Quantum Thermal Hall Effect in a Time-Reversal-Symmetry-Broken Topological Superconductor in Two Dimensions : Approach From Bulk Calculations

TL;DR

This paper demonstrates that two-dimensional topological superconductors with broken time-reversal symmetry exhibit a half-quantized thermal Hall conductivity, derived from bulk calculations, linked to particle-hole symmetry and consistent with conformal field theory predictions.

Contribution

It provides a bulk calculation approach showing half-quantization of thermal Hall conductivity in 2D topological superconductors, without relying on edge state analysis.

Findings

Thermal Hall conductivity is quantized in half-integer multiples of a fundamental unit.

The half-quantization arises from the structure of the BdG Hamiltonian and particle-hole symmetry.

Results agree with conformal field theory predictions for Majorana edge states.

Abstract

We discuss thermal transport of two-dimensional topological superconductors (TSCs) with broken time reversal symmetry, which are described by Bogoliubov-de Gennes (BdG) Hamiltonians. From the calculations of bulk quantities only, without refereeing to Majorana edge states, we show that the thermal Hall conductivity of two-dimensional TSCs in the low-temperature limit is quantized in multiples of $1/2\frac{\pi T}{6}$, which is exactly one half of the value of quantization in the case of the integer quantum Hall effect, and that this exact half-quantization is caused by the structure of the Nambu spinor and the particle-hole symmetry, which BdG Hamiltonians generally have. In the case of spinless chiral p-wave superconductors, this result is in perfect agreement with the argument based on the Ising conformal field theory with the central charge $c=1/2$, which is an effective low-energy theory of the Majorana edge states.