Hall Resistance in the Hopping Regime: A "Hall Insulator"?

Abstract

The Hall conductivity and resistivity of strongly localized electrons at low temperatures and small magnetic fields are obtained. The results depend on whether one uses the conductivity or resistivity tensor to obtain the macroscopic Hall resistivity. In the second case the Hall resistivity always diverges exponentially as $T\to 0$. However, when the Hall resistivity is derived from the conductivity, the resulting temperature dependence is sensitive to the disorder configuration, and 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, and this shows no Hall insulating behavior.