Hall resistance in the hopping regime, a "Hall Insulator"?

TL;DR

This paper investigates the Hall effect in strongly localized electrons, revealing that the macroscopic Hall resistivity can diverge or approach a constant at low temperatures depending on the averaging method, indicating a Hall insulator phase.

Contribution

It clarifies how different averaging procedures affect the observed Hall resistivity in the hopping regime, introducing the concept of a Hall insulator.

Findings

Hall resistivity diverges when averaged via conductivity

Hall resistivity approaches a constant at low T when averaged via resistivity

Transport quantity to average is resistivity under dc conditions

Abstract

The Hall conductivity and resistivity of strongly localized electrons at low temperatures and at small magnetic fields are obtained. It is found that the results depend on whether the conductivity or the resistivity tensors are averaged to obtain the macroscopic Hall resistivity. In the second case the Hall resistivity always {\it diverges} exponentially as the temperature tends to zero. But when the Hall resistivity is derived from the averaged conductivity, the resulting temperature dependence is sensitive to the disorder configuration. Then the Hall resistivity may approach a constant value as $T\to 0$. This is the Hall insulating behavior. It is argued that for strictly dc conditions, the transport quantity that should be averaged is the resistivity.