Anomalous Hall effect in disordered Weyl semimetals

TL;DR

This paper investigates the anomalous Hall effect in disordered Weyl semimetals, distinguishing intrinsic and extrinsic contributions, and analyzing how impurity scattering influences Hall resistivity and its temperature dependence.

Contribution

It provides a detailed theoretical analysis of extrinsic Hall effects in Weyl semimetals, expressing skew scattering in terms of phase shifts and identifying regimes where it dominates.

Findings

Skew scattering dominates in strong or resonant impurity regimes.

Hall resistivity scales as T^2 at low temperatures.

Hall resistivity scales as T^{3/2} at high temperatures.

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.