Disorder-induced modulation of the nonlinear Hall effect in Weyl semimetals

Abstract

We study the effects of impurity scattering on the nonlinear Hall response of Weyl semimetals within the semiclassical Boltzmann approach. We derive the rectified and second-harmonic conductivity tensors for a general momentum-dependent transport relaxation time and evaluate this quantity microscopically for short-range, Gaussian, screened Coulomb, and magnetic impurities. For scalar disorder, the relaxation time is isotropic and chirality independent. The nonlinear Hall response is then determined by the anomalous velocity associated with the Berry curvature, and a finite net response requires energetically inequivalent Weyl nodes to avoid cancellation between opposite chiralities. Polarized magnetic impurities lead to a qualitatively different behavior. We find that interference between the first- and second-order Born amplitudes generates a helicity-dependent anisotropic correction to the relaxation time. This anisotropy changes the tensor structure of the nonlinear Hall conductivity and gives rise to a finite second-harmonic current for suitable orientations of the electric field relative to the impurity polarization. For representative parameters, however, the anisotropic contribution is several orders of magnitude smaller than the dominant isotropic response. These results establish how the microscopic form of impurity scattering enters the nonlinear Hall response of Weyl semimetals through the transport relaxation time.