Electron-phonon interaction in disordered conductors: Static and vibrating scattering potentials

Abstract

Employing the Keldysh diagram technique, we calculate the electron-phonon energy relaxation rate in a conductor with the vibrating and static \ensuremath{\delta}-correlated random electron-scattering potentials. If the scattering potential is completely dragged by phonons, this model yields the Schmid's result for the inelastic electron-scattering rate ${\ensuremath{\tau}}_{e\ensuremath{-}\mathrm{ph}}^{\ensuremath{-}1}.$ At low temperatures the effective interaction decreases due to disorder, and ${\ensuremath{\tau}}_{e\ensuremath{-}\mathrm{ph}}^{\ensuremath{-}1}\ensuremath{\propto}{T}^{4}l$ (l is the electron mean-free path). In the presense of the static potential, quantum interference of numerous scattering processes drastically changes the effective electron-phonon interaction. In particular, at low temperatures the interaction increases, and ${\ensuremath{\tau}}_{e\ensuremath{-}\mathrm{ph}}^{\ensuremath{-}1}\ensuremath{\propto}{T}^{2}/l.$ Along with an enhancement of the interaction, which is observed in disordered metallic films and semiconducting structures at low temperatures, the suggested model allows us to explain the strong sensitivity of the electron relaxation rate to the microscopic quality of a particular film.