Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
By S. Ryu, J. Moore, A. Ludwig. 2010
213 citations recorded by the source corpus.
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 find, 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 governed 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 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.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/07d08584c15c2944250036d5aacfb15c672bea0e
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions (2017, background): “However, the boundary theories of different SPT states have different ’t Hooft anomalies in the global symmetry G [24–27].”
- Fermion Path Integrals And Topological Phases (2015, background): “Several results in this direction were obtained previously in [9], where it was conjectured – correctly, as will become clear – that a fuller picture would result from consideration of global anomalies.”
- Parity-violating hydrodynamics in 2 + 1 dimensions (2011, background): “Equilibrium states in the presence of gravitomagnetic fields were considered previously in [15].”