Long-range electron transport in random trapping models

Abstract

We extend the standard random trapping (RT) model of electron transport on d-dimensional hypercubic lattices to include long-range charge transfer. We show that for RT models, it is possible to decouple exactly the site energy disorder from the distance dependence of the hopping rate. We then apply the exit probability approach developed by us to the formulation of the transport properties. At short times for exchange-type rates, we show that it is the site energy disorder rather than the distance dependence of the hopping rate that determines the short-time dependence of the mean-square displacement. The analytic structure of the short-time expansion is shown to be consistent with the corresponding limit of a typologically disordered random hopping problem. At long times we consider exchange and multipolar models for the hopping rates. For a particle initially placed at the origin, it is shown that the long behavior of the diffusion coefficient [D(t)−D(t=∞)]∼t−d/2, is identical to the asymptotic behavior of D(t) for nearest-neighbor transport. The implications of these results on photoconductivity are discussed.