Ryota Nakai

Laughlin's argument for the quantized thermal Hall effect

We extend Laughlins magnetic-flux-threading argument to the quantized thermal Hall effect. A proper analogue of Laughlins 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.

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

A finite-temperature effective free energy of a quantized thermal Hall system is derived microscopically from the 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 Str\v{e}da formula. In this paper, we consider the two-dimensional Dirac fermion under a static background gravitational field in equilibrium at a finite temperature, and derive microscopically an effective free energy functional of the gravitational field of a Lorentz invariant system by tracing out the Dirac fermionic degrees of freedom. The bulk effective theory is consistently determined via the boundary effective theory of the chiral boundary mode. This bulk effective free energy generates an energy current flowing perpendicular and proportional to the gradient of the gravitational potential, which turns out to represent the quantized thermal Hall effect using Luttingers argument.

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 the spin and orbital parts 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

Particle propagator of the spin Calogero–Sutherland model

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Derivation of Green's function of a spin Calogero–Sutherland model by Uglov's method

factors for conduction and valence energy bands. The crossed susceptibility in two-dimensional quantum spin Hall insulators shows a quantized signature of the

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

{\mathbb{Z}}_{2}

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

topological phase in response to Zeeman coupling via an averaged

Disordered topological quantum critical points in three-dimensional systems

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Quantization of the heat polarization in twisted spacetime

factor, and the quantization persists even when

Effective boundary theory of the quantized thermal Hall effect

{\ensuremath{\sigma}}^{z}