arXiv subjects

Yositake Takane

Publications and source records attributed to Yositake Takane.

At least 37 records · Page 2Linked to original sources

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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arXiv2018

Regularized framework of a Weyl equation for describing a Weyl semimetal: Application to the case with a screw dislocation

The term Weyl semimetal originates from the fact that its energy dispersion obeys a Weyl equation. However, a Weyl equation itself cannot fully describe the electron states in an actual bounded geometry. For example, the appearance of chiral surface states, which is a characteristic feature of a Weyl semimetal, cannot be captured with a Weyl equation. This indicates that some degree of freedom is lost when a Weyl equation is derived from a microscopic model of a Weyl semimetal. To overcome this difficulty, we present a framework consisting of a Weyl equation and a supplementary equation, which can be derived from a microscopic model. Applying this framework to a cylindrical system in the presence of a screw dislocation, we show that it appropriately describes the chiral surface states and one-dimensional chiral modes along a dislocation line. The local charge current induced by these chiral states is determined in an analytical manner.

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arXiv2017

Short Ballistic Josephson Coupling in Planar Graphene Junctions with Inhomogeneous Carrier Doping

We report on short ballistic (SB) Josephson coupling in junctions embedded in a planar heterostructure of graphene. Ballistic Josephson coupling is confirmed by the Fabry-Perot-type interference of the junction critical current $I_c$. An exceptionally large $I_cR_N$ product close to $2Δ_0/e$ ($R_N$; normal-state junction resistance, $Δ_0$ ; zero-temperature superconducting energy gap) is an indication of SB strong Josephson coupling. $I_c$ shows a temperature dependence inconsistent with the conventional short-junction-like behavior; $I_c(T)$ curves deviate systematically from the standard Kulik-Omel'yanchuk prediction. We argue that this feature stems from the planar nature of graphene junction, which is susceptible to the effects of inhomogeneous carrier doping as well in graphene near the superconducting contacts.

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arXiv2017

Chiral surface states on the step edge in a Weyl semimetal

A Weyl semimetal with a pair of Weyl nodes accommodates chiral states on its flat surface if the Weyl nodes are projected onto two different points in the corresponding surface Brillouin zone. These surface states are collectively referred to as a Fermi arc as they appear to connect the projected Weyl nodes. This statement assumes that translational symmetry is present on the surface and hence electron momentum is a conserved quantity. It is unclear how chiral surface states are modified if the translational symmetry is broken by a particular system structure. Here, focusing on a straight step edge of finite width, we numerically analyze how chiral surface states appear on it. It is shown that the chiral surface states are algebraically (i.e., weakly) localized near the step edge. It is also shown that the appearance of chiral surface states is approximately determined by a simple condition characterized by the number of unit atomic layers constituting the step edge together with the location of the Weyl nodes.

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arXiv2017

Andreev Reflection in a Bilayer Graphene Junction: Role of Spatial Variation of the Charge Neutrality Point

A graphene sheet partially covered with a bulk superconductor serves as a normal conductor--superconductor (NS) junction, in which electron transport is mainly governed by Andreev reflection (AR). As excess carriers induced over the covered region penetrate into the uncovered region over a screening length, the charge neutrality point (CNP) in the uncovered region shifts only near the NS interface. We theoretically study the electron transport in a bilayer graphene junction taking account of such spatial variation of the CNP in the electron-doped case. When the Fermi level is close to the CNP away from the NS interface, the AR takes place in a specular manner owing to the diffraction of a reflected hole occurring at a $pn$ junction, which is naturally formed in the uncovered region. It is shown that the differential conductance shows an unusual asymmetric behavior as a function of bias voltage under the influence of the $pn$ junction. It is also shown that, if the Fermi level is located below the CNP, the $pn$ junction gives rise to quasi-bound states near the NS interface, leading to the appearance of resonant peaks in the differential conductance.

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arXiv2016

Disorder effect on chiral edge modes and anomalous Hall conductance in Weyl semimetals

Typical Weyl semimetals host chiral surface states and hence show an anomalous Hall response. Although a Weyl semimetal phase is known to be robust against weak disorder, the influence of disorder on chiral states is not fully clarified so far. We study the behavior of such chiral states in the presence of disorder and its consequences on an anomalous Hall response, focusing on a thin slab of Weyl semimetal with chiral surface states along its edge. It is shown that weak disorder does not disrupt chiral edge states but crucially affects them owing to the renormalization of a mass parameter: the number of chiral edge states changes depending on the strength of disorder. It is also shown that the Hall conductance is quantized when the Fermi level is located near Weyl nodes within a finite-size gap. This quantization of the Hall conductance collapses once the strength of disorder exceeds a critical value, suggesting that it serves as a probe to distinguish a Weyl semimetal phase from a diffusive anomalous Hall metal phase.

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arXiv2016

Finite-size scaling analysis of the conductivity of Dirac electrons on a surface of disordered topological insulators

Two-dimensional (2D) massless Dirac electrons appear on a surface of three-dimensional topological insulators. The conductivity of such a 2D Dirac electron system is studied for strong topological insulators in the case of the Fermi level being located at the Dirac point. The average conductivity $\langleσ\rangle$ is numerically calculated for a system of length $L$ and width $W$ under the periodic or antiperiodic boundary condition in the transverse direction, and its behavior is analyzed by applying a finite-size scaling approach. It is shown that $\langleσ\rangle$ is minimized at the clean limit, where it becomes scale-invariant and depends only on $L/W$ and the boundary condition. It is also shown that once disorder is introduced, $\langleσ\rangle$ monotonically increases with increasing $L$. Hence, the system becomes a perfect metal in the limit of $L \to \infty$ except at the clean limit, which should be identified as an unstable fixed point. Although the scaling curve of $\langleσ\rangle$ strongly depends on $L/W$ and the boundary condition near the unstable fixed point, it becomes almost independent of them with increasing $\langleσ\rangle$, implying that it asymptotically obeys a universal law.

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arXiv2016

Time-dependent Ginzburg-Landau equation and Boltzmann transport equation for charge-density-wave conductors

The time-dependent Ginzburg-Landau equation and the Boltzmann transport equation for one-dimensional charge-density-wave (CDW) conductors are derived from a microscopic model by applying the Keldysh Green's function approach under a quasiclassical approximation. The effects of external electric field and impurity pinning of the CDW are fully taken into account without relying on a phenomenological argument. These equations simultaneously describe spatiotemporal dynamics of both the CDW and quasiparticles, so they serve as a powerful tool to analyze various nonequilibrium phenomena, such as the current conversion between the CDW condensate and quasiparticles mediated by phase slips. It is shown that, in typical situations, the equations correctly describe the nonlinear behavior of electric conductivity in a simpler manner.

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arXiv2016

Weak topological insulators with step edges: Subband engineering and its effect on electron transport

A three-dimensional weak topological insulator (WTI) can be regarded as stacked layers of two-dimensional quantum spin-Hall insulators, each of which accommodates a one-dimensional helical edge mode. Massless Dirac electrons emerge on a side surface of WTIs as a consequence of the hybridization of such helical edge modes. We study the energy spectrum and transport of Dirac electrons on a side surface in the presence of step edges, which significantly modify the way of hybridization. It is shown that pseudo-helical modes with a nearly gapless linear dispersion can be created by manipulating step edges in a certain manner. We numerically calculate the average conductance of weakly disordered WTIs and show that it is markedly enhanced by pseudo-helical modes.

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arXiv2015

Regularization of a massless Dirac model to describe anomalous electromagnetic response of Weyl semimetals

An unbounded massless Dirac model with two nondegenerate Dirac cones is the simplest model for Weyl semimetals, which show the anomalous electromagnetic response of chiral magnetic effect (CME) and anomalous Hall effect (AHE). However, if this model is naively used to analyze the electromagnetic response within a linear response theory, it gives the result apparently inconsistent with the persuasive prediction based on a lattice model. We show that this serious difficulty is related to the breaking of current conservation in the Dirac model due to quantum anomaly and can be removed if current and charge operators are redefined to include the contribution from the anomaly. We demonstrate that the CME as well as the AHE can be properly described using newly defined operators, and clarify that the CME is determined by the competition between the contribution from the anomaly and that from low-energy electrons.

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arXiv2015

Dephasing-Induced Stabilization of a Perfectly Conducting Channel in Disordered Graphene Nanoribbons with Zigzag Edges

Electron transport in a disordered graphene nanoribbon with zigzag edges is crucially affected by a perfectly conducting channel (PCC), which is stabilized if intervalley scattering is ignorable. In the presence of such a PCC, the dimensionless conductance g of the system decreases to the quantized value of g = 1 with increasing system length L. In the realistic case where intervalley scattering is weak but not ignorable, the PCC is gradually destabilized with increasing L, and g eventually decays to zero owing to the onset of Anderson localization. Here, we show that such destabilization of the PCC can be relaxed by pure dephasing. We numerically calculate g in the presence of long-range impurities, which induce weak intervalley scattering, taking the dephasing effect into account. It is demonstrated that, under sufficient dephasing, the decay of g in the regime of g \lesssim 1 is strongly suppressed and the quasi-quantization of g (i.e., g ~ 1) can be observed in a wide region of L.

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arXiv2015

Manipulating quantum channels in weak topological insulator nanoarchitectures

In $strong$ topological insulators protected surface states are always manifest, while in $weak$ topological insulators (WTI) the corresponding metallic surface states are either manifest or hidden, depending on the orientation of the surface. One can design a nanostep on the surface of WTI such that a protected helical channel appears along it. In a more generic WTI nanostructure, multiple sets of such quasi-1D channels emerge and are coupled to each other. We study the response of the electronic spectrum associated with such quasi-1D surface modes against a magnetic flux piercing the system in the presence of disorder, and find a non-trivial, connected spectral flow as a clear signature indicating the immunity of the surface modes to disorder. We propose that the WTI nanoarchitecture is a promising platform for realizing topologically protected nanocircuits immune to disorder.

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arXiv2015

Landau levels on a surface of weak topological insulators

A three-dimensional weak topological insulator (WTI), being equivalent to stacked layers of two-dimensional quantum spin-Hall insulators, accommodates massless Dirac electrons on its side surface. A notable feature of WTIs is that surface states typically consist of two Dirac cones in the reciprocal space. We study the Landau quantization of Dirac electrons of WTIs in a perpendicular magnetic field. It is shown that when the magnetic length $l_B$ is much larger than the interlayer distance $a$, surface electrons are quantized into Landau levels according to the ordinary quantization rule for Dirac electrons. It is also shown that, with decreasing $l_B$ toward $a$, each Landau level and its spin state become modulated in a nontrivial manner. We demonstrate that this is attributed to the mixing of two Dirac cones induced by the discreteness of the layered structure.

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arXiv2014

Effective model for massless Dirac electrons on a surface of weak topological insulators

In a typical situation, gapless surface states of a three-dimensional (3D) weak topological insulator (WTI) appear only on sides, leaving the top and bottom surfaces gapped. To describe massless Dirac electrons emergent on such side surfaces of a WTI, a two-dimensional (2D) model consisting of a series of one-dimensional helical channels is usually employed. Yet, explicit derivation of such a model from a 3D bulk Hamiltonian has been lacking. Here, we explicitly derive an effective 2D model for the WTI surface states starting from a Wilson-Dirac Hamiltonian for the bulk WTI and establish a firm basis to the hitherto hypothesized 2D model. We show that the resulting 2D model accurately reproduces the excitation spectrum of surface Dirac electrons determined by the 3D model. We also show that the 2D model is applicable to a side surface with atomic steps.

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arXiv2014

Delocalization of surface Dirac electrons in disordered weak topological insulators

The spectrum of massless Dirac electrons on the side surface of a three-dimensional weak topological insulator is significantly affected by whether the number of unit atomic layers constituting the sample is even or odd; it has a finite-size energy gap in the even case while it is gapless in the odd case. The conductivity of such a two-dimensional Dirac electron system with quenched disorder is calculated when the Fermi level is located at the Dirac point. It is shown that the conductivity increases with increasing disorder and shows no clear even-odd difference when the aspect ratio of the system is appropriately fixed. From the system-size dependence of the average conductivity, the scaling function $β$ is determined under the one-parameter scaling hypothesis. The result implies that $β= 0$ in the clean limit at which the conductivity is minimized, and that $β> 0$ otherwise. Hence, the system is a perfect metal in the thermodynamic limit except in the clean limit that should be regarded as an unstable fixed point.

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arXiv2014

Local Density of States in a Helical Tomonaga-Luttinger Liquid of Loop and Josephson Junction Geometries

The local density of states (LDOS) in a one-dimensional helical channel of finite length is studied within a Tomonaga-Luttinger model at zero temperature. Two particular cases of loop and Josephson junction geometries are considered. The LDOS, as a function of energy $ω$ measured from the Fermi level, consists of equally spaced spikes of the $δ$-function type, and electron-electron interactions modify their relative height. It is shown that, in the loop geometry, the height of spikes decreases as $ω\to 0$ everywhere in the system. It is also shown that, in the Josephson junction, the behavior of the LDOS significantly depends on the spatial position. At the end points of the junction, the height increases as $ω\to 0$ and its variation is more pronounced than that in the loop case. Away from the end points, the height of spikes shows a non-monotonic $ω$-dependence, which disappears in the long-junction limit.

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arXiv2014

One-dimensional topological insulator: a model for studying finite-size effects in topological insulator thin films

As a model for describing finite-size effects in topological insulator thin films, we study a one-dimensional (1D) effective model of a topological insulator (TI). Using this effective 1D model, we reveal the precise correspondence between the spatial profile of the surface wave function, and the dependence of the finite-size energy gap on the thickness (Lx) of the film. We solve the boundary problem both in the semi-infinite and slab geometries to show that the Lx-dependence of the size gap is a direct measure of the amplitude of the surface wave function at the depth of x=Lx+1 [here, the boundary condition is chosen such that the wave function vanishes at x=0]. Depending on the parameters, the edge state function shows either a damped oscillation (in the "TI-oscillatory" region of FIG. 2, or becomes overdamped (ibid., in the "TI-overdamped" phase). In the original 3D bulk TI, an asymmetry in the spectrum of valence and conduction bands is omnipresent. Here, we demonstrate by tuning this asymmetry one can drive a crossover from the TI-oscillatory to the TI-overdamped phase.

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arXiv2014

Superconducting proximity effect on a two-dimensional Dirac electron system

The superconducting proximity effect on two-dimensional massless Dirac electrons is usually analyzed using a simple model consisting of the Dirac Hamiltonian and an energy-independent pair potential. Although this conventional model is plausible, it is questionable whether it can fully describe the proximity effect from a superconductor. Here, we derive a more general proximity model starting from an appropriate microscopic model for the Dirac electron system in planar contact with a superconductor. The resulting model describes the proximity effect in terms of the energy-dependent pair potential and renormalization term. Within this framework, we analyze the density of states, the quasiparticle wave function, and the charge conservation of Dirac electrons. The result reveals several characteristic features of the proximity effect, which cannot be captured within the conventional model.

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