HALL RESISTANCE IN THE HOPPING REGIME - A HALL INSULATOR

The Hall conductivity and resistivity of strongly localized electrons at low temperatures and small magnetic fields are obtained. The result s 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 --> 0. However, when th e Hall resistivity is derived from the conductivity, the resulting tem perature dependence is sensitive to the disorder configuration, and th e Hall resistivity may approach a constant value as T --> 0. This is t he Hall insulating behavior. It is argued that for strictly de conditi ons the transport quantity that should be averaged is the resistivity, and this shows no Hall insulating behavior.