Anomalous Hall effect in disordered Weyl semimetals

Abstract

We study the anomalous Hall effect in a disordered Weyl semimetal. While the intrinsic contribution is expressed solely in terms of Berry curvature, the extrinsic contribution is given by a combination of the skew scattering and side jump terms. For the model of small size impurities, we are able to express the skew scattering contribution in terms of scattering phase shifts. We identify the regime in which the skew scattering contribution dominates the side-jump contribution: the impurities are either strong or resonant, and at dilute concentration. In this regime, the Hall resistivity $\rho_{xy}$ is expressed in terms of two scattering phases, analogous to the s-wave scattering phase in a non-topological metal. We compute the dependence of $\rho_{xy}$ on the chemical potential, and show that $\rho_{xy}$ scales with temperature as $T^2$ in low temperatures and as $T^{3/2}$ in the high temperature limit.