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

Two dimensional topological superconductors with chiral edge modes are predicted to posses a quantized thermal Hall effect, exactly half that for chiral topological insulators, which is proportional to the Chern number. However not much work has been done in identifying this in the standard models in the literature. Here we introduce a model based on a proximity induced superconducting Bismuth bilayer, to directly calculate the thermal Hall conductance based on the 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.