Universality of ac conduction in disordered solids

TLDR

Ac conduction in diverse disordered solids shows striking similarity, as revealed by experiments, modeling, and simulations. The study argues that this universality arises from percolation processes governing both dc and ac conductivity in the extreme disorder limit. The authors review macroscopic and microscopic models, demonstrating that in the extreme disorder limit the normalized ac conductivity becomes independent of disorder details, and they present three analytical approximations compared with simulations. The two universal ac conductivities are similar yet distinct, exemplifying non‑power‑law universalities, and the model predictions agree qualitatively with experimental observations.

Abstract

The striking similarity of ac conduction in quite different disordered solids is discussed in terms of experimental results, modeling, and computer simulations. After giving an overview of experiment, a macroscopic and a microscopic model are reviewed. For both models the normalized ac conductivity as a function of a suitably scaled frequency becomes independent of details of the disorder in the extreme disorder limit, i.e., when the local randomly varying mobilities cover many orders of magnitude. The two universal ac conductivities are similar, but not identical; both are examples of unusual non-power-law universalities. It is argued that ac universality reflects an underlying percolation determining dc as well as ac conductivity in the extreme disorder limit. Three analytical approximations to the universal ac conductivities are presented and compared to computer simulations. Finally, model predictions are briefly compared to experiment.