Dynamics of a single electron in the disordered Holstein model

We study, at zero temperature, the dynamics of a single electron in a Holstein model augmented by site-diagonal, binary-alloy-type disorder. The average over the phonon vacuum and the alloy configurations is performed within a generalized dynamic coherent potential approximation. We present numerical results for a Bethe lattice with infinite coordination number. In particular, we investigate, in the intermediate electron-phonon coupling regime, the spectral and diffusion properties in the vicinity of the high-energy edge of the lowest polaronic subband. To characterize the diffusion properties, we define a spectrally resolved delocalization time, which is, for a given energy, the characteristic time scale on which the electron leaves a given site. We find the delocalization times substantially enhanced for states with a large phonon content, i.e., in the absence (presence) of alloy-type disorder at the high-energy edge(s) of the polaronic subband (minisubbands). According to their delocalization times, we discriminate between "fast" quasiparticlelike and "sluggish" defectlike polaron states and qualitatively address the issue of trapping of an electronic carrier.