令 和 ３ 年 度
京 都 大 学 大 学 院 理 学 研 究 科

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要旨集

２０２１年１１月１９日（金）物 理 学 第 一 分 野

物理学第一分野ＤＣ３回生研究発表会
場所：オンライン
発表：２０分（別に質問１０分程度）
２０２１年１１月１９日（金）９：００～

開始

目

次

１．Solvent effect of normal alkane on blue phase
Hitoshi Takao（ ９：００）
・・・・・ １
２．Development of a programmable quantum system using single
Ytterbium atoms trapped in an optical tweezer array
Daichi Okuno（ ９：３０）・・・・・ ２
３．Exotic superconductivity associated with parity symmetry breaking
Shota Kanasugi（１０：００）
・・・・・ ３
４．Probing three-state Potts nematic fluctuations by ultrasound attenuation
Kazuhiro Kimura（１０：３０）・・・・・ ４
１１：００～１１：１０ 休憩
５．Role of incoherent carriers in high harmonic generation from atomically thin semiconductors
Kohei Nagai（１１：１０）・・・・・ ５
６．Game-theoretic derivation of Gibbs distribution
Ken Hiura（１１：４０）
・・・・・ ６
７．Stochastic growth of a stable phase from a metastable phase
Mao Hiraizumi（１２：１０）
・・・・・ ７
１２：４０～１３：４０ 昼休み
８．Extended Nielsen-Ninomiya Theorem for Floquet and non-Hermitian Systems
Takumi Bessho（１３：４０）
・・・・・ ８９．Theoretical study on Nonequilibrium many-body phenomena in Floquet systems
Kaoru Mizuta（１４：１０）・・・・・ ９
１０．Non-Hermitian aspect of strongly-correlated electron systems
Yoshihiro Michishita（１４：４０）
・・・・・１０
１１．Novel quantum phases accompanied by rotational symmetry breaking
in strongly correlated electron systems
Hinako Murayama（１５：１０）
・・・・・１１

Solvent effect of normal alkane on blue phase
Soft Matter Physics Group

Hitoshi TAKAO

Abstract We investigated the solvent effect caused by mixing normal alkane molecules withcholesteric blue phase (BP). As the result, we found that BP was stabilized under wide
temperature range by the addition of alkane molecules. we revealed that alkane molecules are
uniformly distributed in BP and weaken chiral interaction.
© 2021 Department of Physics, Kyoto University(Cholesteric) Blue Phase (BP), which appears in narrow temperature region, about 1℃, between cholesteric(Ch) and isotropic (I) phase, has characteristic molecular arrangements. Since strong chiral interaction induces
the short pitch twist of the nematic director, and the cylinder arrangements twisted to radial direction. This isso called “double twist cylinder (DTC)”, which are embedded in cubic lattice of a few hundred nm. Since
DTCs cannot fill up the space continuously, disclination lines should be created and intercalated among DTC
in BPs. Recently, many researchers achieved to expand BP temperature region by addition of polymer andnano-sized molecules etc… to change Frank elasticity and free energy density of system [1,2,3]. However,there are few reports about BP stabilization by mixing simple low molecular organic solvent with BP.
In this study, we investigated solvent effect diluted by normal alkane. As the result, we found that BP wasstabilized under wide temperature range by the addition of alkane molecules (Fig.1). To clarify mechanism of
this effect, we measured the dependence of helical pitch of both BP and Ch phase on solvent concentration.
As the result, it was confirmed that helical pitch equally increases in both phases (Fig.2). Therefore, it is foundthat solvent molecules are not localize in the core of defects and uniformly disperse entirely. Furthermore, we
demonstrated alkane molecules weaken chiral interaction of LC molecules.

650

BP
65.0

I
I-（I+BP）

60.0（I+BP）-BP

BP-（BP+Ch）

55.0

Ch

（BP+Ch）-Ch

50.0

0

2

4

6

8

10

alkane concentration (wt%)

Fig.1:Temperature-concentration phase diagram for BPalkane miscible system..

optical pitch (nm)temperature (℃)

70.0

600

550

Ch

500

BP2
450
400
0

2

4

6

8

10

alkane concentration (wt%)

Fig.2: The dependence of optical pitch of BP and Ch on
alkane concentration.

References[1] H.Kikuchi et al., Nature Material 1, 64-68 (2002)[2] H.Kikuchi et al., Adv. Funct. Mater, 23, 2387-2396 (2013)[3] M.Ozaki et al., Appl. Phys. Express 2, 121501 (2009)

Development of a programmable quantum system using single
Ytterbium atoms trapped in an optical tweezer array
Quantum Optics Group

Daichi Okuno

Abstract We report progress towards the realization of high-fidelity quantum gate operations using
Ytterbium atoms. We have succeeded in two key experiments of trapping and imaging of single atoms andthe excitation to Rydberg states following the excitation to the 3P2 metastable state.
© 2021 Department of Physics, Kyoto University

Recently single atoms trapped by a reconfigurable array of micro-optical traps have been attracting attentions. In
addition, controlled excitation to Rydberg states — highly excited states with an outermost electron(s) occupying theorbit with a large principal quantum number — will produce interactions between atoms in distant sites (typically fewμm), and it enables bottom-up construction of a quantum system for the study of quantum physics, especially neutral
atom quantum computation [1]. In this study, we focus on Ytterbium (Yb) atoms which possesses many advantageous
properties stemming from two valence electrons: the existence of optical transitions between Rydberg states ( (6s)(nl)→ (6p)(nl) ), long-lived metastable excited states, and Zeeman sublevels of nuclear spin in the ground state offermionic isotopes 171Yb or 173Yb which are less sensitive to magnetic fields [2]. Here we report two key experiments
towards the construction of a scalable quantum computer which utilizes above mentioned nature of Yb atoms.
First, we show the result of trapping and imaging of single Ytterbium atoms. We generated two-dimensional arrayof tightly focused light through an objective lens (NA=0.6), by applying multi-tone RF to two orthogonal
Acousto-Optic Deflectors (AODs) which deflect the laser with desired angles in two dimensions. We used 532nm
laser for the trap and this creates quite a deep potential for the ground state atoms, typically ~1mK. We confirmedthat we successfully achieved nearly diffraction-limited beam waist of 1μm by measuring the trap frequency of theatoms in the potential. As shown in Fig. 1, we have succeeded in getting images of single atoms by detecting thefluorescence and observed a stochastic behavior of the loading to the trap, namely each site is filled or empty with
50% probability, due to the pairwise loss assisted by near-resonant red detuned light for the purpose of excluding
multiple atoms in one trap site [3].
Second, we succeeded in the excitation to the Rydberg states from the 3P2 state for atomic clouds with typically
105 atoms. This 3P2 state has long lifetime of the order of seconds. The choice of the metastable state enables coherent
one-photon transitions from the ground state and to Rydberg states, which suppresses decoherence compared with
two-photon excitation method used in alkali atoms [4]. With this new excitation scheme to use the 3P2-Rydberg states,
we observed the spectra associated with target Rydberg states (6s)(nd) 3DJ (J=1,2,3) and (6s)(ns) 3S1, and also their
response to an applied electric field.
We are now working on combining these two experiments, that is to say, we are trying to perform coherent
excitation of single Ytterbium atoms to the 3P2 state and Rydberg states, which is an important step towards thedemonstration of quantum gate operation on single Ytterbium atoms.
References[1] M. Saffman et al., Rev. Mod. Phys. 82,
2313 (2010).
[2] M. Saffman, Nature 567, 468-470(2019).
[3] N. Schlosser et al., Nature 411, 1024-1027(2001).
Figure 1: (a) An image of single atoms trapped in a 5x5 trap array. Yellow[4] I. S. Madjarov et al., Nat. Phys. 16, squares represent region of interests (ROIs) for each trap site. (b) A
857–861 (2020).
histogram of the fluorescence count in each site.

Exotic superconductivity associated withparity symmetry breaking
Condensed Matter Theory Group

Shota Kanasugi

Abstract Superconductivity associated with parity symmetry breaking has been attracted much attention
owing to its exotic properties such as nontrivial topology and nonreciprocal transport. In this work, weclarify a variety of novel interplay between superconductivity and parity symmetry breaking from fresh
viewpoints.
© 2021 Department of Physics, Kyoto University

Unconventional superconductivity is one of the central topics in modern condensed matter physics. In
particular, exotic superconducting phenomena induced by parity symmetry breaking is attracting much attention
since the discovery of noncentrosymmetric (NCS) superconductors [1]. Although the interplay ofsuperconductivity and parity symmetry breaking has been elucidated mainly for NCS superconductors, we canconsider other types of superconductors associated with parity symmetry breaking; (i) superconductors coexistent
with other parity-breaking orders, (ii) locally NCS superconductors, and (iii) superconductors hosting multiple
even- and odd-parity pairing instabilities. However, theoretical understanding for such superconductors is stillinsufficient compared with that for NCS superconductors.
In this work, we investigate the above three types of exotic superconductivity associated with parity symmetry
breaking. Summaries of each study are shown below.
1. Ferroelectric superconductivity and multiorbital/multiband effects [2,3]We study a coexistent phenomenon of superconductivity and ferroelectric-like polar parity-breaking order,that we name the ferroelectric superconductivity (FESC). In particular, we focus on SrTiO3 as a possible candidate
and demonstrate the impacts of the multiorbital/multiband effect on the FESC. By analyzing a multiorbital modelfor SrTiO3, we show that the FESC is stabilized in a very low carrier density regime or high magnetic field regime.
Furthermore, we predict that the FESC in SrTiO3 leads to Weyl superconductivity and odd-frequency pairing.
2. Odd-parity superconductivity in locally noncentrosymmetric crystals with ferromagnetic fluctuations [4]We clarify the novel interplay of ferromagnetic-fluctuation-driven odd-parity superconductivity and locally
NCS crystal structure. To this end, we consider a bilayer triangular lattice Hubbard model relevant to bilayertransition metal dichalcogenides. By analyzing this model, we demonstrate that multiple odd-parity pairing
instabilities are induced owing to the combination of locally NCS crystal structure and ferromagnetic fluctuation.
The results shed light on the possibility of odd-parity superconductivity in ferromagnetic van der Waals materials.
3. Anapole superconductivity from PT-symmetric mixed-parity interband pairing [5]We explore time-reversal-symmetry-breaking mixed-parity superconductivity, which can be stabilized whenthe even- and odd-parity pairing instabilities are competing in one system. We show that such superconducting
states generally exhibit an unusual asymmetric Bogoliubov spectrum in multiband systems. We also demonstratethat the asymmetric Bogoliubov quasiparticles lead to the effective anapole moment of the superconducting state,
which stabilizes a nonuniform FFLO-like superconducting state at zero magnetic fields. Furthermore, we apply
our theory to a recently discovered superconductor UTe2.
References[1] E. Bauer and M. Sigrist, eds., “Noncentrosymmetric Superconductor: Introduction and Overview”, (Springer,
Berlin, 2012).
[2] S. Kanasugi and Y. Yanase, Phys. Rev. B 100, 094504 (2019).
[3] S. Kanasugi, D. Kuzmanovski, A. V. Balatsky, and Y. Yanase, Phys. Rev. B 102, 184506 (2020).
[4] S. Kanasugi and Y. Yanase, Phys. Rev. B 102, 094507 (2020).
[5] S. Kanasugi and Y. Yanase, arXiv:2107.07096 (2021).

Probing three-state Potts nematic fluctuations
by ultrasound attenuation
Kazuhiro Kimura (Condensed Matter Theory Group)
Abstract Motivated by recent studies of three-state Potts nematic states in magic-angle twisted bilayer
graphene and doped-Bi2Se3, we analyze the impact of critical nematic fluctuations on the low energy
properties of phonons. In this study, we propose how to identify the three-state Potts nematic fluctuations
by ultrasound attenuation.
© 2021 Department of Physics, Kyoto University

Recent discoveries of electron-nematic phases, which break a certain point group symmetry of the system, havesuggested that the superconducting pairing mechanism may be closely related to nematicity in some correlated
electron systems. Obviously, the relation between electron-nematic order and unconventional superconductivity isa pressing question in present condensed matter physics.
In the case of magic-angle twisted bilayer graphene [1], an electron-nematic state, which breaks the lattice C3z
symmetry, has been detected [2]. This C3z-broken electron nematic state, referred to as a three-state Potts nematicstate, is of interest for its competition [2] with nematic superconductivity and for the mystery of the Landau level
degeneracy [1]. Moreover, in the case of doped-Bi2Se3, which is a candidate material of nematic superconductors[3], a three-state Potts nematic state has been reported above the superconducting transition temperature [4].
Besides the relationship between nematicity and superconductivity, it is also important to identify the criticalbehavior of electron-nematic states and to distinguish whether it is intrinsic (i.e. induced spontaneously) or
extrinsic (i.e. due to trivial strains or the structural distortion).
We investigate [5] the influence of the nemato-elastic
coupling on the low energy properties of phonons by aphenomenological argument using a Ginzburg-Landau-Wilson
action and a microscopic analysis based on the Hubbard model.
The Gaussian fluctuation analysis shows an isotropic
divergence of the transverse sound attenuation coefficient, incontrast to the case of the C4-breaking bond-order whichshows the strong anisotropy [6]. Moreover, we use amean-field approximation and discuss the impurity effects.
With increasing the impurity scattering, the first-ordertransition line (see Fig. 1) at low temperatures gradually shifts
towards the second-order transition line, rendering the
Fig. 1. Phase diagram of a nematic bond-orderedtransition a weak first-order. Finally, we expect that thestate near the van-Hove filling (N = 1.25). Tc1st
enhancement of the ultrasound attenuation coefficient will be(Tc2nd) is the first (second) order phase transition
clearly observed in the case of the intrinsic electron-nematicline. Two different nematic configurations are shownphase transition, even if it is a weak first-order transition.
as the three arrowheads surrounded by the circle,
which is divided by u3=0 line.

References[1] Y.Cao, et al., Nature 556, 80 (2018), Y. Cao, et al., Nature 556, 43 (2018).
[2] Y. Cao, et al., Science 372, 264 (2021).
[3] K. Matano, et al., Nat. Phys. 12, 852 (2016), S. Yonezawa, et al., Nat. Phys. 13, 123(2017).
[4] Y. Su, et al., Phys. Rev. Lett. 123, 027002 (2019), C.-w. Cho, et al., Nat. Commun. 11, 3056 (2020).
[5] K. Kimura, M. Sigrist, and N. Kawakami, arXiv:2110.01308 (2021).
[6] H. Adachi and M. Sigrist, Phys. Rev. B 80, 155123 (2009).

Role of incoherent carriers in high harmonic generation fromatomically thin semiconductors
Solid State Spectroscopy Group

Kohei Nagai

Abstract We have studied photo-carrier doping effects on high harmonic generation in monolayer
WSe2 by pump and probe spectroscopy. The doping-induced effects suggest that high harmonic
generation is governed by the incoherent carriers that are originally generated by the strong driving
field in addition to the photo-carriers.
© 2021 Department of Physics, Kyoto University

Non-perturbative interaction between strong laser field and solid triggers various coherent electron dynamics,
such as Zener tunneling, Bloch oscillation, and also formation of Floquet state [1,5]. High harmonic generation(HHG), which converts low-energy photons to visible to ultraviolet photons, offers a powerful experimental tool tounderstand the coherent electron dynamics [1-5]. Many theoretical studies have predicted that inter- and intra-bandcurrents created by strong-field driven coherent and incoherent carriers in momentum space radiate high harmonics
in solids [1]. In experimental studies, HHG has been mainly investigated for bulk crystals [1,2]. However,propagation effects in bulk solids obscure the intrinsic harmonic spectrum, which hinders the study of microscopic
mechanisms. To avoid such difficulty, atomically thin semiconductors are an ideal platform [3-5]. Although HHG
from monolayer transition metal dichalcogenides has been successfully explained by inter- and intra-band currents[3,4], there remain several unclear problems; interplay between these mechanisms and also many body effects understrong laser field.
In this study, we experimentally distinguish the role of incoherent carriers in high harmonic generation by using
photo-carrier doping [2]. We fabricated single monolayer WSe2 by mechanical exfoliation. Incoherent carriers withthe density of 1012-1013 cm-2 were injected into the sample by near-infrared (NIR) pulses that are resonant with theabsorption edge of the monolayer (photon energy: 1.63 eV, bandwidth: 10 nm). After the decoherence process ofthe photo-carriers, intense mid-infrared (MIR) pulses (photon energy: 0.26 eV, pulse duration: 60 fs, peak intensity:
0.24 TW/cm2) were shined to generate high harmonics from the photo-doped samples (Fig. 1(a)).
We observed the harmonics from the 5th to 12th order under the MIR driver. Under the photo-carrier doping, asmall enhancement of the 5-th order harmonics (below the absorption edge) and large suppression of higher
harmonics (above the absorption edge) were confirmed as shown in Fig. 1(b). Theoretical calculation using
semiconductor Bloch equation indicates that the enhancement of the 5thorder harmonics is originated from the intraband acceleration of photocarriers. Also, excitation-induced dephasing significantly decrease higherorder interband harmonic yield. Our work reveals that high harmonic
generation is governed by the incoherent carriers that are originallygenerated by the strong driving field in addition to the photo-carriers. They
create additional contribution to the intraband current relevant to lowerorder harmonics and significantly suppress the interband polarization that
contribute to higher-order harmonics than the absorption edge.
References[1] S. Ghimire and D. A. Reis, Nature Physics 15, 10 (2019).
[2] Z. Wang et al., Nature Communications 8, 1686 (2017).
[3] N. Yoshikawa, K. Nagai et al., Nature Communications 10, 3709
(2019).
[4] H. Liu et al., Nature Physics 13, 262 (2017).
[5] K. Nagai et al., Communications Physics 3, 137 (2020).

Fig. 1. (a) Setup of photo-carrier doping
experimentforhighharmonic
generation. (b) Differential harmonic
yield under the photo-doping.

Game-theoretic derivation of Gibbs distribution
Nonlinear Dynamics GroupKen Hiura

Abstract We propose a sequentially predictive form of the work extraction process. In this formulation,
an external agent repeats cyclic operations infinitely many times and extracts work from a heat engine.
We prove that if we impose the second law of thermodynamics in this situation, the empirical averages of
relevant variables must converge to the equilibrium values determined by the Gibbs distribution.
© 2021 Department of Physics, Kyoto University

A thermodynamic theory for mesoscopic systems that are weakly coupled to equilibrium environments, calledstochastic thermodynamics, has been developed over the past two decades and it provides universal relations thatare valid even far from equilibrium such as the fluctuation relations and the Jarzynski equalities. In recent years, it
was found that a game-theoretic approach to stochastic thermodynamics based on martingale theory sheds light onnovel properties in non-equilibrium systems including the stopping time statistics and extreme value statistics [1].
In this presentation, we study the fundamental aspect of statistical mechanics from the viewpoint of martingale
theory as another possible direction of the game-theoretic approach. Specifically, we investigate how the
probabilistic description on the Gibbs distribution emerges from the second law of thermodynamics [2].
It is known that we cannot extract a strictly positive amount of work on average through any cyclic operation if
the heat engine is prepared initially according to the Gibbs distribution [3]. In this presentation, we address theinverse problem: Whether the second law conversely characterizes the Gibbs distribution or not. To this end, we
propose a sequentially predictive formulation of the work extraction where an external agent repeats the extractionof work from a heat engine by cyclic operations based on his predictive strategy (Fig.1). We find that the process ofthe exponential of the accumulated work under a strategy is identified with a martingale process. Based on thisfinding, we show that if we impose the second law of thermodynamics in this situation, the empirical distributionof the initial microscopic states of the engine must converge to the Gibbs distribution of the initial Hamiltonian
under some strategy, even though no probability distributions are assumed. We also propose a protocol where theagent can change only a small number of control parameters. We find that in this situation the sequentially predictive
form of the second law of thermodynamics implies the strong law of large numbers of the conjugate variables withrespect to the control parameters (Fig.2).

Skepticµn − 1

RealityLµn!n = 1

T

T

T

...

! n− 1 = 0

L/ 2 L/ 2T(1 − µn − 1 )L µn − 1 L

T

L/ 2 L/ 2

L

...

T

(1 − µn )L µn L

Fig.1: Schematic of the sequentially predictive protocol insingle-particle ideal-gas engine

References[1] I. Neri, É. Roldán, F. Jülicher, Phys. Rev. X 7, 011019 (2017).
[2] K. Hiura, J. Stat. Phys. 185, 2 (2021).
[3] A. Lenard, J. Stat. Phys. 19, 575 (1978).

Fig. 2: Accumulations of extracted work
for sequences generated by the Gibbs
distributions with various parameters
versus the number of cycles.

Stochastic growth of a stable phase from a metastable phase
Nonlinear Dynamics Group

Hiraizumi Mao

Abstract We propose a stochastic model describing the phase growth accompanying latent heat. By studying themodel on a sparse-randomly lattice, we can identify the metastable phase in addition to the equilibrium properties.
Performing numerical simulation, we find that the growth law is qualitatively different from that of the deterministic
model. © 2021 Department of Physics, Kyoto University
When a metastable phase contacts with a stable phase, the stable phase grows and eventually the metastable phasevanishes. The phenomenon can be described by the time evolution of an order-parameter field that represents theextent of the order. When the order parameter is the only relevant dynamical variable of the system, the solution of
the propagating interface is easily determined. However, when latent heat is generated in the phase growth, thetemperature field evolve, and the order parameter field is also affected accordingly. The set of coupled equations iscalled the phase field model. It has been known that the displacement of the planar interface is proportional to thesquare root of the time interval when the extent of the metastability is less than unity. The behavior was numericallyobserved [1] and recently it has been derived by a systematic perturbation method [2].
However, it is not obvious whether or not the phase-field model is appropriate for describing phase growth.
Following the Onsager principle, we can derive an equation equivalent to the phase-field model. Since the noise
intensity is determined by the fluctuation-dissipation relation of the second kind, the thermal noises are inevitablein the description. Moreover, a typical interface width is on the order of 10−7cm. Thus, the interface may be out of
the mesoscopic description. In the phase-field model, all such properties are universally represented by only thegradient term.
In this presentation, we propose a statistical mechanics model describing the phase growth accompanying latentheat. The model we study is the 𝑞-states Potts model with an additional variable representing kinetic energy at eachsite. For this model on a sparsely random model only in one direction, we calculate the stable and metastable phases
exactly in statistical mechanics. We perform numerical simulation to measure the behavior of the interface in two
dimensions. We find the scaling relation 𝑅(𝑡) = 𝐿𝑥 ℛ̅ (𝐷𝑡/𝐿2𝑥 ) with large 𝐿𝑦 fixed [3]. The scaling function ℛ̅ (𝑧)shows ℛ̅ (𝑧)~𝑧 0.5 for 𝑧 ≪ 𝑧𝑐 and ℛ̅ (𝑧)~𝑧 𝛼 for 𝑧 ≫ 𝑧𝑐 , where the crossover value 𝑧𝑐 and the exponent 𝛼 depends on the temperature of the heat bath in contact with the stable phase. The latter scaling relation is not observedin the phase field model. This result indicates that the stochastic phase growth provides a different universality classfrom that described by the phase-field model.

Fig. 1. One example of the numerical result. Log-log plot of 𝑅/𝐿𝑥 as a function of 𝑧 = 𝑡/𝐿2𝑥 .
The two guidelines represent ℎ(𝑧)~𝑧 0.5 and ℎ(𝑧)~𝑧 0.75.
References[1] H. Lö wen, J. Bechhoefer and L. S. Tuckerman, Phys. Rev. A 45, 2399 (1992).
[2] M. Hiraizumi and S.-i. Sasa, J. Stat. Mech. 103203 (2021).
[3] M. Hiraizumi, H. Ohta and S.-i. Sasa, arXiv:2110.15605.

Extended Nielsen-Ninomiya Theorem
for Floquet and non-Hermitian Systems
Yukawa Institute for Theoretical Physics

Takumi Bessho

Abstract We find an extended version of Nielsen-Ninomiya theorem for Floquet systems andnon-Hermitian systems. As an application, we propose two novel physics. The one is non-Hermitianchiral magnetic effect, and the other is extrinsic boundary states in quantum walks.
© 2021 Department of Physics, Kyoto University

Recently, the study of topological phases has made great progress on highly-controlled nonequilibrium
systems: One is a Floquet system governed by a time-periodic Hamiltonian, and another is a non-Hermitiansystem where an open quantum or classical system effectively obeys a non-Hermitian Hamiltonian. Floquet
systems and non-Hermitian systems are not only desirable platforms to effectively realize topological insulatorsand superconductors but also novel platforms to realize unique topological physics that have no counterpart inequilibrium. A unique physics is the breakdown of Nielsen-Ninomiya theorem assuring a pair-wise creation andannihilation of gapless modes. In Floquet systems, two different schemes to realize a single Weyl mode were
proposed [1,2]. In non-Hermitian systems, a general scheme to obtain a single gapless mode was proposed [3].
Although recent topological classifications [4-7] have clarified the existence or absence of topological invariants
in each symmetry classes and dimensions, they do not provide precise relations between topological invariants
and various topological phenomena. In the present talk, we establish a general theory that gives a precise relation
between the topological invariants and the single gapless modes.
1. Extended Nielsen-Ninomiya theorem [8]In this study, we find and prove formulae of net gapless modes and topological invariants in Floquet andnon-Hermitian systems in a unified manner. For non-Hermitian systems, we refined an observation given by Lee,et al. [3] into a formula, i.e., extended Nielsen-Ninomiya theorem for non-Hermitian systems. For Floquet
systems, we established a topological duality between Floquet and non-Hermitian systems, and applied the duality
to the non-Hermitian formula to obtain the extended Nielsen-Ninomiya theorem for Floquet systems.
2. Non-Hermitian chiral magnetic effect [8]As an application of the extended Nielsen-Ninomiya theorem for non-Hermitian systems, we propose a chiralmagnetic effect by utilizing non-Hermitian spin-selective loss. While the original chiral magnetic effect uses thechiral potential unbalance, our non-Hermitian chiral magnetic effect uses the difference in the imaginary part ofthe energy indicating loss or amplification. We also find a formula of net chiral modes under magnetic field.
3. Extrinsic topology in quantum walks [9]As an application of the extended Nielsen-Ninomiya theorem for Floquet systems, we point out extrinsic
topology in quantum walks. We give a topological classification of boundary states in quantum walks, and showthat the half of boundary states depend on boundary topology rather than bulk topology.
References[1] S. Higashikawa, M. Nakagawa, and M. Ueda, Phys. Rev. Lett. 123, 066403 (2019).
[2] X.-Q. Sun, M. Xiao, T. Bzdušek, S.-C. Zhang, and S. Fan, Phys. Rev. Lett. 121, 196401 (2018).
[3] J. Y. Lee, J. Ahn, H. Zhou, and A. Vishwanath, Phys. Rev. Lett. 123, 206404 (2019).
[4] R. Roy and F. Harper, Phys. Rev. B 96, 155118 (2017).
[5] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Physical Review X 8, 031079 (2018).
[6] K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, Phys. Rev. X 9, 041015 (2019).
[7] H. Zhou and J. Y. Lee, Phys. Rev. B 99, 235112 (2019).
[8] T. Bessho and M. Sato, arXiv:2006.04204 (2020), to appear in Phys. Rev. Lett.
[9] T. Bessho, Ken. Mochizuki, H. Obuse, and M. Sato, in preparation.

Theoretical study on
Nonequilibrium many-body phenomena in Floquet systems
Kaoru Mizuta, Condensed Matter Theory Group
Abstract Floquet systems provide attractive platforms for novel nonequilibrium phases. However,generic Floquet interacting systems suffers from the trivial infinite-temperature steady states due to theheating problem. We have explored nontrivial dynamics and steady states in Floquet interacting systems
beyond the heating problem, exploiting quasi-steady states, dissipation, and many-body scars.
Floquet systems, where the Hamiltonian varies periodically in time, have become one of the most importantnonequilibrium platforms in the past decade. They provide phases of matter inherent in nonequilibrium, such as
time crystals, and various ways to control materials dubbed Floquet engineering. One of the today’s central
questions in Floquet systems is what kind of nonequilibrium phenomena can take place under interactions andperiodic drives, or equivalently by the interplay of many-body and nonequilibrium properties. For tackling thisproblem, Floquet-ETH plays a significant role, which dictates that isolated Floquet interacting systems generally
relax to trivial infinite-temperature states. Thus, in order to find out nontrivial dynamics or steady states in Floquet
interacting systems, we should overcome the trivial physics predicted by Floquet-ETH.
In our study, we have explored the following two cases violating the assumptions of Floquet-ETH to avoid its
trivial physics:(a) Quasi-steady states of Floquet interacting systems in the resonant regime [1,2],(b) Dissipative dynamics of Floquet interacting systems in the high-frequency regime [3].
In the first case (a), while the genuine steady state is still trivial, we have shown that Floquet interacting systems
can host nontrivial quasi-steady states with a sufficiently long lifetime. We have clarified the effective
Hamiltonian for the quasi-steady states when the resonant drive gives a local ZN -symmetry, implying that thesystems emergently obtain a robust ZN -symmetry. This result can be applied to the analysis of time crystals inquasi-steady states [1] and resonant Floquet engineering, simultaneously controlling phases and symmetries [2].
In the second case (b), we have explored dissipative Floquet interacting systems, breaking the isolation. Whenfocusing on the high-frequency regime, isolated Floquet systems are always equivalent to isolated static systems.
By analyzing whether the high-frequency expansion is a Liouvillian, we have discovered that dissipative Floquet
interacting systems generally have no static counterparts in contrast to isolated cases. This implies uniquebehaviors brought by the interplay of dissipation, periodic drive, and interactions. We also note that Floquet-ETH
is just a conjecture verified numerically and experimentally, leaving the possibility of nontrivial physics without
violating the assumptions of Floquet-ETH. This have motivated us to seek for(c) Athermal dynamics and steady states of isolated nonintegrable Floquet interacting systems.
By exploiting quantum many-body scars recently observed in Rydberg atoms, we have succeeded in composing aperiodically-driven model under Rydberg blockade becoming a counterexample to Floquet-ETH [4]. Thiselucidates the possibility of nontrivial quantum many-body phenomena in generic Floquet interacting systems.
In the presentation, after introducing the overview of Floquet systems and our studies, we will concentrate on our
results in Floquet quantum many-body scars [4].
References[1] K. Mizuta, K. Takasan, and N. Kawakami, Phys. Rev. B 100, 020301 (2019)[2] K. Mizuta, K. Takasan, and N. Kawakami, Phys. Rev. A 100, 052109 (2020)[3] K. Mizuta, K. Takasan, and N. Kawakami, Phys. Rev. A 103, L020202 (2021)[4] K. Mizuta, K. Takasan, and N. Kawakami, Phys. Rev. Research, 2, 033284 (2020)

Non-Hermitian aspect of strongly-correlated electron systems

Condensed Matter Theory Group, Yoshihiro Michishita
Abstract:
In this talk, we derive the effective non-Hermitian Hamiltonian in the context of strongly-correlated
electron systems and show its equivalence to the effective non-Hermitian Hamiltonian in the context ofopen quantum systems. Furthermore, we analyze the Kondo physics and nonlinear transport from
non-Hermitian point of view.
© 2021 Department of Physics, Kyoto University

Non-Hermitian physics describes the dynamics of the system in which energy and particle number are notconserved. It often emerges in open systems [1], such as photonics [2,3], cold atoms [4], and active matters [5].
The pioneering work [6] by Shen and Fu has shown that strongly-correlated electron systems (SCES) can also be
described by the effective non-Hermitian Hamiltonian. This statement holds the possibility that the non-Hermitianphenomena seen in photonics or cold atoms can also be seen in SCES, and they can be understood from theunified description by non-Hermitian matrices. However, the circumstances and requirements for the emergenceof the non-Hermitian phenomena are entirely different in open systems and SCES, and the relation between each
description was unclear.
In this talk, we first show that the effective non-Hermitian Hamiltonian emerging in both fields are identical bydescribing SCES as an open quantum system [7]. Then we investigate the Kondo physics, which is one of the
primary topics in SCES, from the point of view of non-Hermitian physics, and show that it can be understood as
the topological change of the exceptional manifolds in the momentum-frequency space [8]. Finally, we analyze
the non-Hermitian effect on the linear and nonlinear transport in SCES and elucidate the effective enhancement oflifetime by the non-orthogonality of eigenstates and the sign change due to the imaginary gap by the
non-Hermitian effect [9,10].

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References[1] Y. Ashida, Z. Gong, and M. Ueda, Advances in Physics, 69, 249-435 (2021)[2] R. El-Ganainy, et al, Nature Physics, 14, 11-19 (2018).
[3] A. Regensburger, et al., Nature, 488, 167-171 (2012).
[4] T. Tomita, et al, Science Advances, 3, e1701513 (2017).
[5] K. Sone, Y. Ashida, and T. Sagawa, Nature communications, 11, 1-11(2020).
[6] H. Shen, and L. Fu, Physical Review Letters, 120, 146402 (2018).
[7] YM, and R. Peters, Physical Review Letters, 124, 196401 (2020).
[8] YM, T. Yoshida, and R. Peters, Physical Review B, 101, 085122 (2020).
[9] YM, and R. Peters, Physical Review B, 103, 195133 (2021).
[10] A. Kofuji, YM, and R. Peters, Physical Review B, 104, 085151 (2021).
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Novel quantum phases accompanied by rotational symmetry breaking
in strongly correlated electron systems
Quantum condensed matter group

Hinako Murayama

Abstract By performing magnetic torque measurements, we have revealed novel quantum phases
accompanied by rotational symmetry breaking in two strongly correlated materials. One is the diagonal
nematic order in a high-Tc cuprate superconductor HgBa2CuO4+, and the other is the anapole order in aspin-orbit assisted Mott insulator Sr2Ir1-xRhxO4. (50 words)© 2021 Department of Physics, Kyoto University

The main issue in solid-state physics has been the investigation of exotic electronic orders and their phasetransitions accompanied by various types of symmetry breaking. An intriguing example is the liquid-solidtransition of electrons in strongly correlated systems; in a metal, electrons move around with interaction like aliquid while they become frozen and arranged on a lattice like a solid by the strong repulsion. Recently, theemergence of new electronic orders breaking the rotational symmetry between the liquid and the solid, which arecalled nematic orders on the analogy of the nematic crystal liquid, has attracted much attention. Here we report
two examples of the nematic orders. The rotational symmetry breaking was probed by ultra-precision
measurements of anisotropy in magnetic torque. As the magnetic torque is a thermodynamic quantity, it provides
thermodynamic evidence for the phase transition, sensitively detecting the rotational symmetry of the orderparameter.
The first finding is the nematic order in hole-doped cuprates [1,2]. Carrier doping on cuprates suppresses theMott insulating phase and induces superconductivity. In hole-doped cuprates, the pseudogap, a partial gap
opening at the Fermi level, appears well above the superconducting transition temperature Tc. It has been widelybelieved that the pseudogap phenomenon is closely related to the mechanism of the high-Tc superconductivity.
Despite tremendous research, however, the nature of the pseudogap state has been elusive. The most controversial
issue is whether the pseudogap formation is a cross-over phenomenon or a phase transition. At an early stage, thepseudogap state has been attributed to a precursor of superconductivity. On the other hand, recent studies report
the observation of symmetry breakings in the pseudogap state, suggesting the phase transition at the pseudogap
onset temperature. We performed magnetic torque measurements on tetragonal HgBa2CuO4+ and revealed thatelectrons exhibit the two-fold in-plane rotational symmetry in the pseudogap state [2]. This provides thethermodynamic evidence for the phase transition accompanied by rotational symmetry breaking at the pseudogap
onset temperature. The nematic order parameter orients to the Cu-Cu bond direction, rotating by 45 degrees fromthat in the orthorhombic YBa2Cu3Oy [1]. The nematic order in HgBa2CuO4+ is called the diagonal nematic order,
which is distinct from the nematic order along the Cu-O-Cu bond direction in YBa2Cu3Oy.
The second finding is the anapole order in a spin-orbit assisted Mott insulator Sr2IrO4[3]. The strong spin-orbit
interaction of Ir 5d orbitals effectively enhances the correlation effect, resulting in the Mott insulating state for the
ground state of Sr2IrO4. The slight Rh substitution of Ir dopes hole carriers, suppressing the Mott insulating phase.
The appearance of the hidden order phase, in which inversion and time-reversal symmetry breaking occurs, hasbeen reported in the vicinity of the Mott insulating phase. However, the nature of the hidden order phase was islargely unexplored. We conducted magnetic torque measurements on Sr2Ir1-xRhxO4. We find that the hidden orderalso breaks the rotational symmetry. We point out the possibility that those symmetry breakings are induced by a
new type of electronic order in which nano-loop current flows between atoms. This order is an anapole orderwhose order parameter resembles the anapole in nuclear physics.
References[1] Y. Sato, H. Murayama, et al., Nature Physics 13, 1074-1078 (2017).
[2] H. Murayama, et al., Nature Communications 10, 3282 (2019).
[3] H. Murayama et al., Physical Review X 11, 011021 (2021).