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

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

doi:10.1016/j.crhy.2013.03.002

Topological insulators/Isolants topologiques

Electromagnetic and thermal responses in topological matter: Topological terms, quantum anomalies and D-branes
[Réponses électromagnétiques et thermiques dans la matière topologique : Termes topologiques, anomalies quantiques et D-branes]

Akira Furusaki ^1,² ; Naoto Nagaosa ^2,³ ; Kentaro Nomura ⁴ ; Shinsei Ryu ⁵ ; Tadashi Takayanagi ^6,⁷

¹ Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama 351-0198, Japan
² RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
³ Department of Applied Physics, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
⁴ Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
⁵ Department of Physics, University of Illinois, 1110 West Green St, Urbana, IL 61801, United States
⁶ Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
⁷ Institute for the Physics and Mathematics of the Universe (IPMU), The University of Tokyo, Kashiwa, Chiba 277-8582, Japan

Comptes Rendus. Physique, Volume 14 (2013) no. 9-10, pp. 871-883.

Résumé
Abstract

Nous traitons des réponses thermiques (ou gravitationnelles) des supraconducteurs topologiques et, plus généralement, des phases topologiques. Ces réponses thermiques (tout comme les réponses électromagnétiques pour la charge électrique conservée) fournissent une définition des isolants et supraconducteurs topologiques, qui reste valable au-delà du modèle à une particule. Pour les phases bidimensionnelles, la formule de Streda de la conductivité de Hall de charge est généralisée à la conductivité de Hall thermique. Appliquée aux états de surface de Majorana des supraconducteurs topologiques, cette formule conduit à des fonctions de réponse croisées entre le moment angulaire et la polarisation thermique. Nous discutons également de la théorie des cordes (D-branes) comme outil systématique pour obtenir ces réponses topologiques. En particulier, nous relions lʼinvariant topologique $Z_{2}$ des isolants topologiques introduit par Kane et Mele (ainsi que ses généralisations à dʼautres classes de symétrie en dimensions arbitraires) à la charge de certaines D-branes (celles qui ne saturent pas la limite de Bogomolʼnyi–Prasad–Sommerfield), et vice versa. Nous établissons ainsi un lien entre la stabilité de ces D-branes et celle des isolants topologiques.

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 $Z_{2}$ 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.

Publié le : 2013-05-02

DOI : 10.1016/j.crhy.2013.03.002

Keywords: Electromagnetic response, Thermal response, Topological classification, Quantum anomaly, Brane theory
Mot clés : Réponse électromagnétique, Réponse thermique, Classification topologique, Anomalie quantique, Théorie des branes

Affiliations des auteurs :

Akira Furusaki ^{1, 2} ; Naoto Nagaosa ^{2, 3} ; Kentaro Nomura ⁴ ; Shinsei Ryu ⁵ ; Tadashi Takayanagi ^{6, 7}

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     title = {Electromagnetic and thermal responses in topological matter: {Topological} terms, quantum anomalies and {D-branes}},
     journal = {Comptes Rendus. Physique},
     pages = {871--883},
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     year = {2013},
     doi = {10.1016/j.crhy.2013.03.002},
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Akira Furusaki; Naoto Nagaosa; Kentaro Nomura; Shinsei Ryu; Tadashi Takayanagi. Electromagnetic and thermal responses in topological matter: Topological terms, quantum anomalies and D-branes. Comptes Rendus. Physique, Volume 14 (2013) no. 9-10, pp. 871-883. doi : 10.1016/j.crhy.2013.03.002. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2013.03.002/

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