Tatsushi Imaeda, Yuki Kawaguchi, Yukio Tanaka, Masatoshi Sato

Journal of the Physical Society of Japan 88 024402 Nov 2018

We investigate the instability due to dynamical axion field near the
topological phase transition of insulators. We first point out that the
amplitude of dynamical axion field is bounded for magnetic insulators in
general, which suppresses the axi...

We classify time-reversal breaking (class A) spinful topological crystalline
insulators with crystallographic non-magnetic (32 types) and magnetic (58
types) point groups. The classification includes all possible magnetic
topological crystalline i...

J. Phys.: Condens. Matter 31 (2019) 105302 Oct 2018

Using a multi-orbital tight-binding model, we have studied the edge states of
zigzag silicene, germanene, and stanene nanoribbons (ZSiNRs, ZGeNRs and ZSnNRs,
respectively) in the presence of the Coulomb interaction and a vertical
electric field. T...

Topological insulators and semimetals as well as unconventional iron-based
superconductors have attracted major recent attention in condensed matter
physics. Previously, however, little overlap has been identified between these
two vibrant fields,...

Takuto Kawakami, Tetsuya Okamura, Shingo Kobayashi, Masatoshi Sato

Phys. Rev. X 8, 041026 (2018) Feb 2018

We present a theory of the high-spin generalization of topological insulators
and their doped superconducting states. The higher-spin topological insulators
involve a pair of bands with opposite parity, and are characterized by
their band ...

Igor Kuzmenko, Tetyana Kuzmenko, Yshai Avishai, Masatoshi Sato

Phys. Rev. B 98, 165139 (2018) Jan 2018

In this work we study the possible occurrence of topological insulators for
2D fermions of high spin. They can be realized in cold fermion systems with
ground-state atomic spin , if the optical potential is properly
designed, and s...

Yuji Ueno, Ai Yamakage, Yukio Tanaka, Masatoshi Sato

Phys. Rev. Lett. 111, 087002 (2013) 111(8) 1-87002 Aug 2013

Crystal point group symmetry is shown to protect Majorana fermions (MFs) in
spinfull superconductors (SCs). We elucidate the condition necessary to obtain
MFs protected by the point group symmetry. We argue that superconductivity in
Sr2RuO4 hosts ...

New J. of Phys. 15, 075010 (2013) 15(July) 75010 Jul 2013

We theoretically investigate the effect of intertube tunneling in topological
superfluid phases of a quasi-one-dimensional Fermi gas with a Rashba-type
spin-orbit interaction. It is shown that the effective Hamiltonian is analogous
to that of a na...

Ai Yamakage, Masatoshi Sato, Keiji Yada, Satoshi Kashiwaya, Yukio Tanaka

Phys. Rev. B 87, 100510(R) (2013) 87(10) 1-100510 Mar 2013

We investigate the effect of helical Majorana fermions at the surface of
superconducting topological insulators (STI) on the Josephson current by
referring to possible pairing states of Cu-doped Bi2Se3. The surface state in
the present STI has a s...

Tatsuki Hashimoto, Keiji Yada, Ai Yamakage, Masatoshi Sato, Yukio Tanaka

J. Phys. Soc. Jpn. 82 (2013) 044704 82(4) 1-44704 Mar 2013

We study electronic properties of a superconducting topological insulator
whose parent material is a topological insulator. We calculate the temperature
dependence of the specific heat and spin susceptibility for four promising
superconducting pai...

Akihiro Ii, Ai Yamakage, Keiji Yada, Masatoshi Sato, Yukio Tanaka

Phys. Rev. B 86, 174512 (2012) 86(17) 1-174512 Nov 2012

We study the charge conductance of an interface between a normal metal and a
superconducting quantum anomalous Hall system, based on the recursive Green's
function. The angle resolved conductance gamma(ky, eV) with the momentum ky
parallel to the ...

Phys. Rev. Lett. 109, 165301 (2012) 109(16) 1-165301 Oct 2012

We here demonstrate that the superfluid 3He-B under a magnetic field in a
particular direction stays topological due to a discrete symmetry, that is, in
a symmetry protected topological order. Due to the symmetry protected
topological order, helic...

New Journal of Physics 14 (2012) 063017 14 Jun 2012

We propose a topological field theory for a spin-less two-dimensional chiral
superconductor that contains fundamental Majorana fields. Due to a fermionic
gauge symmetry, the Majorana modes survive as dynamical degrees of freedom only
at magnetic v...

Prog. Theor. Phys. 127 (2012), 937-974 127(6) 937-974 Jun 2012

For ordinary hermitian Hamiltonians, the states show the Kramers degeneracy
when the system has a half-odd-integer spin and the time reversal operator
obeys \Theta^2=-1, but no such a degeneracy exists when \Theta^2=+1. Here we
point out that for ...

Ai Yamakage, Keiji Yada, Masatoshi Sato, Yukio Tanaka

Phys. Rev. B 85, 180509(R) (2012) 85(18) 1-180509 May 2012

We develop a theory of the tunneling spectroscopy for superconducting
topological insulators (STIs), where the surface Andreev bound states (SABSs)
appear as helical Majorana fermions. Based on the symmetry and topological
nature of parent topolog...

J. Phys. Soc. Jpn. 81, 011013 (2012) 81(1) 1-11013 Dec 2011

Superconductivity is a phenomenon where the macroscopic quantum coherence
appears due to the pairing of electrons. This offers a fascinating arena to
study the physics of broken gauge symmetry. However, the important symmetries
in superconductors ...

Phys. Rev. B 84, 205128 (2011) 84(20) 1-205128 Nov 2011

Topological stability of the edge states is investigated for non-Hermitian
systems. We examine two classes of non-Hermitian Hamiltonians supporting real
bulk eigenenergies in weak non-Hermiticity: SU(1,1) and SO(3,2) Hamiltonians.
As an SU(1,1) Ha...

Phys. Rev. Lett. 107, 217001 (2011) 107(21) 1-217001 Nov 2011

A topological superconductor (TSC) is characterized by the
topologically-protected gapless surface state that is essentially an Andreev
bound state consisting of Majorana fermions. While a TSC has not yet been
discovered, the doped topological ins...

Phys. Rev. B 83, 224511 (2011) 83(22) 1-224511 Jun 2011

A theory of dispersionless Andreev bound states on surfaces of time-reversal
invariant unconventional superconductors is presented. The generalized
criterion for the dispersionless Andreev bound state is derived from the
bulk-edge correspondence, ...

Akihiro Ii, Keiji Yada, Masatoshi Sato, Yukio Tanaka

Mar 2011

We study the edge states for a quantum anomalous Hall system (QAHS) coupled
with a spin-singlet s-wave superconductor through the proximity effect, and
clarify the topological nature of them. When we consider a superconducting pair
potential induc...

Phys. Rev. B 83, 064505 (2011) 83(6) 1-64505 Feb 2011

We study Andreev bound state (ABS) and surface density of state (SDOS) of
non-centrosymmetric superconductor where spin-singlet -wave pairing mixes
with spin-triplet (or -wave one by spin-orbit coupling. For -wave pairing, A...

Phys. Rev. Lett. 105:217001,2010 105(21) 1-217001 Nov 2010

We demonstrate that Majorana fermions exist in edges of systems and in a
vortex core even for superconductors with nodal excitations such as the d-wave
pairing state under a particular but realistic condition in the case with an
anti-symmetric spi...

The non-Abelian topological order for superconductors is characterized by the
existence of zero-energy Majorana fermions in edges of systems and in a vortex
of a macroscopic condensate, which obey the non-Abelian statistics. This paper
is devoted ...

Yukio Tanaka, Yoshihiro Mizuno, Takehito Yokoyama, Keiji Yada, Masatoshi Sato

Phys. Rev. Lett. 105, 097002 (2010) 105(9) 1-97002 Aug 2010

We study edge states of non-centrosymmetric superconductors where
spin-singlet d-wave pairing mixes with spin-triplet p (or f)-wave one by
spin-orbit coupling. For dxy-wave pairing, the obtained Andreev bound state has
an anomalous dispersion as c...

Phys. Rev. B 81, 220504(R) (2010) 81(22) 1-220504 Jun 2010

In this letter, we investigate topological phases of full-gapped odd-parity
superconductors, which are distinguished by the bulk topological invariants and
the topologically protected gapless boundary states. Using the particle-hole
symmetry, we i...

Kenta Esaki, Masatoshi Sato, Mahito Kohmoto, Bertrand I. Halperin

Phys. Rev. B 80, 125405 (2009) 80(12) 1-125405 Sep 2009

We present systematic study of zero modes and gaps by introducing effects of
anisotropy of hopping integrals for a tight-binding model on the honeycomb
lattice in a magnetic field. The condition for the existence of zero modes is
analytically deri...

Phys. Rev. Lett. 103, 020401 (2009) 103(2) 1-20401 Jul 2009

We show that in s-wave superfluids of cold fermionic atoms with
laser-field-generated effective spin-orbit interactions, a topological phase
with gapless edge states and Majorana fermion quasiparticles obeying the
non-Abelian statistics is realize...

Phys. Rev. B79, 214526 (2009) 79(21) 1-214526 Jun 2009

We report intimate relations between topological properties of full gapped
spin-triplet superconductors with time-reversal invariance and the Fermi
surface topology in the normal states. An efficient method to calculate the Z2
invariants and the w...

Propagation of waves in the Cantor-set media is investigated by a
renormalization-group type method. We find fixed points for complete
reflection, , and for complete transmission, . In addition, the
wave numbers for which transmissio...

Phys. Rev. B79, 094504 (2009) 79(9) 1-94504 Mar 2009

The existence of edge states and zero energy modes in vortex cores is a
hallmark of topologically nontrivial phases realized in various condensed
matter systems such as the fractional quantum Hall states, p+ip
superconductors, and Z_2 insulators (...

Propagation of waves through Cantor-set media is investigated by
renormalization-group analysis. For specific values of wave numbers,
transmission coefficients are shown to be governed by the logistic map, and in
the chaotic region, they show sens...

We examine in detail nonperturbative corrections for low lying energies of a
symmetric triple-well potential with non-equivalent vacua, for which there have
been disagreement about asymptotic formulas and controversy over the validity
of the dilut...

We examine an axion string coupled to a Majorana fermion. It is found that
there exist a Majorana-Weyl zero mode on the string. Due to the zero mode, the
axion strings obey non-abelian statistics.

We examine the dependence of the physical quantities of the rotatory
molecular motor, such as the rotation velocity and the proton translocation
rate, on the chemical reaction rate using the model based only on diffusion
process. A peculiar behavi...

We investigate particular models which can be N-fold supersymmetric at
specific values of a parameter in the Hamiltonians. The models to be
investigated are a periodic potential and a parity-symmetric sextic triple-well
potential. Through the quan...

Type A N-fold supersymmetry of one-dimensional quantum mechanics can be
constructed by using sl(2) generators represented on a finite dimensional
functional space. Using this sl(2) formalism we show a general method of
constructing Type A N-fold s...

N-fold supersymmetry is an extension of the ordinary supersymmetry in
one-dimensional quantum mechanics. One of its major property is
quasi-solvability, which means that energy eigenvalues can be obtained for a
portion of the spectra. We show that...

We report general properties of N-fold supersymmetry in one-dimensional
quantum mechanics. N-fold supersymmetry is characterized by supercharges which
are N-th polynomials of momentum. Relations between the anti-commutator of the
supercharges and ...

We report general forms of one family of the N-fold supersymmetry in
one-dimensional quantum mechanics. The N-fold supersymmetry is characterized by
the supercharges which are N-th order in differential operators. The family
reported here is defin...

We report a new type of supersymmetry, "N-fold supersymmetry", in
one-dimensional quantum mechanics. Its supercharges are N-th order polynomials
of momentum: It reduces to ordinary supersymmetry for N=1, but for other values
of N the anticommutato...

The unique Fermi surfaces and their nesting properties of Sr2RuO4 are
considered. The existence of unconventional superconductivity is shown
microscopically, for the first time, from the magnetic interactions (due to
nesting) and the phonon-mediat...

The elucidation of the properties of the instantons in the topologically
trivial sector has been a long-standing puzzle. Here we claim that the
properties can be summarized in terms of the geometrical structure in the
configuration space, the vall...

Conventionally, perturbative and non-perturbative calculations are performed
independently. In this paper, valleys in the configuration space in quantum
mechanics are investigated as a way to treat them in a unified manner. All the
known results o...

Path-integral approach in imaginary and complex time has been proven
successful in treating the tunneling phenomena in quantum mechanics and quantum
field theories. Latest developments in this field, the proper valley method in
imaginary time, its...

Microscopic tests of the exact results are performed in supersymmetric
QCD. We present the complete construction of the multi-instanton in
supersymmetric QCD. All the defining equations of the super instanton are
reduced to the...

Microscopic tests of the exact results are performed in N=2 SU(2)
supersymmetric QCD. We construct the multi-instanton solution in N=2
supersymmetric QCD and calculate the two-instanton contribution to
the prepotential expl...

We study the path-integral formalism in the imaginary-time to show its
validity in a case with a metastable ground state. The well-known method based
on the bounce solution leads to the imaginary part of the energy even for a
state that is only me...

Based on the new valley equation, we propose the most plausible method for
constructing instanton-like configurations in the theory where the presence of
a mass scale prevents the existence of the classical solution with a finite
radius. We call t...

The relation between shapes of cosmic string and baryon number violation is
investigated. If there exist fermionic zero modes on the string, using
bosonization technique, it is possible to obtain the effective action which
describes the fermion co...

The instanton configuration in the SU(2)-gauge system with a Higgs doublet is
constructed by using the new valley method. This method defines the
configuration by an extension of the field equation and allows the exact
conversion of the quasi-zero...

We present a ``topological'' formulation of arbitrarily shaped vortex strings
in four dimensional field theory. By using a large Higgs mass expansion, we
then evaluate the effective action of the closed Abrikosov-Nielsen-Olesen
vortex string. It i...

Part of Nature Physics 15, 41 (2019) (See also arXiv 1809.09977) Mar 2018

Topological Dirac semimetals (TDSs) exhibit bulk Dirac cones protected by
time reversal and crystal symmetry, as well as surface states originating from
non-trivial topology. While there is a manifold possible onset of
superconducting order in suc...

A quantum quench is the simplest protocol to investigate nonequilibrium
many-body quantum dynamics. Previous studies on the entanglement properties of
quenched quantum many-body systems mainly focus on the growth of entanglement
entropy. Several r...

Quantum phase transitions are intriguing and fundamental cooperative
phenomena in physics. Analyzing a superconducting nanowire with spin-dependent
non-Hermitian hopping, we discover a topological quantum phase transition
driven by infinitesimal c...

Exceptional points are universal level degeneracies induced by
non-Hermiticity. Whereas the past decades witnessed their new physics, the
unified understanding has yet to be obtained. Here we present the complete
classification of generic topologi...

Kohei Kawabata, Ken Shiozaki, Masahito Ueda, Masatoshi Sato

Dec 2018

We develop a complete theory of symmetry and topology in non-Hermitian
physics. We demonstrate that non-Hermiticity ramifies the celebrated
Altland-Zirnbauer symmetry classification for insulators and superconductors.
In particular, charge conjuga...

Shingo Kobayashi, Ai Yamakage, Yukio Tanaka, Masatoshi Sato

Dec 2018

In contrast to elementary Majorana particles, emergent Majorana fermions
(MFs) in condensed-matter systems may have electromagnetic multipoles. We
developed a general theory of magnetic multipoles for surface helical MFs on
time-reversal-invariant...

We study the Atiyah-Hirzebruch spectral sequence (AHSS) for equivariant
K-theory in the context of band theory. Various notions in the band theory such
as irreducible representations at high-symmetric points, the compatibility
relation, topologica...

Takuto Kawakami, Tetsuya Okamura, Shingo Kobayashi, Masatoshi Sato

Feb 2018

We present a theory of topological crystalline materials of
electrons. The high spin topological phases are expected to be realized in
cubic crystals with band inversion such as antiperovskite materials, with ${\rm A}=(...

Igor Kuzmenko, Tetyana Kuzmenko, Yshai Avishai, Masatoshi Sato

Jan 2018

In this work we study the possible occurrence of topological insulators for
2D fermions of high spin. They can be realized in cold fermion systems with
ground-state atomic spin , if the optical potential is properly
designed, and s...

Through a nonperturbative analysis on a sextic triple-well potential, we
reveal novel aspects of the dynamical property of the system in connection with
N-fold supersymmetry and quasi-solvability.

The pump process of the ratchet model inspired by the rotatory motor of
ATP synthase is investigated. In this model there are two kinds of
characteristic time. One is dynamical, the relaxation time of the system.
Others are chemical, the che...

Superconductive properties of the two-leg ladder compounds are studied
theoretically. The antiferromagnetic fluctuations are considered because of the
good nesting of the Fermi surfaces. The attractive interaction which is most
likely due to the e...

We consider a system with electron-phonon interaction, antiferromagnetic
fluctuations and disconnected open Fermi surfaces. The existence of odd-parity
superconductivity in this circumstance is shown for the first time. If it is
applied to the qua...

We calculate the cross sections of the baryon and lepton number violating
processes. The proper valley method enables us to calculate the multi-boson
processes, which have the possibility to observation. The mass corrections of
the gauge boson, Hi...