arXiv subjects

Ryota Nakai

Publications and source records attributed to Ryota Nakai.

26 records · Page 2Linked to original sources

arXiv2017

Laughlin's argument for the quantized thermal Hall effect

We extend Laughlin's magnetic-flux-threading argument to the quantized thermal Hall effect. A proper analogue of Laughlin's adiabatic magnetic-flux threading process for the case of the thermal Hall effect is given in terms of an external gravitational field. From the perspective of the edge theories of quantum Hall systems, the quantized thermal Hall effect is closely tied to the breakdown of large diffeomorphism invariance, that is, a global gravitational anomaly. In addition, we also give an argument from the bulk perspective in which a free energy, decomposed into its Fourier modes, is adiabatically transferred under an adiabatic process involving external gravitational perturbations.

cond-mat.mes-hall↗

arXiv2016

Crossed responses of spin and orbital magnetism in topological insulators

Crossed magnetic responses between spin and orbital angular momentum are studied in time-reversal symmetric topological insulators. Due to spin-orbit coupling in the quantum spin Hall systems and three-dimensional topological insulators, the magnetic susceptibility has crossed (intersectional) components between spin and orbital part of magnetism. In this study, the crossed susceptibility for the orbital magnetization is studied in two- and three-dimensional topological insulator models, in which an external magnetic field interacts with the electron spin by Zeeman coupling via distinct g-factors for conduction and valence energy bands. The crossed susceptibility in two-dimensional quantum spin Hall insulators shows a quantized signature of the $\mathbb{Z}_2$ topological phase in response to Zeeman coupling via an averaged g-factor, and the quantization persists even when $σ^z$-conservation of electrons is broken by a tilted magnetic field. The bulk orbital magnetization is interpreted by the persistent edge current attributed to the chiral anomaly at the (1+1)-dimensional boundary. In three-dimensional topological insulators, we found that the crossed susceptibility is proportional to the difference of g-factors of conduction and valence electrons, which is qualitatively different from the two-dimensional case. Steep changes of the crossed susceptibility in three dimensions at the phase transition points are explained by the surface Dirac fermion theory. Finally, dependence of the crossed susceptibility on g-factors in two- and three-dimensional cases is discussed from the viewpoint of time-reversal and particle-hole symmetries.

cond-mat.mes-hall↗

arXiv2016

Finite-temperature effective boundary theory of the quantized thermal Hall effect

A finite-temperature effective free energy of the boundary of a quantized thermal Hall system is derived microscopically from the bulk two-dimensional Dirac fermion coupled with a gravitational field. In two spatial dimensions, the thermal Hall conductivity of fully gapped insulators and superconductors is quantized and given by the bulk Chern number, in analogy to the quantized electric Hall conductivity in quantum Hall systems. From the perspective of effective action functionals, two distinct types of the field theory have been proposed to describe the quantized thermal Hall effect. One of these, known as the gravitational Chern-Simons action, is a kind of topological field theory, and the other is a phenomenological theory relevant to the Středa formula. In order to solve this problem, we derive microscopically an effective theory that accounts for the quantized thermal Hall effect. In this paper, the two-dimensional Dirac fermion under a static background gravitational field is considered in equilibrium at a finite temperature, from which an effective boundary free energy functional of the gravitational field is derived. This boundary theory is shown to explain the quantized thermal Hall conductivity and thermal Hall current in the bulk by assuming the Lorentz symmetry. The bulk effective theory is consistently determined via the boundary effective theory

cond-mat.mes-hall↗

arXiv2014

Disorder effects on thermal transport on the surface of topological superconductors by the self-consistent Born approximation

We have studied the longitudinal thermal conductivity of the surface of a three-dimensional time-reversal symmetric topological superconductor with random disorder. Majorana fermions on the surface of topological superconductors have a response to the gravitational field, which is realized as a thermal response to the temperature gradient inside of the material. Because of the presence of both time-reversal symmetry and particle-hole symmetry, disorder on the surface emerges in the Hamiltonian only as spatial deformations of the pair potential. In terms of the gravitational field, the disorder results in spatial fluctuations of the metric. We consider disorder effects on the thermal conductivity perturbatively within the self-consistent Born approximation. The density of states is calculated with the Green's function technique and the thermal conductivity of the surface modes is derived through the electronic conductivity using Wiedemann-Franz law for the Majorana fermions.

cond-mat.supr-con↗

arXiv2014

Particle Propagator of Spin Calogero-Sutherland Model

Explicit-exact expressions for the particle propagator of the spin 1/2 Calogero-Sutherland model are derived for the system of a finite number of particles and for that in the thermodynamic limit. Derivation of the expression in the thermodynamic limit is also presented in detail. Combining this result with the hole propagator obtained in earlier studies, we calculate the spectral function of the single particle Green's function in the full range of the energy and momentum space. The resultant spectral function exhibits power-law singularity characteristic to correlated particle systems in one dimension.

cond-mat.str-el↗

arXiv2012

Time-reversal symmetric Kitaev model and topological superconductor in two dimensions

A time-reversal invariant Kitaev-type model is introduced in which spins (Dirac matrices) on the square lattice interact via anisotropic nearest-neighbor and next-nearest-neighbor exchange interactions. The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z_2 gauge fields. The Majorana fermion model can be viewed as a model of time-reversal invariant superconductor and is classified as a member of symmetry class DIII in the Altland-Zirnbauer classification. The ground-state phase diagram has two topologically distinct gapped phases which are distinguished by a Z_2 topological invariant. The topologically nontrivial phase supports both a Kramers' pair of gapless Majorana edge modes at the boundary and a Kramers' pair of zero-energy Majorana states bound to a 0-flux vortex in the π-flux background. Power-law decaying correlation functions of spins along the edge are obtained by taking the gapless Majorana edge modes into account. The model is also defined on the one-dimension ladder, in which case again the ground-state phase diagram has Z_2 trivial and non-trivial phases.

cond-mat.str-el↗

arXiv2010

Disordered topological quantum critical points in three-dimensional systems

Generic non-magnetic disorder effects onto those topological quantum critical points (TQCP), which intervene the three-dimensional topological insulator and an ordinary insulator, are investigated. We first show that, in such 3-d TQCP, any backward scattering process mediated by the chemical-potential-type impurity is always canceled by its time-reversal (T-reversal) counter-process, because of the non-trivial Berry phase supported by these two processes in the momentum space. However, this cancellation can be generalized into only those backward scattering processes which conserve a certain internal degree of freedom, i.e. the parity density, while the `absolute' stability of the TQCP against any non-magnetic disorders is required by the bulk-edge correspondence. Motivated by this, we further derive the self-consistent-Born phase diagram in the presence of generic non-magnetic disorder potentials and argue the behaviour of the quantum conductivity correction in such cases. The distinction and similarity between the case with only the chemical-potential-type disorder and that with the generic non-magnetic disorders are finally summarized.

cond-mat.mes-hall↗

arXiv2008

Derivation of Green's Function of Spin Calogero-Sutherland Model by Uglov's Method

Hole propagator of spin 1/2 Calogero-Sutherland model is derived using Uglov's method, which maps the exact eigenfunctions of the model, called Yangian Gelfand-Zetlin basis, to a limit of Macdonald polynomials (gl_2-Jack polynomials). To apply this mapping method to the calculation of 1-particle Green's function, we confirm that the sum of the field annihilation operator on Yangian Gelfand-Zetlin basis is transformed to the field annihilation operator on gl_2-Jack polynomials by the mapping. The resultant expression for hole propagator for finite-size system is written in terms of renormalized momenta and spin of quasi-holes and the expression in the thermodynamic limit coincides with the earlier result derived by another method. We also discuss the singularity of the spectral function for a specific coupling parameter where the hole propagator of spin Calogero-Sutherland model becomes equivalent to dynamical colour correlation function of SU(3) Haldane-Shastry model.

cond-mat.str-el↗