Generalizated effective-medium approximation for hopping transport in topologically disordered systems

A generalized effective-medium approximation (EMA) for hopping transport in topologically disordered systems such as amorphous semiconductors or impur ity bands of crystalline semiconductors is derived. In contrast with previo us theories we are able to include the influence of closed loops in the pat h summation. These terms are responsible for the algebraic long-time tails of the velocity autocorrelation function which also show up as non-analytic terms in the low-frequency part of the ac conductivity. If the closed-loop contributions are neglected the two-site EMA of Gochanour et al. and Movag har et al. is re-obtained. We have tested the results of the present theory against simulations for an r-hopping network.