Studies of ac hopping conduction at low temperatures

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Abstract
A method is presented that makes computer simulations of hopping conduction in symmetric hopping models with thermally activated jump rates possible at arbitrarily low temperatures. The method utilizes the ac Miller-Abrahams electrical equivalent circuit which is systematically reduced by the general star-mesh transformation until one ends up with an admittance matrix referring to the voltage generators. From this matrix the conductivity is easily calculated. Results from simulations of hopping in two dimensions are presented and compared to the predictions of the effective-medium approximation (EMA). Generally there is good agreement, with some deviation at the lowest temperatures. It is shown that, as the temperature goes to zero, the frequency-dependent conductivity in the EMA becomes universal, i.e., independent of the activation energy probability distribution. The computer simulations confirm the existence of universality, although there is no exact agreement between the simulations and the EMA universality prediction.