arXiv subjects

Yositake Takane

Publications and source records attributed to Yositake Takane.

At least 55 records · Page 3Linked to original sources

arXiv2013

Unified description of Dirac electrons on a curved surface of topological insulators

Existence of a protected surface state described by a massless Dirac equation is a defining property of the topological insulator. Though this statement can be explicitly verified on an idealized flat surface, it remains to be addressed to what extent it could be general. On a curved surface, the surface Dirac equation is modified by the spin connection terms. Here, in the light of the differential geometry, we give a general framework for constructing the surface Dirac equation starting from the Hamiltonian for bulk topological insulators. The obtained unified description clarifies the physical meaning of the spin connection.

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arXiv2013

Perfectly conducting channel on the dark surface of weak topological insulators

A weak topological insulator (WTI) bears, generally, an even number of Dirac cones on its surface; they are susceptible of doubling, while on the surface of a certain orientation it shows no Dirac cone. On this "dark" surface of a WTI, we predict the existence of a single pair of isolated 1D perfectly conducting channels that forms either a closed loop or a segment of a line. The former is associated typically with a single atomic-layer-thick island formed on the dark surface, while the latter is shown to be the consequence of a pair of crystal (screw) dislocations terminating on the dark surface.

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arXiv2013

Protection of the surface states in topological insulators: Berry phase perspective

The metallic surface state of a topological insulator (TI) is not only topologically protected, but exhibits a remarkable property of inducing an effective vector potential on curved surfaces. For an electron in the surface state of a spherical or a cylindrical TI (TI nanoparticle or nanowire) a pseudo-magnetic monopole or a fictitious solenoid is effectively induced, encoding the geometry of the system. Here, by taking an example of a hyperbolic surface we demonstrate that as a consequence of this property stemming from its active spin degree of freedom, the surface state is by itself topologically protected.

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arXiv2012

Spherical topological insulator

The electronic spectrum on the spherical surface of a topological insulator reflects an active property of the helical surface state that stems from a constraint on its spin on a curved surface. The induced effective vector potential (spin connection) can be interpreted as an effective vector potential associated with a fictitious magnetic monopole induced at the center of the sphere. The strength of the induced magnetic monopole is found to be g=2pi, -2pi, being the smallest finite (absolute) value compatible with the Dirac quantization condition. We have established an explicit correspondence between the bulk Hamiltonian and the effective Dirac operator on the curved spherical surface. An explicit construction of the surface spinor wave functions implies a rich spin texture possibly realized on the surface of topological insulator nanoparticles. The electronic spectrum inferred by the obtained effective surface Dirac theory, confirmed also by the bulk tight-binding calculation, suggests a specific photo absorption/emission spectrum of such nanoparticles.

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arXiv2012

Finite-size energy gap in weak and strong topological insulators

The non-trivialness of a topological insulator (TI) is characterized either by a bulk topological invariant or by the existence of a protected metallic surface state. Yet, in realistic samples of finite size this non-trivialness does not necessarily guarantee the gaplessness of the surface state. Depending on the geometry and on the topological indices, a finite-size energy gap of different nature can appear, and correspondingly, exhibits various scaling behaviors of the gap. The spin-to-surface locking provides one of such gap-opening mechanisms, resulting in a power-law scaling of the energy gap. Weak and strong TI's show different degrees of sensitivity to the geometry of the sample. As a noteworthy example, a strong TI nanowire of a rectangular prism shape is shown to be more gapped than that of a weak TI of precisely the same geometry.

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arXiv2012

Quasiclassical Theory of the Josephson Effect in Ballistic Graphene Junctions

The stationary Josephson effect in a system of ballistic graphene is studied in the framework of quasiclassical Green's function theory. Reflecting the ultimate two-dimensionality of graphene, a Josephson junction involving a graphene sheet embodies what we call a planar Josephson junction, in which superconducting electrodes partially cover the two-dimensional graphene layer, achieving a planar contact with it. For capturing this feature we employ a model of tunneling Hamiltonian that also takes account of the effects of inhomogeneous carrier density. Within the effective mass approximation we derive a general formula for the Josephson current, revealing characteristic features of the superconducting proximity effect in the planar Josephson junction. The same type of analysis has been equally applied to mono-, bi- and arbitrary $N$-layer cases.

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arXiv2012

Dirac Electrons on a Sharply Edged Surface of Topological Insulators

An unpaired gapless Dirac electron emergent at the surface of a strong topological insulator (STI) is protected by the bulk-surface correspondence and believed to be immune to backward scattering. It is less obvious, however, and yet to be verified explicitly whether such a gapless Dirac state is smoothly extended over the entire surface when the surface is composed of more than a single facet with different orientations in contact with one another at sharp corner edges (typically forming a steplike structure). In the realistic situation that we consider, the anisotropy of the sample leads to different group velocities in each of such facets. Here, we propose that much insight on this issue can be obtained by studying the electronic states on a hyperbolic surface of an STI. By explicitly constructing the surface effective Hamiltonian, we demonstrate that no backward scattering takes place at a concave $90^\circ$ step edge. A strong renormalization of the velocity in the close vicinity of the step edge is also suggested.

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arXiv2012

Perfectly conducting channel and its robustness in disordered carbon nanostructures

We report our recent numerical study on the effects of dephasing on a perfectly conducting channel (PCC), its presence believed to be dominant in the transport characteristics of a zigzag graphene nanoribbons (GNR) and of a metallic carbon nanotubes (CNT). Our data confirms an earlier prediction that a PCC in GNR exhibits a peculiar robustness against dephasing, in contrast to that of the CNT. By studying the behavior of the conductance as a function of the system's length we show that dephasing destroys the PCC in CNT, whereas it stabilizes the PCC in GNR. Such opposing responses of the PCC against dephasing stem from a different nature of the PCC in these systems.

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arXiv2011

Spin Berry phase in the Fermi arc states

Unusual electronic property of a Weyl semi-metallic nanowire is revealed. Its band dispersion exhibits multiple subbands of partially flat dispersion, originating from the Fermi arc states. Remarkably, the lowest energy flat subbands bear a finite size energy gap, implying that electrons in the Fermi arc surface states are susceptible of the spin Berry phase. This is shown to be a consequence of spin-to-surface locking in the surface electronic states. We verify this behavior and the existence of spin Berry phase in the low-energy effective theory of Fermi arc surface states on a cylindrical nanowire by deriving the latter from a bulk Weyl Hamiltonian. We point out that in any surface state exhibiting a spin Berry phase pi, a zero-energy bound state is formed along a magnetic flux tube of strength, hc/(2e). This effect is highlighted in a surfaceless bulk system pierced by a dislocation line, which shows a 1D chiral mode along the dislocation line.

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arXiv2011

Spin Berry phase in anisotropic topological insulators

Three-dimensional topological insulators are characterized by the presence of protected gapless spin helical surface states. In realistic samples these surface states are extended from one surface to another, covering the entire sample. Generally, on a curved surface of a topological insulator an electron in a surface state acquires a spin Berry phase as an expression of the constraint that the effective surface spin must follow the tangential surface of real space geometry. Such a Berry phase adds up to pi when the electron encircles, e.g., once around a cylinder. Realistic topological insulators compounds are also often layered, i.e., are anisotropic. We demonstrate explicitly the existence of such a pi Berry phase in the presence and absence (due to crystal anisotropy) of cylindrical symmetry, that is, regardless of fulfilling the spin-to-surface locking condition. The robustness of the spin Berry phase pi against cylindrical symmetry breaking is confirmed numerically using a tight-binding model implementation of a topological insulator nanowire penetrated by a pi-flux tube.

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arXiv2011

Electronic States and Local Density of States in Graphene with a Corner Edge Structure

We study electronic states of semi-infinite graphene with a corner edge, focusing on the stability of edge localized states at zero energy. The 60°, 90°, 120° and 150° corner edges are examined. The 60° and 120° corner edges consist of two zigzag edges, while 90° and 150° corner edges consist of one zigzag edge and one armchair edge. We numerically obtain the local density of states (LDOS) on the basis of a nearest-neighbor tight-binding model by using Haydock's recursion method. We show that edge localized states appear along a zigzag edge of each corner edge structure except for the 120° case. To provide insight into this behavior, we analyze electronic states at zero energy within the framework of an effective mass equation. The result of this analysis is consistent with the behavior of the LDOS.

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arXiv2011

Weak topological insulator with protected gapless helical states

A workable model for describing dislocation lines introduced into a three-dimensional topological insulator is proposed. We show how fragile surface Dirac cones of a weak topological insulator evolve into protected gapless helical modes confined to the vicinity of dislocation line. It is demonstrated that surface Dirac cones of a topological insulator (either strong or weak) acquire a finite-size energy gap, when the surface is deformed into a cylinder penetrating the otherwise surface-less system. We show that when a dislocation with a non-trivial Burgers vector is introduced, the finite-size energy gap play the role of stabilizing the one-dimensional gapless states.

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arXiv2011

Josephson Current through a Planar Junction of Graphene

Josephson effect in a planar graphene junction is studied by assuming that the coupling of a graphene sheet and two superconductors deposited on its top is described by a tunneling Hamiltonian. This model properly takes account of the proximity effect characteristic to a planar junction, and allows us to treat monolayer and bilayer cases in a parallel manner. Applying a quasiclassical Green's function approach to it we analyze the Josephson critical current $I_{\rm c}$ in a short-junction limit. As a characteristic feature of the planar junction we find that $I_{\rm c}$ is a concave function of temperature at the strong coupling limit while it crosses over to a convex function with decreasing the coupling strength. We also find different chemical-potential dependences of $I_{\rm c}$ in the monolayer and bilayer cases.

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arXiv2010

Nonuniversal Shot Noise in Disordered Quantum Wires with Channel-Number Imbalance

The number of conducting channels for one propagating direction is equal to that for the other direction in ordinary quantum wires. However, they can be imbalanced in graphene nanoribbons with zigzag edges. Employing the model system in which a degree of channel-number imbalance can be controlled, we calculate the shot-noise power at zero frequency by using the Boltzmann-Langevin approach. The shot-noise power in an ordinary diffusive conductor is one-third of the Poisson value. We show that with increasing the degree of channel-number imbalance, the universal one-third suppression breaks down and a highly nonuniversal behavior of shot noise appears.

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arXiv2010

Anomalous Enhancement of the Boltzmann Conductivity in Disordered Zigzag Graphene Nanoribbons

We study the conductivity of disordered zigzag graphene nanoribbons in the incoherent regime by using the Boltzmann equation approach. The band structure of zigzag nanoribbons contains two energy valleys, and each valley has an excess one-way channel. The crucial point is that the numbers of conducting channels for two propagating directions are imbalanced in each valley due to the presence of an excess one-way channel. It was pointed out that as a consequence of this imbalance, a perfectly conducting channel is stabilized in the coherent regime if intervalley scattering is absent. We show that even in the incoherent regime, the conductivity is anomalously enhanced if intervalley scattering is very weak. Particularly, in the limit of no intervalley scattering, the dimensionless conductance approaches to unity with increasing ribbon length as if there exists a perfectly conducting channel. We also show that anomalous valley polarization of electron density appears in the presence of an electric field.

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arXiv2009

Electronic transport properties of graphene nanoribbons

We will present brief overview on the electronic and transport properties of graphene nanoribbons focusing on the effect of edge shapes and impurity scattering. The low-energy electronic states of graphene have two non-equivalent massless Dirac spectrum. The relative distance between these two Dirac points in the momentum space and edge states due to the existence of the zigzag type graphene edges are decisive to the electronic and transport properties of graphene nanoribbons. In graphene nanoribbons with zigzag edges, two valleys related to each Dirac spectrum are well separated in momentum space. The propagating modes in each valley contain a single chiral mode originating from a partially flat band at band center. This feature gives rise to a perfectly conducting channel in the disordered system, if the impurity scattering does not connect the two valleys, i.e. for long-range impurity potentials. On the other hand, the low-energy spectrum of graphene nanoribbons with armchair edges is described as the superposition of two non-equivalent Dirac points of graphene. In spite of the lack of well-separated two valley structures, the single-channel transport subjected to long-ranged impurities is nearly perfectly conducting, where the backward scattering matrix elements in the lowest order vanish as a manifestation of internal phase structures of the wavefunction. Symmetry considerations lead to the classification of disordered zigzag ribbons into the unitary class for long-range impurities, and the orthogonal class for short-range impurities. However, no such crossover occurs in armchair nanoribbons.

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arXiv2009

Conductance Distribution in Disordered Quantum Wires with a Perfectly Conducting Channel

We study the conductance of phase-coherent disordered quantum wires focusing on the case in which the number of conducting channels is imbalanced between two propagating directions. If the number of channels in one direction is by one greater than that in the opposite direction, one perfectly conducting channel without backscattering is stabilized regardless of wire length. Consequently, the dimensionless conductance does not vanish but converges to unity in the long-wire limit, indicating the absence of Anderson localization. To observe the influence of a perfectly conducting channel, we numerically obtain the distribution of conductance in both cases with and without a perfectly conducting channel. We show that the characteristic form of the distribution is notably modified in the presence of a perfectly conducting channel.

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arXiv2009

Spin Injection and Detection in a Mesoscopic Superconductor at Low Temperatures

We theoretically study nonequilibrium spin transport in a superconducting wire connected by tunnel junctions to two ferromagnetic metal wires, each of which serves as an injector or detector of spin-polarized electron current. We present a set of Boltzmann equations to determine nonequilibrium quasiparticle distributions in this system, and obtain an analytical expression for the nonlocal spin signal in the case of small injection current. It is shown that the quasiparticle distribution in the ferromagnetic metal for detection strongly affects the magnitude of the spin signal. At low temperatures, since nonequilibrium quasiparticles created by the tunneling from the superconductor dominate thermally excited ones, the spin signal becomes independent of temperature. This explains the convergence of the spin signal with decreasing temperature observed in a recent experiment by Poli \textit{et al}.

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