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-ph), and the electron-phonon relaxation time tau(e-ph) (from 10(-2) to 10(-5) s) for NbxSi1-x Anderson insulator thin films. We show that the usual equation tau(e-ph) = C(e)/G(e-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.