### 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 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 language | English (US) |
---|---|

Pages (from-to) | 871-883 |

Number of pages | 13 |

Journal | Comptes Rendus Physique |

Volume | 14 |

Issue number | 9-10 |

DOIs | |

State | Published - Nov 1 2013 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Comptes Rendus Physique*,

*14*(9-10), 871-883. https://doi.org/10.1016/j.crhy.2013.03.002

**Electromagnetic and thermal responses in topological matter : Topological terms, quantum anomalies and D-branes.** / Furusaki, Akira; Nagaosa, Naoto; Nomura, Kentaro; Ryu, Shinsei; Takayanagi, Tadashi.

Research output: Contribution to journal › Short survey

*Comptes Rendus Physique*, vol. 14, no. 9-10, pp. 871-883. https://doi.org/10.1016/j.crhy.2013.03.002

}

TY - JOUR

T1 - Electromagnetic and thermal responses in topological matter

T2 - Topological terms, quantum anomalies and D-branes

AU - Furusaki, Akira

AU - Nagaosa, Naoto

AU - Nomura, Kentaro

AU - Ryu, Shinsei

AU - Takayanagi, Tadashi

PY - 2013/11/1

Y1 - 2013/11/1

N2 - 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.

AB - 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.

KW - Brane theory

KW - Electromagnetic response

KW - Quantum anomaly

KW - Thermal response

KW - Topological classification

UR - http://www.scopus.com/inward/record.url?scp=84889578790&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84889578790&partnerID=8YFLogxK

U2 - 10.1016/j.crhy.2013.03.002

DO - 10.1016/j.crhy.2013.03.002

M3 - Short survey

VL - 14

SP - 871

EP - 883

JO - Comptes Rendus Physique

JF - Comptes Rendus Physique

SN - 1631-0705

IS - 9-10

ER -