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arXiv · 1407.7043

Torsion, Parity-odd Response and Anomalies in Topological States

Onkar Parrikar·Taylor L. Hughes·Robert G. Leigh
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Abstract

We study the response of a class of topological systems to electromagnetic and gravitational sources, including torsion and curvature. By using the technology of anomaly polynomials, we derive the parity-odd response of a massive Dirac fermion in $d=2+1$ and $d=4+1$, which provides a simple model for a topological insulator. We discuss the covariant anomalies of the corresponding edge states, from a Callan-Harvey anomaly-inflow, as well as a Hamiltonian spectral flow point of view. We also discuss the applicability of our results to other systems such as Weyl semi-metals. Finally, using dimensional reduction from $d=4+1$, we derive the effective action for a $d=3+1$ time-reversal invariant topological insulator in the presence of torsion and curvature, and discuss its various physical consequences.

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Onkar Parrikar, Taylor L. Hughes, Robert G. Leigh. 2014-07-25. Torsion, Parity-odd Response and Anomalies in Topological States. https://doi.org/10.1103/physrevd.90.105004

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