R-ε percolation in moderate-field hopping transport

Abstract

The problem of the onset of nonlinear hopping conductivity in disordered systems is addressed using the Mott model. Four effects have been proposed which lead to nonlinearities in the current as a function of the applied electric field in moderate fields. In previous (R percolation) work, a model was used which circumvented two of these effects and evaluated the relative importance of the other two. In the present (R-ε percolation) work, one of the other effects is included, and it is argued that the remaining effect does not play a role in the resulting model. As in the work for R percolation, a technique is used which employs a percolative approach on the scale of a macrobond and an effective-medium theory on a scale larger than a macrobond. The result is that the current is superlinear, in accordance with previous (but less rigorous) results.