Topological response in Weyl semimetals and the chiral anomaly

TL;DR

This paper explains how topological transport effects in Weyl semimetals, such as the anomalous Hall and chiral magnetic effects, are unified under the concept of the chiral anomaly, described by a space-time dependent theta-term.

Contribution

It introduces a unified topological framework for Weyl semimetals' responses using a dynamic theta-term that persists despite symmetry-breaking perturbations.

Findings

Topological responses are described by a space-time dependent theta-term.

The theta-term accounts for both anomalous Hall and chiral magnetic effects.

These effects survive weak symmetry-breaking perturbations.

Abstract

We demonstrate that topological transport phenomena, characteristic of Weyl semimetals, namely the semi-quantized anomalous Hall effect and the chiral magnetic effect (equilibrium magnetic-field-driven current), may be thought of as two distinct manifestations of the same underlying phenomenon, the chiral anomaly. We show that the topological response in Weyl semimetals is fully described by a $\theta$-term in the action for the electromagnetic field, where $\theta$ is not a constant parameter, like e.g. in topological insulators, but is a field, which has a linear dependence on the space-time coordinates. We also show that the $\theta$-term and the corresponding topological response survive for sufficiently weak translational symmetry breaking perturbations, which open a gap in the spectrum of the Weyl semimetal, eliminating the Weyl nodes.