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arXiv:1705.04394

Topological response of gapped fermions to a $\text{U}(1)$ Gauge field

Bruno Mera

Published May 11, 2017• 4 citations
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Abstract

We present a detailed path integral derivation of the topological response of gapped free fermions, in $2+1$ dimensions, to an external $\text{U}(1)$ Gauge field. The well-known Hall response is obtained by identifying the Chern-Simons term in the effective action with the correct coefficient. We extend the result to $2d+1$ dimensions in which the response is associated to a Chern-Simons term with a coefficient related to a characteristic class coming from topological band theory. We comment on the bulk-to-boundary principle which arises naturally when one considers the theory on a manifold with boundary.

DOI
10.48550/arxiv.1705.04394

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