Mechanisms of magnetoresistance in variable-range-hopping transport for two-dimensional electron systems

The temperature and magnetic-field dependencies of hopping transport in dilutely doped δ layers have been measured under the conditions for which the variable-range mechanism applies. We trace the transition from negative magnetoresistance in low fields to positive magnetoresistance in high fields. In the range of intermediate fields, the resistance in the perpendicular orientation appears to be several times less than that in the parallel one. It is shown that this ‘‘inverted’’ relation cannot be accounted for in terms of the interference of alternative hopping paths alone. We note also a distinct nonmonotonic variation of the resistance with magnetic field in the perpendicular orientation. The results are explained by considering both the interference of alternative hopping paths and the influence of a magnetic field on the density of states at the Fermi level, which defines the magnitude of Mott’s ${\mathit{T}}_0$ parameter in variable-range hopping.