Anomalous Hall effect in disordered Weyl semimetals

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 ${\ensuremath{\rho}}_{xy}$ is expressed in terms of two scattering phases, analogous to the $s$-wave scattering phase in a nontopological metal. We compute the dependence of ${\ensuremath{\rho}}_{xy}$ on the chemical potential and show that ${\ensuremath{\rho}}_{xy}$ scales with temperature as ${T}^{2}$ in low temperatures and as ${T}^{3/2}$ in the high-temperature limit.