Ac hopping conduction at extreme disorder takes place on the percolating cluster

TL;DR

This paper demonstrates that at extreme disorder, ac conduction predominantly occurs on the percolating cluster, challenging traditional views and providing an analytical model that fits universal ac conductivity without fitting parameters.

Contribution

It reveals that ac conduction at extreme disorder is mainly on the percolating cluster and introduces an analytical model based on the effective medium approximation and Alexander-Orbach conjecture.

Findings

AC conduction is carried mainly by the percolating cluster.

Traditional theories underestimate the contribution of the percolating cluster.

The analytical fit matches universal ac conductivity without fitting parameters.

Abstract

Simulations of the random barrier model show that ac currents at extreme disorder are carried almost entirely by the percolating cluster slightly above threshold; thus contradicting traditional theories contributions from isolated low-activation-energy clusters are negligible. The effective medium approximation in conjunction with the Alexander-Orbach conjecture leads to an excellent analytical fit to the universal ac conductivity with no nontrivial fitting parameters.