Quantized Thermal Hall Conductance and the Topological Phase Diagram of a Superconducting Bismuth Bilayer

TL;DR

This paper models a superconducting Bismuth bilayer to calculate its thermal Hall conductance, demonstrating quantized plateaus in various topological phases and establishing a method to map topological phase diagrams from heat conductance data.

Contribution

It introduces a lattice model of a topological superconductor based on Bismuth bilayer and demonstrates a real-space technique to identify topological phases via thermal Hall conductance.

Findings

Quantized thermal Hall plateaus observed in multiple topological phases

Thermal Hall conductance correlates with Chern number and parity invariant

Method enables phase diagram mapping from heat conductance in real space

Abstract

Two dimensional topological superconductors with chiral edge modes are predicted to posses a quantized thermal Hall effect proportional to the Chern number, exactly half that for chiral topological insulators. However not much work has been done in identifying the quantized heat conductance in the literature, even for some of the standard models of topological superconductivity. Here we introduce a model based on a proximity induced superconducting Bismuth bilayer, and directly calculate the thermal Hall conductance of this lattice model. This model serves as a demonstration of the state of the art possible in such a calculation, as well as introducing an interesting paradigmatic topological superconductor with a rich phase diagram. We demonstrate the quantized thermal Hall plateaus in several different topological phases, and compare this to numerical calculations of the Chern number, as well as analytical calculations of the Chern number's parity invariant. We demonstrate that it is possible to get a reasonable topological phase diagram from the quantized thermal Hall calculations. The technique used can be applied to wide range of models directly in real space.