arXiv subjects

Yositake Takane

Publications and source records attributed to Yositake Takane.

At least 19 recordsLinked to original sources

arXiv2026

Josephson phase shift and diode effect due to the inverse spin Hall effect

We theoretically study the direct and inverse spin Hall effects in a superconductor-normal metal-uperconductor junction induced by a spin-orbit interaction that is invariant under spatial inversion. We show that a supercurrent induces a spin Hall effect, leading to a static spin accumulation with opposite polarizations at the two edges, analogous to that in normal conductors. For the inverse effect, we consider a spatially inhomogeneous static magnetic field and show that it induces an anomalous phase shift, which, in the presence of higher harmonics, results in a diode effect. Unlike Rashba systems studied previously, the present mechanism does not require broken structural inversion symmetry, since an inhomogeneous magnetic field, equivalent to a spin current, breaks the inversion symmetry extrinsically.

cond-mat.mes-hall↗

arXiv2026

Boundary Potential Method for Describing Electron Teleportation in an Interferometer with a Topological Superconductor

One-dimensional topological superconductors accommodate a pair of Majorana zero modes at their ends. In an interferometer containing such a topological superconductor, electron transport is significantly affected by the Majorana zero modes constituting a nonlocal state localized near both ends of the superconductor. When the number of electrons $\mathcal{N}$ in the superconductor is constrained by a charging effect, the resonant tunneling through the nonlocal state is expected to result in unusual transport properties. This resonant tunneling, called electron teleportation, is not easy to describe because there is no simple method to handle the constraint on $\mathcal{N}$. Here, we propose a boundary potential method based on scattering theory for calculating the conductance of the interferometer under a given constraint on $\mathcal{N}$. This method enables us to calculate the conductance taking account of relevant charging energy and details of the system.

cond-mat.mes-hall↗

arXiv2025

Majorana Zero Mode Induced by a Screw Dislocation on the Surface of an Iron-based Superconductor

We propose a simple scenario to describe a dislocation-induced Majorana zero mode on the surface of an iron-based superconductor, using an illustrative model with a cylindrical hole of radius $R$ perpendicular to its top surface. Topological surface states on the inner surface of the hole form an effective chiral $p$-wave superconductor. When the top surface has a perpendicular magnetization, chiral Majorana modes appear near the circular edge of the hole. Since the corresponding wavefunctions obey an antiperiodic boundary condition in the circumferential direction, a Majorana zero mode at zero energy does not appear. However, if a screw dislocation is inserted through the hole, the antiperiodic boundary condition is transformed into a periodic one, resulting in the appearance of a Majorana zero mode. This Majorana zero mode remains in the no-hole limit of $R \to 0$. We confirm this scenario by numerical simulation and effective theory. A method of creating a Majorana zero mode in the absence of the surface magnetization is briefly described.

cond-mat.supr-con↗

arXiv2024

Electron Transport along Screw Dislocations in a Strong Topological Insulator

In a three-dimensional strong topological insulator, gapless helical surface states appear everywhere on its surface. In the presence of a screw dislocation, gapless helical modes also appear in the vicinity of the corresponding dislocation line. Let us focus on a case where a pair of screw dislocations connects the top and bottom surfaces of a strong topological insulator with a shape of rectangular parallelepiped. The dislocation-induced helical modes are expected to act as one-dimensional conduction channels connecting the top and bottom surfaces. To examine this expectation, we calculate the two-terminal conductance between a pair of electrodes placed on the top and bottom surfaces. We found that the dislocation-induced helical modes and the helical surface states on the side surface contribute to the two-terminal conductance. The contribution of the dislocation-induced helical modes becomes more dominant than that of the helical surface states in certain situations.

cond-mat.mes-hall↗

arXiv2023

Bulk--boundary correspondence in a non-Hermitian quantum spin-Hall insulator

We focus on a scenario of non-Hermitian bulk--boundary correspondence that uses a topological invariant defined in a bulk geometry under a modified periodic boundary condition. Although this has succeeded in describing the topological nature of various one-dimensional non-Hermitian systems, its application to two-dimensional systems has been limited to a non-Hermitian Chern insulator. Here, we adapt the scenario to a non-Hermitian quantum spin-Hall insulator to extend its applicability. We show that it properly describes the bulk--boundary correspondence in the non-Hermitian quantum spin-Hall insulator. A phase diagram derived from the bulk--boundary correspondence is shown to be consistent with spectra of the system under an open boundary condition.

cond-mat.mes-hall↗

arXiv2023

Probability Conservation and Localization in a One-Dimensional Non-Hermitian System

We consider transport through a non-Hermitian conductor connected to a pair of Hermitian leads and analyze the underlying non-Hermitian scattering problem. In a typical non-Hermitian system, such as a Hatano--Nelson-type asymmetric hopping model, the continuity of probability and probability current is broken at a local level. As a result, the notion of transmission and reflection probabilities becomes ill-defined. Instead of these probabilities, we introduce the injection rate $R_{\rm I}=1-|{\cal R}|^2$ and the transmission rate $R_{\rm T}=|{\cal T}|^2$ as relevant physical quantities, where ${\cal T}$ and ${\cal R}$ are the transmission and reflection amplitudes, respectively. In a generic non-Hermitian case, $R_{\rm I}$ and $R_{\rm T}$ have independent information. We provide a modified continuity equation in terms of incoming and outgoing currents, from which we derive a global probability conservation law that relates $R_{\rm I}$ and $R_{\rm T}$. We have tested the usefulness of our probability conservation law in the interpretation of numerical results for non-Hermitian localization and delocalization phenomena.

cond-mat.mes-hall↗

arXiv2022

Bulk--Boundary Correspondence and Boundary Zero Modes in a Non-Hermitian Kitaev Chain Model

We study a non-Hermitian Kitaev chain model that contains three sources of non-Hermiticity: a constant imaginary potential, asymmetry between hopping amplitudes $t_{\rm R}$ and $t_{\rm L}$ in the right and left directions, and imbalance in pair potentials $Δ_{\rm c}$ and $Δ_{\rm a}$ for pair creation and annihilation, respectively. We show that bulk--boundary correspondence holds in this system; two topological invariants defined in bulk geometry under a modified periodic boundary condition correctly describe the presence or absence of a pair of boundary zero modes in boundary geometry under an open boundary condition. One topological invariant characterizes a topologically nontrivial phase with a line gap and the other characterizes that with a point gap. The latter appears only in the asymmetric hopping case of $t_{\rm R} \neq t_{\rm L}$. These two nontrivial phases are essentially equivalent except for their gap structures. Indeed, the boundary zero modes do not disappear across the boundary between them. We also show that the boundary zero modes do not satisfy the Majorana condition if $Δ_{\rm c} \neq Δ_{\rm a}$ and/or $t_{\rm R} \neq t_{\rm L}$.

cond-mat.mes-hall↗

arXiv2022

Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence

A non-Hermitian Chern insulator with gain/loss-type non-Hermiticity shows a peculiar gap closing; when a nontrivial Chern insulator phase changes to a gapless phase, conduction and valence bands are combined into one band owing to destabilization of chiral edge states. A previous recipe of non-Hermitian bulk-boundary correspondence is insufficient for this system since such a gap closing is beyond its scope. Here, we revise the recipe by taking the peculiar gap closing into account and apply it to the non-Hermitian Chern insulator. We demonstrate that the bulk-boundary correspondence holds in the system including a destabilization of chiral edge states. A phase diagram derived from the bulk-boundary correspondence is shown to be consistent with spectra of the system.

cond-mat.mes-hall↗

arXiv2021

Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators

A second-order topological insulator on a two-dimensional square lattice hosts zero-dimensional states inside a band gap. They are localized near $90^{\circ}$ and $270^{\circ}$ corners constituting an edge of the system. When the edge is in a staircase form consisting of these two corners, two families of edge states (i.e., one-dimensional states localized near the edge) appear as a result of the hybridization of zero-dimensional states. We identify symmetry that makes them gapless. We also show that a pair of nontrivial winding numbers associated with this symmetry guarantee a gapless spectrum of edge states, indicating that bulk--boundary correspondence holds in this topological insulator with a staircase edge.

cond-mat.mes-hall↗

arXiv2021

Bulk-Boundary Correspondence in a Non-Hermitian Chern Insulator

A scenario of non-Hermitian bulk--boundary correspondence proposed for one-dimensional topological insulators is adapted to a non-Hermitian Chern insulator to examine its applicability to two-dimensional systems. This scenario employs bulk geometry under a modified periodic boundary condition and boundary geometry under an open boundary condition. The bulk geometry is used to define a topological number, whereas the boundary geometry is used to observe the presence or absence of a topological boundary state. It is demonstrated that the bulk--boundary correspondence holds in a two-dimensional Chern insulator with gain/loss-type non-Hermiticity; a nontrivial Chern number calculated in the bulk geometry is in one-to-one correspondence with the presence of a topological boundary state in the boundary geometry. This approach enables us to determine a phase diagram in the boundary geometry.

cond-mat.mes-hall↗

arXiv2020

Generalized Bloch band theory for non-Hermitian bulk-boundary correspondence

Bulk-boundary correspondence is the cornerstone of topological physics. In some non-Hermitian topological system this fundamental relation is broken in the sense that the topological number calculated for the Bloch energy band under the periodic boundary condition fails to reproduce the boundary properties under the open boundary. To restore the bulk-boundary correspondence in such non-Hermitian systems a framework beyond the Bloch band theory is needed. We develop a non-Hermitian Bloch band theory based on a modified periodic boundary condition that allows a proper description of the bulk of a non-Hermitian topological insulator in a manner consistent with its boundary properties. Taking a non-Hermitian version of the Su-Schrieffer-Heeger model as an example, we demonstrate our scenario, in which the concept of bulk-boundary correspondence is naturally generalized to non-Hermitian topological systems.

cond-mat.mes-hall↗

arXiv2020

Unified Formula for Stationary Josephson Current in Planar Graphene Junctions

The stationary Josephson current in a ballistic graphene system is theoretically studied with focus on a planar junction consisting of a monolayer graphene sheet on top of which a pair of superconducting electrodes is deposited. To characterize such a planar junction, we employ two parameters: the coupling strength between the graphene sheet and the superconducting electrodes, and a potential drop induced in the graphene sheet by direct contact with the electrodes. We derive a general formula for the Josephson current by taking these parameters into account in addition to other basic parameters, such as temperature and chemical potential. The resulting formula applies to a wide range of parameters and reproduces previously reported results in certain limits.

cond-mat.mes-hall↗

arXiv2020

Zero-Energy State Localized near an Arbitrary Edge in Quadrupole Topological Insulators

A two-dimensional quadrupole topological insulator on a square lattice is a typical example of a higher-order topological insulator. It hosts an edge state localized near each of its $90^{\circ}$ corners at an energy $E$ inside the band gap, where $E$ is set equal to zero for simplicity. Although the appearance of an edge state has been shown in simple systems with only $90^{\circ}$ corners, it is uncertain whether a similar localized state can appear at $E = 0$ near a complicated edge consisting of multiple $90^{\circ}$ and $270^{\circ}$ corners. Here, we present a numerical method to determine the wavefunction of a zero-energy state localized near an arbitrary edge. This method enables us to show that one localized state appears at $E = 0$ if the edge consists of an odd number of corners. In contrast, the energy of localized states inevitably deviates from $E = 0$ if the edge includes an even number of corners.

cond-mat.mes-hall↗

arXiv2019

Generalized bulk-edge correspondence for non-hermitian topological systems

A modified periodic boundary condition adequate for non-hermitian topological systems is proposed. Under this boundary condition a topological number characterizing the system is defined in the same way as in the corresponding hermitian system and hence, at the cost of introducing an additional parameter that characterizes the non-hermitian skin effect, the idea of bulk-edge correspondence in the hermitian limit can be applied almost as it is. We develop this framework through the analysis of a non-hermitian SSH model with chiral symmetry, and prove the bulk-edge correspondence in a generalized parameter space. A finite region in this parameter space with a nontrivial pair of chiral winding numbers is identified as topologically nontrivial, indicating the existence of a topologically protected edge state under open boundary.

cond-mat.mes-hall↗

arXiv2019

Persistent current due to a screw dislocation in Weyl semimetals: Role of one-dimensional chiral states

A Weyl semimetal pierced by a screw dislocation accommodates one-dimensional (1D) chiral states along the corresponding dislocation line. As these states propagate in a particular direction determined by their chirality, a persistent current (i.e., charge current in equilibrium) is expected to appear in the interior of the system. To confirm this expectation, we numerically calculate the charge current in a Weyl semimetal in the presence of a screw dislocation. It is shown that a significant charge current is induced by the 1D chiral states near the dislocation. We also analyze the spatial distribution of the charge current focusing on the top and bottom surfaces of the system, at which the screw dislocation is terminated, and give an overview of how the charge current due to the dislocation is converted to that carried by other states near the termination point of the dislocation.

cond-mat.mes-hall↗

arXiv2019

Spontaneous charge current in a doped Weyl semimetal

A Weyl semimetal hosts low-energy chiral surface states, which appear to connect a pair of Weyl nodes in reciprocal space. As these chiral surface states propagate in a given direction, a spontaneous circulating current is expected to appear near the surface of a singly connected Weyl semimetal. This possibility is examined by using a simple model with particle-hole symmetry. It is shown that no spontaneous charge current appears when the Fermi level is located at the band center. However, once the Fermi level deviates from the band center, a spontaneous charge current appears to circulate around the surface of the system and its direction of flow is opposite for the cases of electron doping and hole doping. These features are qualitatively unchanged even in the absence of particle-hole symmetry. The circulating charge current is shown to be robust against weak disorder.

cond-mat.mes-hall↗

arXiv2019

Gauge-invariant cutoff for Dirac electron systems with a vector potential

The continuum Dirac model with an unbounded energy spectrum is widely used to describe low-energy states in various electron systems, such as graphene, topological insulators, and Weyl semimetals. However, if it is applied to analyze the electromagnetic response of electrons to a vector potential, we often find an unphysical result that breaks gauge invariance. This is an artifact caused by an energy or wavenumber cutoff, which is used to avoid divergence of the response. Here, we propose a modified energy cutoff procedure that preserves the gauge invariance. We use this procedure to calculate the response functions in a two-dimensional massless Dirac electron system. It is shown that the resulting functions properly describe the electromagnetic response in a gauge-invariant manner.

cond-mat.mes-hall↗

arXiv2019

Regularized continuum model of a Weyl semimetal for describing anomalous electromagnetic response

Although the Weyl model with an unbounded linear energy spectrum appropriately describes low-energy electron states in a Weyl semimetal, it cannot capture the anomalous electromagnetic response of the chiral magnetic effect (CME) and anomalous Hall effect (AHE) in a straightforward manner. Here, we propose a regularized continuum model by modifying the Weyl model and show that it properly describes the CME and AHE in a unified manner. It turns out that the absence of the CME at equilibrium is guaranteed by a basic nature of the Berry curvature. We also show that the original Weyl model can properly describe the CME if an energy cutoff procedure is appropriately applied, although it fails to describe the AHE in its present form.

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