Cross-Correlated Responses of Topological Superconductors and Superfluids

TL;DR

This paper investigates the unique thermal and rotational responses of topological superconductors and superfluids, revealing cross-correlated effects and extending the understanding of their electromagnetic and gravitational analogies.

Contribution

It generalizes the Strěda formula to thermal Hall conductivity and predicts novel cross-correlated responses in 3D topological superconductors and superfluids.

Findings

Generalized Strěda formula for thermal Hall conductivity

Predicted cross-correlation between angular momentum and entropy polarization

Linked results to gravitoelectromagnetism and topological magnetoelectric effects

Abstract

We study nontrivial responses of topological superconductors and superfluids to the temperature gradient and rotation of the system. In two-dimensional gapped systems, the Str\v{e}da formula for the electric Hall conductivity is generalized to the thermal Hall conductivity. Applying this formula to the Majorana surface states of three-dimensional topological superconductors predicts cross-correlated responses between the orbital angular momentum and thermal polarization (entropy polarization). These results can be naturally related to the gravitoelectromagnetism description of three-dimensional topological superconductors and superfluids, analogous to the topological magnetoelectric effect in ${\mathbb{Z}}_2$ topological insulators.