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T. Fukui

Publications and source records attributed to T. Fukui.

At least 55 records · Page 3Linked to original sources
arXiv2012

Bulk-edge correspondence for Chern topological phases: A viewpoint from a generalized index theorem

We explore the bulk-edge correspondence for topological insulators (superconductors) without time-reversal symmetry from the point of view of the index theorem for open spaces. We assume generic Hamiltonians not only with a linear dispersion but also with higher order derivatives arising from generic band structures. Using a generalized index theorem valid for such systems, we show the equivalence between the spectral flow of the edge states and the Chern numbers specifying the bulk systems.

cond-mat.mes-hall↗
arXiv2011

Majorana fermions and Z$_2$ vortices on a square lattice

We present a simple model of Majorana fermions on a square lattice, and study zero-energy states due to Z$_2$ vortices. We show the relationship between the Chern number of the ground state and the number of the zero-energy states by numerical calculations for finite systems. We also discuss the relationship for the bulk system by observing the change of the spectral asymmetry. We finally present an effective continuum model with O(2) gauge potential which shows a topological change of the index at a half-flux.

cond-mat.supr-con↗
arXiv2011

Longitudinal and transverse exciton spin relaxation times in single InP/InAsP/InP nanowire quantum dots

We have investigated the optical properties of a single InAsP quantum dot embedded in a standing InP nanowire. A regular array of nanowires was fabricated by epitaxial growth and electron-beam patterning. The elongation of transverse exciton spin relaxation time of the exciton state with decreasing excitation power was observed by first-order photon correlation measurements. This behavior is well explained by the motional narrowing mechanism induced by Gaussian fluctuations of environmental charges in the InP nanowire. The longitudinal exciton spin relaxation time was evaluated by the degree of the random polarization of emission originating from exciton state confined in a single nanowire quantum dots by using Mueller Calculus based on Stokes parameters representation.

cond-mat.mes-hall↗
arXiv2010

Z$_2$ index theorem for Majorana zero modes in a class D topological superconductor

We propose a Z$_2$ index theorem for a generic topological superconductor in class D. Introducing a particle-hole symmetry breaking term depending on a parameter and regarding it as a coordinate of an extra dimension, we define the index of the zero modes and corresponding topological invariant for such an extended Hamiltonian. It is shown that these are related with the number of the zero modes of the original Hamiltonian modulo two.

cond-mat.supr-con↗
arXiv2010

Majorana zero modes bound to a vortex line in a topological superconductor

We explore Majorana zero modes bound to a vortex line in a three dimensional topological superconductor model, focusing our attention on the validity of the index theorem previously derived. We first solve the Bogoliubov-de Gennes equation at the zero energy to obtain the analytical index. We next calculate the topological index given by the order parameters. It turns out that they indeed coincide and that index theorem, which has been derived on the implicit assumption that a defect is point-like, is also valid for a line defect.

cond-mat.supr-con↗
arXiv2009

A Z$_2$ index of Dirac operator with time reversal symmetry

With time reversal symmetry a Dirac operator has vanishing index and Chern number. We show that we can nevertheless define a nontrivial Z$_2$ index as well as a corresponding topological invariant given by gauge field, which implies that such a Dirac operator is topologically nontrivial.

cond-mat.mes-hall↗
arXiv2009

Quantization of non-Abelian Berry phase for time reversal invariant systems

We present a quantized non-Abelian Berry phase for time reversal invariant systems such as quantum spin Hall effect. Ordinary Berry phase is defined by an integral of Berry's gauge potential along a loop (an integral of the Chern-Simons one-form), whereas we propose that a similar integral but over five dimensional parameter space (an integral of the Chern-Simons five-form) is suitable to define a non-Abelian Berry phase. We study its global topological aspects and show that it is indeed quantized into two values. We also discuss its close relationship with the nonperturbative anomalies.

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↗
arXiv2007

Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields

We discuss topological aspects of electronic properties of graphene, including edge effects, with the tight-binding model on a honeycomb lattice and its extensions to show the following: (i) Appearance of the pairn of massless Dirac dispersions, which is the origin of anomalous properties including a peculiar quantum Hall effect (QHE), is not accidental to honeycomb, but is rather generic for a class of two-dimensional lattices that interpolate between square and $π$-flux lattices. Persistence of the peculiar QHE is interpreted as a topological stability. (ii) While we have the massless Dirac dispersion only around E=0, the anomalous QHE associated with the Dirac cone unexpectedly persists for a wide range of the chemical potential. The range is bounded by van Hove singularities, at which we predict a transition to the ordinary fermion behavior acompanied by huge jumps in the QHE with a sign change. (iii) For edges we establish a coincidence between the quantum Hall effect in the bulk and the quantum Hall effect for the edge states, which is a manifestation of the topological bulk-edge correspondence. We have also explicitly shown that the E=0 edge states in honeycomb in zero magnetic field persist in magnetic field.

cond-mat.mes-hall↗
arXiv2006

Quantum spin Hall effect in three dimensional materials: Lattice computation of Z$_2$ topological invariants and its application to Bi and Sb

We derive an efficient formula for Z$_2$ topological invariants characterizing the quantum spin Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numerical calculations for realistic models even in three dimensions. Based on this, we study the quantum spin Hall effect in Bi and Sb in quasi-two and three dimensions using a tight-binding model.

cond-mat.mes-hall↗
arXiv2006

Topological analysis of the quantum Hall effect in graphene: Dirac-Fermi transition across van Hove singularities and the edge vs bulk quantum numbers

Inspired by a recent discovery of a peculiar integer quantum Hall effect (QHE) in graphene, we study QHE on a honeycomb lattice in terms of the topological quantum number, with two-fold interests: First, how the zero-mass Dirac QHE around the center of the tight-binding band crosses over to the ordinary finite-mass fermion QHE around the band edges. Second, how the bulk QHE is related with the edge QHE for the entire spectrum including Dirac and ordinary behaviors. We find the following: (i) The zero-mass Dirac QHE persists up to the van Hove singularities, at which the ordinary fermion behavior abruptly takes over. Here a technique developed in the lattice gauge theory enabled us to calculate the behavior of the topological number over the entire spectrum. This result indicates a robustness of the topological quantum number, and should be observable if the chemical potential can be varied over a wide range in graphene. (ii) To see if the honeycomb lattice is singular in producing the anomalous QHE, we have systematically surveyed over square-honeycomb-$π$-flux lattices, which is scanned by introducing a diagonal transfer $t'$. We find that the massless Dirac QHE forms a critical line, that is, the presence of Dirac cones in the Brillouin zone is preserved by the inclusion of $t'$ and the Dirac region sits side by side with ordinary one persists all through the transformation. (iii) We have compared the bulk QHE number obtained by an adiabatic continuity of the Chern number across transformation and numerically obtained edge QHE numbers calculated from the whole energy spectra for sample with edges, which shows that the bulk QHE number coincides, as in ordinary lattices, with the edge QHE number throughout the lattice transformation.

cond-mat.mes-hall↗
arXiv2006

Topological aspects of quantum spin Hall effect in graphene: Z$_2$ topological order and spin Chern number

For generic time-reversal invariant systems with spin-orbit couplings, we clarify a close relationship between the Z$_2$ topological order and the spin Chern number proposed by Kane and Mele and by Sheng {\it et al.}, respectively, in the quantum spin Hall effect. It turns out that a global gauge transformation connects different spin Chern numbers (even integers) modulo 4, which implies that the spin Chern number and the Z$_2$ topological order yield the same classification. We present a method of computing spin Chern numbers and demonstrate it in single and double plane of graphene.

cond-mat.mes-hall↗
arXiv2005

Topological Description of (Spin) Hall Conductances on Brillouin Zone Lattices : Quantum Phase Transitions and Topological Changes

It is widely accepted that topological quantities are useful to describe quantum liquids in low dimensions. The (spin) Hall conductances are typical examples. They are expressed by the Chern numbers, which are topological invariants given by the Berry connections of the ground states. We present a topological description for the (spin) Hall conductances on a discretized Brillouin Zone. At the same time, it is quite efficient in practical numerical calculations for concrete models. We demonstrate its validity in a model with quantum phase transitions. Topological changes supplemented with the transition is also described in the present lattice formulation.

cond-mat.mes-hall↗
arXiv2005

Exact renormalization group approach to a nonlinear diffusion equation

The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first introduced, and next a new regularization scheme is presented. It is shown that the renormalization of an action functional in the generating functional leads to an anomalous diffusion exponent in full order of the perturbation series with respect to a nonlinearity.

cond-mat.stat-mech↗
arXiv2005

On the finite temperature Drude weight of the anisotropic Heisenberg chain

We present a study of the Drude weight $D(T)$ of the spin-1/2 $XXZ$ chain in the gapless regime. The thermodynamic Bethe ansatz (TBA) is applied in two different ways. In the first application we employ the particle basis of magnons and their bound states. In this case we rederive and considerably extend earlier work in the literature. However, in the course of our investigation we find arguments that cast doubt on the applicability of the TBA in this case. In a second application by use of the spinon and anti-spinon particle basis we obtain completely different results. Only for anisotropy parameter $Δ$ close to 0 we find that $D(T)$ is a monotonously decaying function of temperature. For $Δ$ close to 1 the behaviour is entirely different showing a finite temperature maximum. Also for the isotropic antiferromagnetic chain ($Δ=1$) the results for $D(T)$ are finite for T=0 as well as for $T>0$ with an infinite positive slope at T=0.

cond-mat.str-el↗
arXiv2004

Perturbative calculation of the spin-wave dispersion in a disordered double-exchange model

We study the spin-wave dispersion of localized spins in a disordered double-exchange model using the perturbation theory with respect to the strength of the disorder potential. We calculate the dispersion upto the next-leading order, and extensively examine the case of one-dimension. We show that in that case, disorder yields anomalous gapped-like behavior at the Fermi wavenumber of the conduction electrons.

cond-mat.str-el↗