Influence of Electron-Phonon Coupling on Transport near a Mobility Edge

The authors treat electronic transport in disordered systems, including the electron-phonon interaction, on both sides of a mobility edge ${\epsilon }_c$ on the same footing. By application of a mode-coupling approximation self-consistent equations are derived from which one gets the matrices describing density relaxation due to both coherent tunneling processes and hopping processes. The resulting conductivity interpolates between a metallic behavior well above and a hopping behavior well below ${\epsilon }_c$.