Magnetoconductance measurements in the variable-range-hopping regime

Magnetoconductance measurements in the strongly localized regime have been made on a thin 119-Å granular ${\mathrm{In}}_2$ ${\mathrm{O}}_{3\mathrm{-}\mathrm{x}}$ film which exhibited variable-range hopping in its resistance. Some of the predictions suggested by Sivan, Entin-Wohlman, and Imry where observed in the magnetoconductance (MC) data including the $B^2$ dependence of the MC in low magnetic fields and the positive sign of the MC at higher fields. However, there was no tendency for the MC to saturate at higher fields, nor did the MC take on negative values in the more weakly disordered films. Our MC data were in conflict with Faran and Ovadyahu’s observations of a $T^{\mathrm{-}1}$ dependence of the MC. Electron-electron interaction effects dominated the electronic transport properties in the liquid-helium temperature range.