Universality of AC conductivity: Random site-energy model with Fermi statistics

Abstract

The universality of the frequency-dependent (AC) conduction of many disordered solids in the extreme-disorder limit has been demonstrated experimentally. Theoretically, this universality has been established with different techniques and for various models. A popular model that has been extensively investigated and for which AC universality was established is the symmetric random-barrier model without Fermi statistics. However, for the more realistic model of random site-energies and Fermi statistics AC universality has never been rigorously established. In the present work we perform a numerical study of the latter model for a regular lattice in two dimensions. In addition, we allow for variable-range hopping. Our main conclusion is that AC universality appears to hold for this realistic model. The obtained master curve for the conductivity and the one obtained for the random-barrier model in two dimensions appear to be the same.