Electromagnetic and thermal responses in topological matter: topological terms, quantum anomalies and D-branes

TL;DR

This paper explores the electromagnetic and thermal responses in topological matter, linking topological insulators and superconductors to string theory D-branes, and generalizing response formulas to include thermal effects.

Contribution

It introduces a unified framework connecting topological responses in condensed matter with string theory D-branes, extending topological invariants to thermal and gravitational contexts.

Findings

Generalized Strěda formula to thermal Hall conductivity

Predicted cross-correlated responses in topological superconductors

Linked topological invariants to D-brane charges in string theory

Abstract

We discuss the thermal (or gravitational) responses in topological superconductors and in topological phases in general. Such thermal responses (as well as electromagnetic responses for conserved charge) provide a definition of topological insulators and superconductors beyond the single-particle picture. In two-dimensional topological phases, 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 angular momentum and thermal polarization (entropy polarization). We also discuss a use of D-branes in string theory as a systematic tool to derive all such topological terms and topological responses. In particular, we relate the $\mathbb{Z}_2$ index of topological insulators introduced by Kane and Mele (and its generalization to other symmetry classes and to arbitrary dimensions) to the K-theory charge of non-BPS D-branes, and vice versa. We thus establish a link between the stability of non-BPS D-branes and the topological stability of topological insulators.