The Hall effect and localized transport

Historically, in measurements of electron transport in disordered two-dimensional systems, an Arrhenius Hall carrier density has never been observed alongside an Arrhenius conductivity, when the Fermi level is below a mobility edge. This has long been an issue with respect to claiming observation of transport via activation to a mobility edge. In this work, an Arrhenius conductivity and Arrhenius Hall carrier density have been observed alongside one another in such a system. Measurements were made of a two-dimensional electron gas hosted in a gated GaAs/Al0.33Ga0.67As heterostructure. Furthermore, in the regime of Arrhenius conductivity and Arrhenius carrier density, the mobility is shown to be independent of the position of the Fermi level below the mobility edge. A transition between carrier density and mobility dominating the resistivity temperature dependence has been observed, as the Fermi level is varied.