On the theory of hopping conductivity in disordered systems

Abstract

Starting with the linearised master equation, the authors present a first-principles theory of conductivity for disordered systems. The theory is valid for all situations to which the master equation description applies. The path summation and configurational average are evaluated by generalising relations obtained from exactly soluble models. Both symmetric and asymmetric energy-dependent transition frequencies are considered. In the latter case they are able to define an energy-dependent conductivity from which it is possible to evaluate the thermopower. All electronic transport properties, including the frequency-dependent conductivity can be evaluated self-consistently, the only input parameter being the density of states. Numerical results for the DC conductivity and thermopower are presented using several model density-of-states functions. For random statistics, the results are in complete agreement with percolation theory for low densities (temperature). The theory is exact in the high-density (temperature) limit.