arXiv subjects

Y. Hatsugai

Publications and source records attributed to Y. Hatsugai.

At least 19 recordsLinked to original sources

arXiv2023

Higher-order topological heat conduction on a lattice for detection of corner states

A heat conduction equation on a lattice composed of nodes and bonds is formulated assuming the Fourier law and the energy conservation law. Based on this equation, we propose a higher-order topological heat conduction model on the breathing kagome lattice. We show that the temperature measurement at a conner node can detect the corner state which causes rapid heat conduction toward the heat bath, and that several-nodes measurement can determine the precise energy of the corner states.

cond-mat.mes-hall↗

arXiv2022

Edge states of a diffusion equation in one dimension: Rapid heat conduction to the heat bath

We propose a one-dimensional (1D) diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period $a$. We solve the time evolution of the field (temperature) profile from a given initial distribution, by diagonalising the Hamiltonian, i.e., the Laplacian with alternating diffusion constants, and expanding the temperature profile by its eigenstates. We show that there are basically phases with or without edge states. The edge states affect the heat conduction around heat baths. In particular, rapid heat transfer to heat baths would be observed in a short time regime, which is estimated to be $t<10^{-2}$s for $a\sim 10^{-3}$m system and $t< 1$s for $a\sim 10^{-2}$m system composed of two kinds of familiar metals such as titanium, zirconium and aluminium, gold, etc. We also discuss the effective lattice model which simplifies the calculation of edge states up to high energy. It is suggested that these high energy edge states also contribute to very rapid heat conduction in a very short time regime.

cond-mat.mes-hall↗

arXiv2018

Circularly polarized topological edge states derived from optical Weyl points in semiconductor-based chiral woodpile photonic crystals

The polarizations of topological edge modes in the vicinity of optical Weyl points were numerically studied in chiral photonic crystals. We investigated two kinds of rotationally stacked woodpile structures in which planar rod arrays were vertically stacked one-by-one with an in-plane rotation angle of 60 or 45 degrees. Both structures showed pairs of optical Weyl points having topological numbers of opposite signs for photonic bands in low orders. Topological edge states derived from the Weyl points appeared below the light line, and were strongly confined at the air interfaces in a length shorter than the wavelength. Their polarizations in a direction perpendicular to the propagation direction were found to be one particular circular polarization that depended on the handedness of the structural chirality. Since these chiral photonic crystals can be fabricated using semiconductor materials such as GaAs or Si, the obtained robust planar waveguides for circularly polarized light at the interface between air and the semiconductor structure can be useful not only in photonics but also in spintronics or quantum information technology through spin-photon interfaces.

physics.optics↗

arXiv2018

Entanglement polarization for the topological quadrupole phase

We propose the entanglement dipole polarization to describe the topological quadrupole phase. The quadrupole moment can be regarded as a pair of the dipole moment, in which the total dipole moment is canceled. The entanglement polarization, we propose, is useful to detect such a constituent dipole polarization. We first introduce partitions of sites in the unit cell and divide the system into two subsystems. Then, introducing an entanglement Hamiltonian by tracing out one of the subsystems partly, we compute the dipole polarization of the occupied states associated with the entanglement Hamiltonian, which is referred to as the entanglement polarization. Although the total dipole polarization is vanishing, those of the subsystems can be finite. The entanglement dipole polarization is quantized by reflection symmetries. We also introduce the entanglement polarization of the edge states, which reveals that the edge states themselves are gapped and topologically nontrivial. Therefore, such edge states yield the zero energy edge states if the system has boundaries. This is the origin of the corner states.

cond-mat.mes-hall↗

arXiv2016

Lattice realization of the generalized chiral symmetry in two dimensions

While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, such a generalized symmetry was so far defined only for a continuous low-energy Hamiltonian. Here we show that the generalized chiral symmetry can be rigorously defined for lattice fermions as well. A key concept is a continuous "algebraic deformation" of Hamiltonians, which generates lattice models with the generalized chiral symmetry from those with the conventional chiral symmetry. This enables us to explicitly express zero modes of the deformed Hamiltonian in terms of that of the original Hamiltonian. Another virtue is that the deformation can be extended to non-uniform systems, such as fermion-vortex systems and disordered systems. Application to fermion vortices in a deformed system shows how the zero modes for the conventional Dirac fermions with vortices can be extended to the tilted case.

cond-mat.mes-hall↗

arXiv2016

A spin pump characterized by entanglement Chern numbers

We study a spin pump on a two-leg ladder chain of the Rice--Mele model. To characterize the spin pump, we propose the Chern number for the many-body ground state of the entanglement Hamiltonian, which is referred to as the entanglement Chern number. We show that this model has two phases distinguished by the entanglement Chern numbers. These two phases can be experimentally verified in cold atoms.

cond-mat.mes-hall↗

arXiv2016

Bulk-edge correspondence in topological pumping

The topological pumping [1-3] is revisited from a view point of the bulk-edge correspondence. Shift of the center of mass (CM) as a pumped charge is explicitly given by the Berry connection in time direction. We show that observed pumping is due to the bulk, but its quantization is guaranteed by singular motion of the CM caused by edge states. This is the bulk-edge correspondence in the topological pumping. A gauge invariant form of the pumped charge is proposed by the temporal gauge and is used to establish this bulk-edge correspondence.

cond-mat.mes-hall↗

arXiv2015

Disentangled topological numbers by a purification of entangled mixed states for non-interacting fermion systems

We argue that the entanglement Chern number proposed recently is invariant under the adiabatic deformation of a gapped many-body groundstate into a {\it disentangled/purified} one, which implies a partition of the Chern number into subsystems (disentangled Chern number). We generalize the idea to another topological number, the Z$_2$ Berry phase for a system with particle-hole symmetry, and apply it to a groundstate in a weak topological phase where the Chern number vanishes but the groundstate nevertheless has edge states. This entanglement Berry phase is especially useful for characterizing random systems with nontrivial edge states.

cond-mat.mes-hall↗

arXiv2015

Flat bands in Weaire-Thorpe model and silicene

In order to analytically capture and identify peculiarities in the electronic structure of silicene, Weaire-Thorpe(WT) model, a standard model for treating three-dimensional (3D) silicon, is applied to silicene with the buckled 2D structure. In the original WT model for four hybridized $sp^3$ orbitals on each atom along with inter-atom hopping, the band structure can be systematically examined in 3D, where flat (dispersionless) bands exist as well. For examining silicene, here we re-formulate the WT model in terms of the overlapping molecular-orbital (MO) method which enables us to describe flat bands away from the electron-holesymmetric point. The overlapping MO formalism indeed enables us to reveal an important difference: while in 3D the dipersive bands with cones are sandwiched by doubly-degenerate flat bands, in 2D the dipersive bands with cones are sandwiched by triply-degenerate and non-degenerate (nearly) flat bands, which is consistent with the original band calculation by Takeda and Shiraishi. Thus emerges a picture for why the whole band structure of silicene comprises a pair of dispersive bands with Dirac cones with each of the band touching a nearly flat (narrow) band at $Γ$. We can also recognize that, for band engineering, the bonds perpendicular to the atomic plane are crucial, and that a ferromagnetism or structural instabilities are expected if we can shift the chemical potential close to the flat bands.

cond-mat.mes-hall↗

arXiv2014

Entanglement Chern number for an extensive partition of a topological ground state

If an extensive partition in two dimensions yields a gapful entanglement spectrum of the reduced density matrix, the Berry curvature based on the corresponding entanglement eigenfunction defines the Chern number. We propose such an entanglement Chern number as a useful, natural, and calculable topological invariant, which is potentially relevant to various topological ground states. We show that it serves as an alternative topological invariant for time-reversal invariant systems and as a new topological invariant for a weak topological phase of a superlattice Wilson-Dirac model. In principle, the entanglement Chern number can also be effective for interacting systems such as topological insulators in contrast to $Z_2$ invariants.

cond-mat.mes-hall↗

arXiv2013

Chiral symmetry and fermion doubling in the zero-mode Landau levels of massless Dirac fermions with disorder

The effect of disorder on the Landau levels of massless Dirac fermions is examined for the cases with and without the fermion doubling. To tune the doubling a tight-binding model having a complex transfer integral is adopted to shift the energies of two Dirac cones, which is theoretically proposed earlier and realizable in cold atoms in an optical lattice. In the absence of the fermion doubling, the $n=0$ Landau level is shown to exhibit an anomalous sharpness even if the disorder is uncorrelated in space (i.e., large K-K' scattering). This anomaly occurs when the disorder respects the chiral symmetry of the Dirac cone.

cond-mat.mes-hall↗

arXiv2013

Symmetry protected weak topological phases in a superlattice

We explore novel topological phases realized in a superlattice system based on the Wilson-Dirac model. Our main focus is on a two-dimensional analogue of weak topological insulator phases. We find such phases as those characterized by gapless edge states that are protected by symmetry but sensitive to the orientation of the edge relative to the superlattice structure. We show that manifest and hidden reflection symmetries protect such weak topological phases, and propose bulk Z2 indices responsible for the topological protection of the edge states.

cond-mat.mes-hall↗

arXiv2012

Chiral symmetry and its manifestation in optical responses in graphene: interaction and multi-layers

Chiral symmetry, fundamental in the physics of graphene, guarantees the existence of topologically stable doubled Dirac cones and anomalous behaviors of the zero-energy Landau level in magnetic fields. The crucial role is inherited in the optical responses and many-body physics in graphene, which are explained in this paper. We also give an overview of multilayer graphene from the viewpoint of the optical properties and their relation with the chiral symmetry.

cond-mat.mes-hall↗

arXiv2011

Chiral Symmetry and Electron-Electron Interaction in Many-Body Gap Formation in Graphene

We study a many-body ground state of graphene in perpendicular magnetic fields. Chiral symmetry in graphene enables us to determine the many-body ground state, which turns out to be a doubly degenerate chiral condensate for the half-filled (undoped) case. In the ground state a prominent charge accumulation emerges along zigzag edges. We also show that gapless excitations are absent despite the presence of the robust edge modes, which is consistent with the Chern number C = 0.

cond-mat.mes-hall↗

arXiv2010

$Z_Q$ Topological Invariants for Polyacetylene, Kagome and Pyrochlore lattices

Adiabatic $Z_Q$ invariants by quantized Berry phases are defined for gapped electronic systems in $d$-dimensions ($Q=d+1$). This series includes Polyacetylene, Kagome and Pyrochlore lattice respectively for $d=1,2$ and 3. The invariants are quantum $Q$-multimer order parameters to characterize the topological phase transitions by the multimerization. This fractional quantization is protected by the global $Z_Q$ equivalence. As for the chiral symmetric case, a topological form of the $Z_2$-invariant is explicitly given as well.

cond-mat.mes-hall↗

arXiv2009

Symmetry protected Z2-quantization and quaternionic Berry connection with Kramers degeneracy

As for a generic parameter dependent hamiltonian with the time reversal (TR) invariance, a non Abelian Berry connection with the Kramers (KR) degeneracy are introduced by using a quaternionic Berry connection. This quaternionic structure naturally extends to the many body system with the KR degeneracy. Its topological structure is explicitly discussed in comparison with the one without the KR degeneracy. Natural dimensions to have non trivial topological structures are discussed by presenting explicit gauge fixing. Minimum models to have accidental degeneracies are given with/without the KR degeneracy, which describe the monopoles of Dirac and Yang. We have shown that the Yang monopole is literally a quaternionic Dirac monopole. The generic Berry phases with/without the KR degeneracy are introduced by the complex/quaternionic Berry connections. As for the symmetry protected $\mathbb{Z}_2$ quantization of these general Berry phases, a sufficient condition of the $\mathbb{Z}_2$-quantization is given as the inversion/reflection equivalence. Topological charges of the SO(3) and SO(5) nonlinear $σ$-models are discussed in their relation to the Chern numbers of the $CP^1 $ and $HP^1$ models as well.

cond-mat.mes-hall↗

arXiv2008

Bulk-edge correspondence in graphene with/without magnetic field: Chiral symmetry, Dirac fermions and Edge states

There are two types of edge states in graphene with/without magnetic field. One is a quantum Hall edge state, which is topologically protected against small perturbation. The other is a chiral zero mode that is localized near the boundary with/without magnetic field. The latter is also topological but is guaranteed to be zero energy by the chiral symmetry, which is also responsible for massless Dirac like dispersion. Conceptual roles of the edge states are stressed and reviewed from a view point of the bulk-edge correspondence and the topological order.

cond-mat.mes-hall↗

arXiv2008

Topological meaning of Z$_2$ numbers in time reversal invariant systems

We show that the Z$_2$ invariant, which classifies the topological properties of time reversal invariant insulators, has deep relationship with the global anomaly. Although the second Chern number is the basic topological invariant characterizing time reversal systems, we show that the relative phase between the Kramers doublet reduces the topological quantum number Z to Z$_2$.

cond-mat.mes-hall↗