Nonlinear dc conductivity in disordered metals near the metal-insulator transition

Abstract

A detailed study of the nonlinear dc conductivity of two disordered alloys, ${\mathrm{Ge}}_{\mathrm{x}}$${\mathrm{Au}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ and ${\mathrm{C}}_{\mathrm{x}}$${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$, is carried out near their metal-insulator transition for electric fields up to 500 V/m at 1.3 K <T<4.2 K and, for ${\mathrm{C}}_{\mathrm{x}}$${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$, down to 15 mK. Analysis of the \ensuremath{\sigma}(E) data in the context of an electron-gas-heating model yields unexpectedly long electron-phonon relaxation times. Above 1 K the hot-electron model is not sufficient to explain these results. We propose that the electric field also acts directly on the localizing electrons, which leads to an ${E}^{1/3}$ dependence of the conductivity.