Hopping-to-band transitions in disordered electronic systems

We investigate the effect polaron formation has on the transport of an electron among a band of tight binding sites interacting with a thermal bath of phonons. At T = 0 we show that interactions with phonons stabilize Anderson localized states by the formation of self-trapped species. A localization criterion is then derived which defines the strength of the transfer matrix element needed for given values of the site energy disorder and the phonon coupling to destroy the stability of the self-trapped states. The Anderson upper limit criterion is recovered in the limit that the phonon coupling vanishes. The conductivity is then calculated as a function of the site energy disorder if using small polaron theory. A hopping-to-band transition is shown to exist for small values of W at a temperature ∼ 1/9 θ_D (the Debye temperature). Thermally activated Arrenhius behavior and variable range hopping obtain in the hopping regime. The conductivity in the metallic or low temperature regime vanishes as W^-1. The relation to Mooij correlations is discussed.