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arXiv · 1211.0533

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

Akira Furusaki·Naoto Nagaosa·Kentaro Nomura·Shinsei Ryu·Tadashi Takayanagi
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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 Strěda 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.

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Akira Furusaki, Naoto Nagaosa, Kentaro Nomura, Shinsei Ryu, Tadashi Takayanagi. 2012-11-02. Electromagnetic and thermal responses in topological matter: topological terms, quantum anomalies and D-branes. https://doi.org/10.1016/j.crhy.2013.03.002

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