Observation of a nondivergent Hall coefficient for a localized two-dimensional electron gas

Abstract

We have studied the Hall coefficient for a two-dimensional electron gas in a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterojunction characterized by variable range hopping. We find the value of the Hall coefficient remains approximately classical, ${\mathit{R}}_{\mathit{H}}$=1/nec, for diverging longitudinal resistivity over a broad range of localization strength. The results show the behavior of a recently proposed Hall insulator in which ${\mathrm{\ensuremath{\sigma}}}_{\mathit{x}\mathit{x}}$\ensuremath{\rightarrow}0, ${\mathrm{\ensuremath{\sigma}}}_{\mathit{x}\mathit{y}}$\ensuremath{\rightarrow}0, and ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{x}}$\ensuremath{\rightarrow}\ensuremath{\infty} but ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{y}}$\ensuremath{\rightarrow}const for T\ensuremath{\rightarrow}0.