Electron glass in a three-dimensional system

We report on nonequilibrium transport features observed in experiments using three-dimensional amorphous indium-oxide films. It is demonstrated that all the features that characterize intrinsic electron glasses which heretofore were seen in two-dimensional samples are also observed in field-effect measurements of systems that exhibit three-dimensional variable range hopping. In particular, a memory dip is observed in samples configured with gate. The memory-dipwidth and magnitude support models that associate the phenomenon with the Coulomb gap. The memory dip and the glassy effects disappear once the quenched disorder in the system is reduced and the system becomes diffusive. This happens when the Ioffe-Regel dimensional parameter k(F)l exceeds approximate to 0.3, which is the critical value for the metal-to-insulator transition in all versions of the amorphous indium oxides [Phys. Rev. B 86, 165101 (2012)]. This confirms that being in the Anderson localized phase is a prerequisite for observing the memory dip and the associated glassy effects. The results of the gating experiments suggest that the out-of-equilibrium effect caused by inserted charge extends over spatial scales considerably larger than the screening length.