ribbon. The latter is caused by thethe results converge. In order to draw a map of

localized electronic states at a zigzag edge,

both

a

plane-wave

The

basis

set

self-consistent

171

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

which agrees with literature [1]. In the next

References

fiscal year, we are going to characterize the[1] P.L. Giunta and S.P. Kelty: J. Chem. Phys.,
114 (2001) 1807.

distribution of local charge densities of thearmchair-edged graphene ribbon and to unveil[2] J. Li, K. Arima et al.: JSAP (The Japan

its relationship with an STM image around theSociety of Applied Physics) fall meeting

Fermi level.

(2020) 05-101.

Regarding this project, we had three oral

[3] J. Li, K. Arima et al.: JSPE (The Japan

presentations at domestic meetings in 2020 [2-Society for Precision Engineering) fall4].

meeting (2020) 517.
[4] J. Li, K. Arima et al.: JVSS (The Japan(a)Society of Vacuum and Surface Science)(b)

meeting (2020) 1Ba03.

Fig. 1 (a) Simulated STM image of zigzagedged graphene nanoribbon (C28). (b) A
carbon network is superimposed in theimage in (a).

172

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

A theoretical study on the effect of impurity doping on thethermoelectric performance of environmental friendly silicide SrSi2
Tsutomu Iida, Naomi Hirayama, Daishi Shiojiri, Tomoyuki Kadono, and Masato Yamaguchi
Department of Materials Science and Technology, Faculty of Industrial Science and Technology,
Tokyo University of Science, 6-3-1 Niijyuku, Katsushika-ku, Tokyo, 125-8585, Japan
properties from theoretical considerations.
This year, we carried out DFT calculations of
the transport characteristics of α-SrSi2 using the
Heyd–Scuseria–Ernzerhof screened hybrid
functional,
andthencomparedtheexperimentallymeasuredthermoelectric
properties with the computational results.
The bandgap of the polycrystalline α-SrSi2grown by vertical Bridgman method estimatedfrom the carrier density dependence on
temperature was 13.1meV. When the mixing
parameter of the Hartree-Fock contribution to
the exact exchange was 18.7%, the bandgap was
estimated to be 13.27 meV, which almost
reproduces the experimental Eg value.
Furthermore, Seebeck coefficients were
calculated using the Boltzmann transport theory,and the results obtained using the chemical
potential that matches the carrier concentration,
which was determined experimentally, were ingood agreement with the temperaturedependence of the Seebeck coefficient obtained
experimentally. It was concluded that firstprinciples calculations using the hybrid
functional can successfully predict thethermoelectric transport properties of narrowgap thermoelectric semiconductors.

Thermoelectric semiconductors, especiallythose operating at low temperatures, areexpected to be applied to power generation
systems that utilize the vaporization of liquefied
natural gas as cold heat energy sources, and to
self-powered wireless sensors.
α-SrSi2 has been identified as a potential TE
material, and its main attributes are its lightweight, its non-toxicity, and the worldwide
abundance of its constituent elements. α-SrSi2
has relatively good power generation
performance, with a dimensionless figure of
merit ZT = ~0.15 at 300 K [1] and p-typeconduction when the composition is
stoichiometric. For practical use, in order tofurther improve the p-type thermoelectricperformance and achieve n-type conduction of
α-SrSi2 so as to configure pn devices, it would
be necessary to quantitatively understand theelectronic structure through experimental
studies and theoretical calculations.
The electrical properties of polycrystalline αSrSi2 have been examined by M. Imai et al. [2],who revealed that α-SrSi2 is a narrow-gap
semiconductor with an energy gap of 35 meV
and that its dominant carriers are holes. Theirresults, however, were not consistent with theresultsofprevious
electronic-structure
calculations for which density-functional theory(DFT) with the conventional generalized
gradient approximation was used. Most of thecalculated bandgap values were about 0 eV orless, which is much smaller than theexperimentally observed values. This difference
makes it difficult to predict the thermoelectric

References[1] S. K. Singh and M. Imai, Intermetallics 127,
106981 (2020).
[2] M. Imai, T. Naka, T. Furubayashi, H. Abe, T.
Nakama, and K. Yagasaki, Appl. Phys. Lett. 86,
032102 (2005).

173

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

STM simulations for Si(111)7 × 7 surfaces
Kei TANIMOTO and Ken HATTORI

Graduate School of Science and Technology, Nara Institute of Science and Technology,
Takayama, Ikoma, Nara 630-0192
Using

scanning

tunneling

microscopy

The small-size 4 × 4 surface has an advantage(STM), author's group has been studied ironsilicides formation on Si(111) [1] prepared inof fast calculation compared to that in the 7 × 7

ultra-high vacuum. In the initial stage of

surface, maintaining the specific 7 × 7 surface

property (dimer － adatom － stacking-fault

Si(111) 7 × 7 with isolated Fe atoms, we

structure): 4 Si adatoms on 2 × 2 T4 sites, and 2

experimental STM images [2]. Using the super4 × 4 unit cell.

of 4 restatoms terminated with H atom, in aobserved 5 different adsorption types inOn the basis of these results we extended

computing system in the institute for solid statephysics,

wecarried

out

first

principles

the calculations to 7 × 7 surfaces in this year,

calculations for several configurations of Fe

firstly focusing a clean surface using theatoms on Si(111)4 × 4 surface in the last year.

calculation package of Simulation Tool for

Fig. 1. Schematics of clean Si(111) 7 × 7 surface model in side (upper left) and top (upper right)

views, and simulated STM images in filled states (left panel) and empty states (right panel) at
different sample bias voltages (Vs). The red arrow represents side-viewing direction.

174

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Atom TEchnology (STATE)-Senri [3]. The

structure capturing an Fe atom, extension of thecalculated clean 7 × 7 model consists of a Si

adatom-layer, six Si-layers, and a bottom H-

Fe adsorption configurations in the 4 × 4

models.

terminated layer, with 347 atoms. All atoms

The

authors

thankProfs.

Morikawa,

except the last Si layer and bottom H layer are

Hamada, and Inagaki in Osaka University, andfully relaxed at <0.05 eV⁄Å from atomic

Prof. Yanagisawa in Ryukyu University for

positions predicted in the 4 × 4 model, under

their great support in STATE-Senri calculations.

images are simulated using a special STM

References

displaying tool [4].

[1] K. Kataoka, K. Hattori, Y. Miyatake, and H.

700 bands without spin polarization. STM

Daimon, Phys. Rev. B 74 (2006) 155406.

The obtained STM simulation images in Fig.
1 display 12 adatoms in a 7 × 7 unit cell at the[2] K. Kataoka, Dr.. Thesis, Nara Institute ofall Vs, and successfully 6 restatoms at Vs = -1.0

Science and Technology, Nara (2006).

V. We also recognize that corner adatoms[3] Y. Morikawa, Phys. Rev. B {\bf 63} (2001)(COA) are brighter (higher) than center

033405, and references therein.

adatoms (CEA), and atoms on a faulted half[4] The precise STM calculation tool has been

(FH) unit cell are brighter (higher) than thosedeveloped by Prof. I. Hamada in Osaka

on an unfaulted half (UH) unit cell, in filled

University and Prof. S. Yanagisawa in Ryukyu

states. These features are consistent with the

University.

experimental results. The relaxed 7 × 7 cleansurface structure can be applied for the starting175

Activity Report 2020 / 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
Magnesium (Mg) has been of increasinglyinterest

from

the

engineeringradius. On the other hand, changes in USFE

viewpoint,

and SSFE for the second-pyramidal slip were

because of its low density and relatively highnot monotonic with respect to the atomic radius

specific strength.

of the solute atom.

In this study, we calculate generalized

In Mg-Y alloy, enhanced activation of

stacking fault energy (GSFE) surface, topyramidal slips improves ductility. It has been

evaluate activation of each slip system in Mg,

suggested that the activation of pyramidal slips

using first-principles calculations. In GSFE

was attributed to intrinsic I1 stacking fault (SF)calculations for pyramidal slips, it is importantenergy stabilized by Yttrium addition. We

to take account of relaxation of atomic

investigated defect nucleation in the vicinity ofconfiguration perpendicular to the slip direction.

a pre-existing intrinsic I1 SF by molecular

For the first-pyramidal slip, out-plane atomic

dynamics simulations. While formation of (11-relaxations were observed during the slip21) twin was observed under shear stress onprocess. The out-plane atomic relaxations(0001)

reduce the GSFE and cause an energy

dislocations were generated with SFs for higher

minimum on the curve, corresponding to theresolved shear stress for pyramidal slips. The

stable stacking fault energy (SSFE). For the

dissociation reactions of the dislocations at thesecond-pyramidal

atomicside ends of the I1 SF were energeticallyrelaxation perpendicular to the slip direction

evaluated, and it was implied that nucleation of

was associated with the stable stacking fault.

the <c+a> dislocations on the first-pyramidal

slip,

in-planealong[11-20],<c+a>partialplanes is more favorable than on the second-

In order to investigate effects of alloying
elements, we carried out the GSFE calculations

pyramidal planes.

with alloy models in which one solute atom

References

was substituted at the slip plane. The unstable[1] R. Hori: Master Thesis, Shinshu Univ.

stacking fault energy (USFE) and SSFE for the(2021).

first-pyramidal slip were more reduced by[2] S. Yoshikawa and D. Matsunaka: Comp.

addition of the solute atom of the larger atomic

Mater. Sci. 179 (2020) 109

176

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Elucidation of the mechanism of self-ordering phenomena
at the interface between organic and inorganic materials
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 an interface system between

surface dimer was investigated to explicitly

an inorganic solid surface and organic molecules,

account for Ge(001) surface dimer conditions.

PTCDAs on Ge(001) surface using the Density

On the Ge(001) clean surface, the obtained

Functional Theory (DFT) calculations with theactivation barriers for dimer flipping underclimbing image nudged elastic band method andvarious dimer configurations are enough small

kinetic Monte Carlo simulation. All MPI

to overcome at high temperature as well known

parallelized DFT calculations were performed

in many previous experiments. The activation

using Vienna Ab initio Simulation Package

barrier of surface dimers between adsorbed(VASP) version 5.4.4 on the ISSP's newmolecules was larger than that of the clean

supercomputer system.

surface, but sufficient to overcome it at 500K.

First, we elucidated the hopping mechanismof the isolated adsorbed PTCDA molecules on
Ge(001) surface. [1] Subsequently, we simulated
that a PTCDA molecule hops on the Ge(001)under the intermolecular interactions as shownin Fig. 1. It was found that lone adsorbed
PTCDA molecules cannot hop on Ge(001). On
the other hand, they can hop under theintermolecularinteractions

at

500K.

Successively, we performed kinetic Monte Carlo
Fig. 1: The hopping of PTCDA on Ge(001)under the intermolecular interaction.

simulations using the activation energies
obtained by DFT calculations for the hopping of
PTCDA

moleculesinvariousproximity

adsorption configurations at medium coverage.

References

As a result, the formation of one-dimensional[1] T. Shiota, W. Mizukami, H. Tochihara, K.

molecular chains was confirmed.

Yagyu, T. Suzuki, and Y. Aoki, J. Phys. Chem. C
124, 24704 (2020)

Next, the flip-flop motion of the Ge(001)177

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study on Machine Learning Model of Carrier Dynamics
in Semiconductor Devices
Masakazu Muraguchi
Faculty of Engineering, Hokkaido University of Science,
Maeda, Teine, Sapporo 006-8585
variation of the electron density distribution
using time evolution calculations. For
example, the transmission probability with
impurity in the nanowire is sensitive to theposition shift of impurities for y-direction(see Fig.1). As the machine learning method,a Random Forest (RF) is employed formodeling. The mean absolute error isevaluated. As the result, the accuracy of themodel is improved by performing machinelearning based on the extracted features. The
proposed method provides a new perspective
for analyzing the motion of electrons in
nanoscale semiconductors.

In a two-dimensional nanowire systemwith random impurity distribution, wedeveloped a model to predict the electrontransmission probability from the impurity
distribution by combining the time evolutionof the electron wave function and machinelearning.
Electron conduction in nanoscale twodimensional wires with random impurity
distribution is investigated. To prepare thedataset for machine learning, the timedevelopment of an electron wave-packet is
calculated, and obtain the transmission
probability. The time-dependent schrödinger
equation is solved where the finite difference
method is employed with the second-order
split operator method [1,2]. Note that asupercomputer system was used for thesetime-consuming time evolution calculations.
Then, a model that can predict thetransmission probability of electron wave
packets from the space distribution of
impurities build by using the machinelearning. Through this process, the ways to
extract the features of the transmission on
this system is investigated.
The impurity distribution can be
reproduced when the central coordinates areavailable. Therefore, this can be used as afeature. However, this does not directly
include the whole shape of the potential
distribution. Therefore, the features of thesystem were extracted by analyzing the time

Fig.1 Transmission probabilities with the electronenergy where the positions of impurities are shifted
3.3 nm to y-direction between the case (a) and (b).

References[1] N. Watanabe and M. Tsukada: Phys. Rev. B 62
(2000) 2914.
[2] T.Shiokawa, M. Muraguchi and K. shiraishi, Jpn. J.
Appl. Phys. 58 (2019) 112002.

178

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Temperature dependence of liquid ethanol based on semiclassical Kramers-Heisenberg formulation
Ryosuke YAMAMURA, Kento AKIHIRO, Nozomu FUTAMATA, and Osamu
TAKAHASHI
Basic Chemistry Program, Graduate School of Advanced Science and Engineering,
Hiroshima University, Higashihiroshima, Hiroshima 739-8526, JapanThe hydrogen bonding in the condensed
phase

plays

a

important

role

in

the

understanding related liquid such as water andliquid alcohols. We have studied temperaturedependence of liquid ethanol using X-ray
emission spectroscopy (XES) theoretically andexperimentally. The approach of combining
theoreticalandexperimental

methodsis

Fig A: XES spectra based on

important for obtaining the hydrogen bonding

SCKH at 240K and 340K

information. The experimental XES warecarried out using the BL07SU HORNET station

extracted randomly. The number of snapshots

at SPring-8.

are 100 for each temperature. XES spectra canbe

In theoretical method, combining molecular

calculatedbyapplying

semi-classicaldensity

Kramers-Heisenberg (SCKH) formulation to thefunctional theory (DFT) calculations performed.

electronic state of each snapshots. Fig A shows

To construct structure of ethanol in liquid phase

the XES spectra based on SCKH. The calculatedclassical MD are adopted in the NVT ensemble

spectra well correspond to the experimental

at 240 K and 340K and 1 bar using GROMACS

spectra. Now, we analyze the MD snapshots and5.1.4 with OPLS force field. To calculate theinvestigate the relationship between XES

XES spectra, the DFT calculation performed

spectra and hydrogen bonding.

using deMon2K program package. The detail ofReferences

DFT calculation method are following the[1] M. P. Ljungberget, et al.: J. Chem. Phys. 146

previous studied for methanol [1] and ethanol(2017) 134596[2]. In short, the[2] O. Takahashi, et al.: J. Chem. Phys. B 49

dynamics

simulations

(MD)

and

17 ethanol cluster obtained(2017) 11163

from final snapshot of MD simulations are

179

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of analysis method for molecular crystal surface
using wave number space-resolved photoelectron spectroscopy
Kaori Niki
Graduate school of science
Chiba University, Yayoi-cho, Inage-ku, Chiba 263-0022
PTCDA does not contain transition elements, theBy using wave number space photoelectron
spectroscopy, it has become possible to obtain acalculation cost is low. Periodic DFT

photoelectron momentum maps (PMMS) of acalculations were carried out with VASP code

molecular thin film in a short time. This allowed

using the projector augmented wave (PAW)

us to obtain tomography of the wavefunction. It

method with a plane wave energy cutoff of 400

is suggested that more information can be[eV] and the PBE exchange-correlation

obtained by analyzing PMMS in detail. We havefunctional. The criterion convergence chosen forbeen analyzing the surface of molecular crystals

the SCF cycle was 10-8 eV, and optimization

with the aim of establishing a method for

were considered converged once theanalyzing momentum maps based on theforces on all atoms were lower than 10‐8 [eV/Å]

multiple scattering method. For the initial state,

The slab was 12.1 x 12.1 [Å] large, and 10 [Å]

we refer to the electronic state of the adsorption

thick (60 Ag atoms, 2PTCDA per unit cell)systeminitiowith a vacuum separation 20 [Å]. The three

Simulation Packge (VASP) [1,2]. So far, welowest layers were frozen during optimizations.

have suggested that by PMMS, it may be

The Brillouin zone was sampled with apossible to identify the adsorption position of

4x4x1 k-point grid. Electron occupancies

molecules adsorbed on the substrate surface [3].

were determined according to a Methfessel-

In 2020, we expanded the sample to a more

Paxton scheme (order1) with an energy

complex system. We placed VASP on thesmearing of 0.2[eV].

calculatedbyVienna Ab

As a result of structural optimization, PTCDASupercomputer of Institute for Solid State
Physics and performed two calculations.

was curved in an arc with respect to the surface.

1. Structural optimization and multiple

PMMS calculations (using our computer) were

scattering calculation of PTCDA / Ag (111).

performed using these coordinates. The PMMS

3,4,9,10-

has changed significantly compared to the

Perylenetetracarboxylic dianhydride (PTCDA)

results without the substrate. When I did thewas set to the Short-bridge site on Ag (111), andsame calculation on multiple sites, I found thatstructural optimization was performed. Since

PMMS was different for each site. This indicatesThe

initialpositionof180

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

based on the paper [5].

the possibility of obtaining information on theadsorption position from PMMS.

Figure 1 shows the temperature dependence

2. Structure optimization and multipleof energy. The horizontal axis is temperature,scattering calculation of CuPc and TiSe2

and the longitudinal axis is energy, white

In order to calculate the PMMS of Copper (Ⅱ)

triangles are the CDW layer, and black squares

phthalocyanine (CuPc) / TiSe2, the structure of

are the normal phase. From this calculation, it

CuPc and TiSe2 was optimized. First, we

was found that 200K at which the phase

performed structural optimization of CuPc.

transition occurs is approximately σ = 0.3. This

CuPc has a large number of constituent atoms

calculation provided us with a guideline to use σ

and contains transition elements with spin. The= 0.1 for low temperature calculations and σ =calculation cost is high and the calculation

0.4 for room temperature calculations in future.

method is complicated. Highest Occupied
Molecular Orbital (HOMO) -1 was not
calculated

in

the

correct position when

Generalized Gradient Approximation (GGA)
was used as a functional. It has been reported
that HOMO -1 can be calculated correctly using
the hybrid functional according to Heyd et al.
(HSE), but the calculation cost is high [4]. We

Figure 1. Energy dependence of sigma

also tried this, but couldn't succeed.

Using these calculation results obtained, we

Next, the structure of TiSe2 was optimized.

plan to calculate the structural optimization and

TiSe2 takes the CDW layer at low temperatureelectronic state of the adsorption system in 2021.

and undergoes a phase transition to the normal

References

phase at around 200 K [5]. To obtain information[1] G. Kresse, and J. Furthmuller: Phys. Rev. B,

about

54, (1996) 11169.

therelationshipbetweenσandtemperature during smearing, we calculated the[2]G. Kresse, and J. Hafner: Phys. Rev. B, 49

temperature dependence of the charge density(1994) 14251.

wave (CDW) structure and the normal phase.

layers of TiSe2. The calculation conditions are[3] K. Niki. M. Nozaki, S. Kurihara, and N.
Komiya: Vac. Surf. Sci. Jpn. 63 (2020) 336.
[4] K. Sch¨onauer et. al.: Phys. Rev. Lett. 94(2016) 205144.

the same as those described above. The normal[5] F.J. Di Salvo, D.E. Moncton, and J.V.

layer extended the (1x1) structure to (2x2). For

Waszczak: Phys. Rev. B: 14 (1976) 4321.

Structural optimization was performed for two

the CDW layer, the coordinates were entered181

Activity Report 2020 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analysis of local quantities of electron ﬁeld inmaterial surface
Masahiro FUKUDA
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

The local physical quantities, which is deﬁned in the framework of quantum ﬁeld theory (energy-momentum tensor density, current
density, chiral current density, and so on), aresigniﬁcant to understand physical or chemical
properties of surface materials, since it is noteasy to be explained by bulk feature in solids
such as a band structure.

ative stress as shown in Fig. 1 (d) reveals the“liquid” character of bulk metallicity. These
characterizations will help us to understandchemical bond formation between a material
surface and a molecular cluster deeply.

In the previous work, we developed a program code which enables us to calculate local physical quantities as a post-process calculation from OpenMX [1] (DFT calculation
program code) in order to evaluate the local
physical quantities in large periodic systems.
To proceed the discussion on a relation between the chemical bonding and the local electronic stress, recent research revealed the importance of evaluation of local physical quantities in a certain energy range. Therefore,
in this project, we developed a program code
which enables us to calculate local physicalquantities in a speciﬁed energy range or orbitals.
The physical and chemical nature aroundthe interaction region between atoms in
Ag(FCC) were investigated as a demonstration. In Fig. 1 (a), the positive stress (tensile stress) and the eigenvectors form the spindle structure [2], which visualize a covalentbonding state. On the other hands, in Fig. 1(b), the negative stress (compress stress) andthe eigenvectors form the anti-spindle structure [2], which visualize an anti-bonding state.
Moreover, the distribution of the isotropic neg-(a) DOS(b) −5eV < E < −4eV(c) −4eV < E < −3eV(d) −1eV < E < 1eV

Figure 1: (a) Density of state, (b)-(d) distributions of maximum eigenvalues and eigenvectors of the electronic stress tensor density ofAg(FCC).

References[1] OpenMX, http://www.openmx-square.org/.
[2] A. Tachibana, “New Aspects of Quantum
Electrodynamics”, Springer (2017)182