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

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.

16 pages, 2 figures; Submitted to a topical issue of the Comptes Rendus de l Academie des Sciences (CRAS)

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Cited by in corpus (20)

• Classification of topological quantum matter with symmetries
• Chiral anomaly and transport in Weyl metals
• Negative longitudinal magnetoresistance in Dirac and Weyl metals
• Anyon condensation and its applications
• Higher Dimensional Quantum Hall Effect as A-Class Topological Insulator
• Density response in Weyl metals
• Mirror Anomaly in Dirac Semimetals
• Chern-Simons Theory and Wilson Loops in the Brillouin Zone
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Altermagnetism-Induced Parity Anomaly in Weak Topological Insulators
• Hamiltonian approach to the torsional anomalies and its dimensional ladder
• Fermionic currents in topologically nontrivial braneworlds
• Quarter-quantized thermal Hall effect with parity anomaly
• Band spectrum is D-brane
• Axion gravitodynamics, Lense-Thirring effect, and gravitational waves
• Gravitational waves propagation in nondynamical Chern-Simons gravity
• Conformal energy currents on the edge of a topological superconductor
• Index of Dirac operators and classification of topological insulators
• Extended Dynamical Symmetries of Landau Levels in Higher Dimensions
• Quantum-geometric thermal conductivity of superconductors