Simple mechanism that breaks the Hall effect linearity at low temperatures

TL;DR

This paper demonstrates that weak localization and antilocalization effects in inhomogeneous systems cause deviations from the expected linear Hall resistance at low temperatures, contrasting with uniform media where linearity persists.

Contribution

It introduces a mean-field model to show how inhomogeneities lead to non-linear Hall resistance, providing a new understanding of low-temperature Hall effect behavior.

Findings

Weak localization/antilocalization cause non-linearity in inhomogeneous media.

In uniform media, Hall resistance remains linear at low temperatures.

The model predicts observable deviations in experimental measurements.

Abstract

Hall resistance $R_{\textrm{xy}}$ is commonly suggested to be linear-in-magnetic-field $B$, provided the field is small. We argue here that at low temperatures this linearity is broken due to weak localization/antilocalization phenomena in inhomogeneous systems, while in a uniform medium these effects do not affect the linear field dependence of $R_{\textrm{xy}}(B)$. We calculate the Hall resistance for different two-component media using a mean-field approach and show that this non-linearity is experimentally observable.