Temperature Dependence of the Anomalous Hall Effect from Electron Interactions

TL;DR

This paper investigates how electron-electron interactions influence the temperature dependence of the anomalous Hall effect in disordered conductors, revealing specific asymptotic behaviors in different dimensions.

Contribution

It provides a microscopic analysis showing the significant role of electron interactions in the anomalous Hall effect's temperature dependence, including in non-superconducting materials.

Findings

Low-temperature dependence in 3D: $rac{ ext{constant} imes \

Low-temperature dependence in 2D: $ ext{log}[ ext{log}(T_0/T)]$

Potential explanation for unconventional temperature dependence observed in HgCr$_2$Se$_4$

Abstract

We consider the impact of electron-electron interactions on the temperature dependence of the anomalous Hall effect in disordered conductors. The microscopic analysis is carried out within the diagrammatic approach of the linear response Kubo-Streda formula with an account of both extrinsic skew-scattering and side-jump mechanisms of the anomalous Hall effect arising in the presence of spin-orbit coupling. We demonstrate the importance of electron interactions in the Cooper channel even for nominally non-superconducting materials and find that the corresponding low-temperature dependence of the anomalous Hall conductivity is asymptotically of the form $\sqrt{T}/\ln(T_0/T)$ in three dimensions and $\ln[\ln(T_0/T)]$ in two dimensions, where the scale of $T_0$ is parametrically of the order of Fermi energy. These results, in particular, may provide an explanation for the recently observed unconventional temperature dependence of the anomalous Hall effect in HgCr$_2$Se$_4$.