Transition to exponential relaxation in weakly disordered electron glasses

The out-of-equilibrium excess conductance of electron-glasses ΔG(t) typically relaxes with a logarithmic time dependence. Here it is shown that the log(t) relaxation of a weakly disordered InxO film crosses over asymptotically to an exponential dependence ΔG(t)exp{-[t/τ]}. This allows for assigning a well-defined relaxation-time τ(a) for a given system disorder (characterized by the Ioffe-Regel parameter kF). Near the metal-insulator transition, τ(a) obeys the scaling relation τ() [(kF)C-kF] with the same critical disorder (kF)C where the zero-temperature conductivity of this system vanishes. The latter defines the position of the disorder-driven metal-to-insulator transition which is a quantum-phase transition. In this regard the electron glass differs from classical glasses, such as the structural glass and spin glass. The ability to experimentally assign an unambiguous relaxation time allows us to demonstrate the steep dependence of the electron-glass dynamics on carrier concentration.