Role of Disorder in Third-order Anomalous Hall Effect in Time-reversal Symmetric Systems

TL;DR

This paper explores how impurity scattering influences the third-order anomalous Hall effect in Dirac materials, highlighting the roles of intrinsic and extrinsic contributions and their dependence on disorder and Fermi surface properties.

Contribution

It provides a theoretical analysis of disorder effects on TOAHE using semiclassical Boltzmann theory and a Dirac model, revealing new insights into extrinsic mechanisms like skew-scattering and side-jump.

Findings

Disorder affects TOAHE through skew-scattering and side-jump mechanisms.

Intrinsic and extrinsic contributions have distinct dependencies on disorder.

Fermi surface anisotropy influences the magnitude of the effect.

Abstract

The third-order anomalous Hall effect (TOAHE) driven by Berry connection polarizability in Dirac materials offers a promising avenue for exploring quantum geometric phenomena. We investigate the role of impurity scattering on TOAHE using the semiclassical Boltzmann framework, via a comparison of the intrinsic contributions (stemming from the Berry connection polarizability) with the extrinsic contributions caused by the disorder. To validate our theoretical findings, we employ a generalized two-dimensional low-energy Dirac model to analytically assess the intrinsic and extrinsic contributions to the TOAHE. Our analysis reveals distinct disorder-mediated effects, including skew-scattering and side-jump contributions. We also elucidate their intriguing dependencies on Fermi surface anisotropy and discuss opportunities for experimental exploration.