TY - JOUR

T1 - Finite-temperature effective boundary theory of the quantized thermal Hall effect

AU - Nakai, Ryota

AU - Ryu, Shinsei

AU - Nomura, Kentaro

N1 - Publisher Copyright:
© 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

PY - 2016/2/10

Y1 - 2016/2/10

N2 - 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 Strěda 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.

AB - 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 Strěda 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.

KW - effective field theory

KW - gravitational response

KW - thermal Hall effect

KW - topological insulators

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U2 - 10.1088/1367-2630/18/2/023038

DO - 10.1088/1367-2630/18/2/023038

M3 - Article

AN - SCOPUS:84960145843

VL - 18

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 2

M1 - 023038

ER -