arXiv subjects

Ken-Ichiro Imura

Publications and source records attributed to Ken-Ichiro Imura.

50 records · Page 3Linked to original sources

arXiv2010

Mesoscopic spin Hall effect along a potential step in graphene

We consider a straight one-dimensional potential step created across a graphene flake. Charge and spin transport through such a potential step are studied in the presence of both intrinsic and extrinsic (Rashba) spin-orbit coupling (SOC). At normal incidence electrons are completely reflected when the Rashba interaction (with strength $λ_R$) is dominant whereas they are perfectly transmitted if the two types of SOC are exactly balanced. At normal incidence, the transmission probability of the step is thus controlled continuously from 0 to 1 by tuning the ratio of the two types of SOC. Besides the transport of charge in the direction normal to the barrier, we show the existence of a spin transport along the barrier. The magnitude of the spin Hall current is determined by a subtle interplay between the height of the potential step and the position of Fermi energy. It is demonstrated that contributions from inter-band matrix elements and evanescent modes are dominant in spin transport. Moreover, in the case of vanishing extrinsic SOC ($λ_R =0$), each channel carries a conserved spin current, in contrast to the general case of a finite $λ_R$, in which only integrated spin current is a conserved quantity. Finally, we provide a quasi-classical picture of the charge and spin transport by imaging flow lines over the entire sample and Veselago lensing (negative refraction) in the case of a $p-n$ junction.

cond-mat.mes-hall↗

arXiv2010

Zigzag edge modes in Z2 topological insulator: reentrance and completely flat spectrum

The spectrum and wave function of helical edge modes in Z_2 topological insulator are derived on a square lattice using Bernevig-Hughes-Zhang (BHZ) model. The BHZ model is characterized by a "mass" term M (k) that is parameterized as M (k) = Delta - B k^2. A topological insulator realizes when the parameters Delta and B fall on the regime, either 0 < Delta /B < 4 or 4 < Delta /B < 8. At Delta /B = 4, which separates the cases of positive and negative (quantized) spin Hall conductivities, the edge modes show a corresponding change that depends on the edge geometry. In the (1,0)-edge, the spectrum of edge mode remains the same against change of Delta /B, although the main location of the mode moves from the zone center for Delta /B < 4, to the zone boundary for Delta /B > 4 of the 1D Brillouin zone. In the (1,1)-edge geometry, the group velocity at the zone center changes sign at Delta /B = 4 where the spectrum becomes independent of the momentum, i.e. flat, over the whole 1D Brillouin zone. Furthermore, for Delta/B < 1.354..., the edge mode starting from the zone center vanishes in an intermediate region of the 1D Brillouin zone, but reenters near the zone boundary, where the energy of the edge mode is marginally below the lowest bulk excitations. On the other hand, the behavior of reentrant mode in real space is indistinguishable from an ordinary edge mode.

cond-mat.mes-hall↗

arXiv2010

Analytic Theory of Edge Modes in Topological Insulators

Spectrum and wave function of gapless edge modes are derived analytically for a tight-binding model of topological insulators on square lattice. Particular attention is paid to dependence on edge geometries such as the straight (1,0) and zigzag (1,1) edges in the thermodynamic limit. The key technique is to identify operators that combine to annihilate the edge state in the effective one-dimensional (1D) model with momentum along the edge. In the (1,0) edge, the edge mode is present either around the center of 1D Brillouin zone or its boundary, depending on location of the bulk excitation gap. In the (1,1) edge, the edge mode is always present both at the center and near the boundary. Depending on system parameters, however, the mode is absent in the middle of the Brillouin zone. In this case the binding energy of the edge mode near the boundary is extremely small; about $10^{-3}$ of the overall energy scale. Origin of this minute energy scale is discussed.

cond-mat.mes-hall↗

arXiv2010

(De)confinement of supercurrent in Z_2 Topological Insulators

It is shown that the electric supercurrent flows in a Z_2 topological insulator with U_em(1) X U_z(1) (electromagnetic and spin) gauge symmetries. When U_z(1) is broken, a dissipationless electric current is still possible to flow locally but net charge transfer is absent, i.e., current is confined. In the Kane-Mele model for graphene, this confining-deconfining (superconducting) transition is driven by the Rashba spin-orbit interaction, which breaks U_z(1).

cond-mat.mes-hall↗

arXiv2009

Weak (anti-)localization in doped Z_2-topological insulator

Localization properties of the doped Z_2-topological insulator are studied by weak localization theory. The disordered Kane-Mele model for graphene is taken as a prototype, and analyzed with attention to effects of the topological mass term, inter-valley scattering, and the Rashba spin-orbit interaction. The known tendency of graphene to anti-localize in the absence of inter-valley scattering between K and K' points is naturally placed as the massless limit of Kane-Mele model. The latter is shown to have a unitary behavior even in the absence of magnetic field due to the topological mass term. When inter-valley scattering is introduced, the topological mass term leaves the system in the unitary class, whereas the ordinary mass term, which appears if A and B sublattices are inequivalent, turns the system to weak localization. The Rashba spin-orbit interaction in the presence of K-K' scattering drive the system to weak anti-localization in sharp contrast to the ideal graphene case.

cond-mat.mes-hall↗

arXiv2009

Anti-localization of graphene under substrate electric field

A simple criterion is provided how the (anti-)localization properties of graphene are determined in the presence of inter-valley scattering, Kane-Mele topological mass term, and Rashba spin-orbit interaction (SOI). A set of (pseudo) time-reversal operations show that the number of effective internal degrees of freedom, such as spin and pseudo-spins distinguishing the sublattice and the valley, is the crucial parameter for localization. It is predicted that perpendicular electric field due to gate voltage of the substrate drives the system to anti-localization by enhancing the Rashba SOI.

cond-mat.mes-hall↗

arXiv2008

Quantum Hall effect in bilayer and multilayer graphenes with finite gate voltage

We discuss the quantum Hall effect of bilayer graphene with finite gate voltage where the Fermi energy exceeds the interlayer hopping energy. We calculated magnetic susceptibility, diagonal and off-diagonal conductivities in finite-magnetic-field formalism, and observed crossover of integer quantum Hall effect from two independent monolayer type system to strongly coupled bilayer systems by changing the ratio of interlayer hopping energy and the gate voltage. We also discuss the case of multilayer systems with Bernal stacking

cond-mat.mes-hall↗

arXiv2008

Colossal spin fluctuations in a molecular quantum dot magnet with ferromagnetic electrodes

We study electronic transport through a magnetic molecule with an intrinsic spin $S$ coupled to two magnetic electrodes, in the incoherent regime. The molecule is modeled as a single resonant level with large Coulomb repulsion (no double occupancy). The molecular spin is isotropic and it interacts with the electronic spin through an exchange interaction. Using an alternative method to the usual master equation approach, we are able to obtain analytical formulas for various physical quantities of interest, such as the mean current and the current fluctuations, but also the mean value of $J_z$ -the $z$ component of the total spin on the molecule- and its fluctuations. This allows us to understand how the electronic current between the magnetized electrodes can control the polarization of the molecular spin. We observe in particular that the fluctuations of $J_z$ reach unexpectedly high values.

cond-mat.mes-hall↗

arXiv2007

Numerical study of transport through a single impurity in a spinful Tomonaga-Luttinger liquid

The single impurity problem in a spinful Tomonaga-Luttinger liquid is studied numerically using path-integral Monte Carlo methods. The advantage of our approach is that the system allows for extensive analyses of charge and spin conductance in the non-perturbative regime. By closely examining the behavior of conductances at low temperatures, in the presence of a finite backward scattering barrier due to the impurity, we identified four distinct phases characterized by either perfect transmission or reflection of charge and spin channels. Our phase diagram for an intermediate scattering strength is consistent with the standard perturbative renormalization group (RG) analysis in the limit of weak and strong backward scattering, in the sense that all our phase boundaries interpolate the two limiting cases. Further investigations show, however, that precise location and form of our phase boundaries are not trivially explained by the standard RG analysis, e.g., some part of the phase diagram looks much similar to the weak backscattering limit, whereas some other part is clearly derived from the opposite limit. In order to give a more intuitive interpretation of such behaviors, we also reconsidered our impurity problem from the viewpoint of a quantum Brownian motion picture.

cond-mat.mes-hall↗

arXiv2007

Characterization of two-dimensional fermionic insulating states

Inspired by the duality picture between superconductivity and insulator in two spatial dimension, we conjecture that the order parameter, suitable for characterizing 2D fermionic insulating state, is the disorder operator, usually known in the context of statistical transformation. Namely, the change of the phase of the disorder operator along a closed loop measures the particle density accommodating inside this loop. Thus, identifying this (doped) particle density with the dual counterpart of the magnetic induction in 2D SC, we can naturally introduce the disorder operator as the dual order parameter of 2D insulators. The disorder operator has a branch cut emitting from this ``vortex'' to the single infinitely far point. To test this conjecture against an arbitrary 2D lattice models, we have chosen this branch cut to be compatible with the periodic boundary condition and obtain a general form of its expectation value for non-interacting metal/insulator wavefunction, including gapped mean-field order wavefunction. Based on this expression, we observed analytically that it indeed vanishes for a wide class of band metals in the thermodynamic limit. In insulating states, on the other hand, it is quantified by the localization length or the real-valued gauge invariant 2-from dubbed as the quantum metric tensor.

cond-mat.str-el↗

arXiv2006

Full counting statistics for transport through a molecular quantum dot magnet

Full counting statistics (FCS) for the transport through a molecular quantum dot magnet is studied theoretically in the incoherent tunneling regime. We consider a model describing a single-level quantum dot, magnetically coupled to an additional local spin, the latter representing the total molecular spin s. We also assume that the system is in the strong Coulomb blockade regime, i.e., double occupancy on the dot is forbidden. The master equation approach to FCS introduced in Ref. [12] is applied to derive a generating function yielding the FCS of charge and current. In the master equation approach, Clebsch-Gordan coefficients appear in the transition probabilities, whereas the derivation of generating function reduces to solving the eigenvalue problem of a modified master equation with counting fields. To be more specific, one needs only the eigenstate which collapses smoothly to the zero-eigenvalue stationary state in the limit of vanishing counting fields. We discovered that in our problem with arbitrary spin s, some quartic relations among Clebsch-Gordan coefficients allow us to identify the desired eigenspace without solving the whole problem. Thus we find analytically the FCS generating function in the following two cases: i) both spin sectors lying in the bias window, ii) only one of such spin sectors lying in the bias window. Based on the obtained analytic expressions, we also developed a numerical analysis in order to perform a similar contour-plot of the joint charge-current distribution function, which have recently been introduced in Ref. [13], here in the case of molecular quantum dot magnet problem.

cond-mat.mes-hall↗

arXiv2005

Noncommutative geometry and nonabelian Berry phase in the wave-packet dynamics of Bloch electrons

Motivated by a recent proposal on the possibility of observing a monopole in the band structure, and by an increasing interest on the role of Berry phase in spintronics, we studied the adiabatic motion of a wave packet of Bloch functions, under a perturbation varying slowly and incommensurately to the lattice structure. We show using only the fundamental principles of quantum mechanics that its effective wave-packet dynamics is conveniently described by a set of equations of motion (EOM) for a semiclassical particle coupled to a nonabelian gauge field associated with a geometric Berry phase. Our EOM can be viewed as a generalization of the standard Ehrenfest's theorem, and their derivation was asymptotically exact in the framework of linear response theory. Our analysis is entirely based on the concept of local Bloch bands, a good starting point for describing the adiabatic motion of a wave packet. One of the advantages of our approach is that the various types of gauge fields were classified into two categories by their different physical origin: (i) projection onto specific bands, (ii) time-dependent local Bloch basis. Using those gauge fields, we write our EOM in a covariant form, whereas the gauge-invariant field strength stems from the noncommutativity of covariant derivatives along different axes of the reciprocal parameter space. The degeneracy of Bloch bands makes the gauge fields nonabelian. We applied our formalism to the analyses on various types of Hall and polarization currents. We highlighted their behavior under time reversal (T) and space inversion (I). The concept of parity polarization current was also introduced. Together with charge/spin Hall/polarization currents, this type of orbital current is expected to be a potential probe for detecting and controling Berry phase.

cond-mat.mes-hall↗

arXiv2001

Discrete Thermodynamic Bethe Ansatz

We propose discrete TBA equations for models with discrete spectrum. We illustrate our construction on the Calogero-Moser model and determine the discrete 2-body TBA function which yields the exact N-body Calogero-Moser thermodynamics. We apply this algorithm to the Lieb-Liniger model in a harmonic well, a model which is relevant for the microscopic description of harmonically trapped Bose-Einstein condensates in one dimension. We find that the discrete TBA reproduces correctly the N-body groundstate energy of the Lieb-Liniger model in a harmonic well at first order in perturbation theory, but corrections do appear at second order.

cond-mat.stat-mech↗

arXiv1999

Plateau transitions in fractional quantum Hall liquids

Effects of backward scattering between fractional quantum Hall (FQH) edge modes are studied. Based on the edge-state picture for hierarchical FQH liquids, we discuss the possibility of the transitions between different plateaux of the tunneling conductance $G$. We find a selection rule for the sequence which begins with a conductance $G=m/(mp\pm 1)$ ($m$: integer, $p$: even integer) in units of $e^2/h$. The shot-noise spectrum as well as the scaling behavior of the tunneling current is calculated explicitly.

cond-mat↗