Singular effect of disorder on electronic transport in strongly coupled electron-phonon systems

We solve the disordered Holstein model in three dimensions considering the phonon variables to be classical. After mapping out the phases of the "clean" strong coupling problem, we focus on the effect of disorder at strong electron-phonon (EP) coupling. The presence of even weak disorder (i) enormously enhances the resistivity (rho) at T=0, simultaneously suppressing the density of states at the Fermi level, (ii) suppresses the temperature dependent increase of rho, and (iii) leads to a regime with drho/dT<0. We locate the origin of these anomalies in the disorder induced tendency towards polaron formation, and the associated suppression in effective carrier density and mobility. These results, explicitly at "metallic" density, are of direct relevance to disordered EP materials such as covalent semiconductors, the manganites, and to anomalous transport in the A-15 compounds.