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.
Related
- Bipolarized Weyl semimetals and quantum crystal valley Hall effect in two-dimensional altermagnetic materials
- Valley Berry curvature dipole induced nonlinear valley Hall effect
- Anomalous Hall Response Induced by Correlated Disorder in the Breathing Kagome Lattice Mn3Sn
- Helicity-engineered nonlinear optical responses in photo-excited topological semimetals
- Linear and nonlinear transport responses of topological nodal-line semimetals
BibTeX
@misc{canas2026disorderinduced,
title = {{Disorder-induced modulation of the nonlinear Hall effect in Weyl semimetals}},
author = {Juan A. Cañas and Daniel A. Bonilla and A. Martín-Ruiz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20471},
eprint = {2609.20471},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20471},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Disorder-induced modulation of the nonlinear Hall effect in Weyl semimetals
AU - Juan A. Cañas
AU - Daniel A. Bonilla
AU - A. Martín-Ruiz
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20471
UR - https://arxiv.org/abs/2609.20471
AB - 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.
ER -