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

Akira Furusaki, Naoto Nagaosa, Kentaro Nomura, Shinsei Ryu, Tadashi Takayanagi

Research output: Contribution to journalShort surveypeer-review

18 Scopus citations


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 Z2 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.

Original languageEnglish (US)
Pages (from-to)871-883
Number of pages13
JournalComptes Rendus Physique
Issue number9-10
StatePublished - Nov 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


  • Brane theory
  • Electromagnetic response
  • Quantum anomaly
  • Thermal response
  • Topological classification


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