Disorder in the non-linear anomalous Hall effect of $\mathcal{P}\mathcal{T}$-symmetric Dirac fermions

TL;DR

This paper demonstrates that disorder significantly influences the non-linear anomalous Hall effect in $ ext{PT}$-symmetric Dirac fermions, often surpassing intrinsic contributions, and highlights the importance of extrinsic mechanisms in experimental observations.

Contribution

It reveals that disorder effects dominate the non-linear anomalous Hall effect in $ ext{PT}$-symmetric systems, challenging the previous focus on intrinsic mechanisms.

Findings

Disorder contributions can overshadow intrinsic effects in NLAHE.

Berry curvature dipole, skew scattering, and side-jump are key extrinsic terms.

NLAHE at realistic densities is likely dominated by extrinsic disorder effects.

Abstract

The study of the non-linear anomalous Hall effect (NLAHE) in $\mathcal{P}\mathcal{T}$-symmetric systems has focussed on intrinsic mechanisms. Here we show that disorder contributes substantially to NLAHE and often overwhelms intrinsic terms. We identify terms to zeroth order in the disorder strength involving the Berry curvature dipole, skew scattering and side-jump, all exhibiting a strong peak as a function of the Fermi energy, a signature of interband coherence. Our results suggest NLAHE at experimentally relevant transport densities in $\mathcal{P}\mathcal{T}$-symmetric systems is likely to be extrinsic.