2010/10/31 by Shinsei Ryu, Joel E. Moore, Andreas W. W. Ludwig · 312 citations
Physics and Astronomy · #Atomic and Subatomic Physics Research #Condensed matter physics #Geometry #Gravitation #Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Superconductivity #Symmetry (geometry) #Topological Materials and Phenomena #Topological insulator #Topology (electrical circuits) #cond-mat.str-el #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.85.045104
published in Physical Review B 85(4) (American Physical Society) · 16 pages, 2 figures
openalex publication_date 2012/01/05 · arxiv created 2012/06/12 · arxiv updated 2012/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
One of the defining properties of the conventional three-dimensional (``ℤ2'' or ``spin-orbit'') topological insulator is its characteristic magnetoelectric effect, as described by axion electrodynamics. In this paper, we discuss an analog of such a magnetoelectric effect in the thermal (or gravitational) and magnetic dipole responses in all symmetry classes that admit topologically nontrivial insulators or superconductors to exist in three dimensions. In particular, for topological superconductors (or superfluids) with time-reversal symmetry, which lack SU(2) spin rotation symmetry (e.g., due to spin-orbit interactions), such as the B phase of 3He, the thermal response is the only probe that can detect the nontrivial topological character through transport. We show that, for such topological superconductors, applying a temperature gradient produces a thermal- (or mass-) surface current perpendicular to the thermal gradient. Such charge, thermal, or magnetic dipole responses provide a definition of topological insulators and superconductors beyond the single-particle picture. Moreover, we find, for a significant part of the ``tenfold'' list of topological insulators found in previous work in the absence of interactions, that in general dimensions, the effective field theory describing the space-time responses is governed by a field theory anomaly. Since anomalies are known to be insensitive to whether the underlying fermions are interacting, this shows that the classification of these topological insulators is robust to adiabatic deformations by interparticle interactions in general dimensionality. In particular, this applies to symmetry classes DIII, CI, and AIII in three spatial dimensions, and to symmetry classes D and C in two spatial dimensions.