Onset of nonlinear hopping conduction in R-percolation

Abstract

The problem of nonlinear transport in disordered Anderson insulators is addressed. In previous theoretical works, four nonlinear effects have been proposed, and their relative importance is currently not clear. Eliminating two by an appropriate choice of model, the other two, namely the field-induced charge redistribution, and the backward flow on segments of the percolation path, are studied here in detail near the onset of nonlinear behaviour. The model is a reasonable representation of impurity conduction, so results can be compared with experiment. An expansion of the current density to third order in the field has been developed, and used to construct an algorithm for a computer simulation study using percolation theory. Strong fluctuations of conductance existing on a scale less than a correlation length of the current-carrying percolation cluster are accounted for in detail, while the small fluctuations which exist on a larger scale are treated by effective medium theory.