Topological response in Weyl semimetals and the chiral anomaly

We demonstrate that topological transport phenomena, characteristic of Weyl semimetals, namely the semiquantized 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, for example, 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.

Figure 1

Landau level dispersion for $b\ne 0$ (top) and $b=0$ (bottom) cases. It is clear that in the $b\ne 0$ case there is an extra field-dependent electron density in the $n=0$ Landau level, given by Eq. (62).