Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors

Details Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors

2010-10-05

arxiv.org/abs/1010.0936v1

Physics

Condensed Matter

Strongly Correlated Electrons

15 pages, 2 figures

Scientific paper

One of the defining properties of the conventional three-dimensional ("$\mathbb{Z}_2$-", or "spin-orbit"-) topological insulator is its characteristic magnetoelectric effect, as described by axion electrodynamics. In this paper, we discuss an analogue of such a magnetoelectric effect in the thermal (or gravitational) and the magnetic dipole responses in all symmetry classes which admit topologically non-trivial 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 $^3$He, the thermal response is the only probe which can detect the non-trivial 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 show, for a significant part of the `ten-fold' 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 described by a field theory anomaly. Since anomalies are known to be insensitive to whether the underlying fermions are interacting or not, this shows that the classification of these topological insulators is robust to interparticle interactions in general dimensionality. This includes symmetry classes DIII, CI, and AIII in three spatial dimensions, and symmetry classes D and C in two spatial dimensions.

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