Dynamical Properties near the Metal-Insulator Transition: Evidence for Electron-Assisted Variable Range Hopping

We report independent measurements (between 20 and 200 mK) of the electronic specific heat $C_e$, the electron-phonon coupling $G_{e-\mathrm{ph}}$, and the electron-phonon relaxation time ${\tau }_{e-\mathrm{ph}}$ (from ${10}^{-2\mathrm{}}$ to ${10}^{-5\mathrm{}}\mathrm{s}$) for ${\mathrm{Nb}}_x{\mathrm{Si}}_{1-x}$ Anderson insulator thin films. We show that the usual equation ${\tau }_{e-\mathrm{ph}}{=C}_e{/G}_{e-\mathrm{ph}}$ holds only if the resistance is solely related to the electron temperature. We conclude that at sufficiently low temperatures variable range hopping transport is assisted by electron-electron interactions alone and is independent of the phonon distribution.