AC Hopping Conduction At Extreme Disorder Takes Place On The Bond Invasion Percolation Cluster

TL;DR

This paper argues that ac conduction in highly disordered solids occurs on the bond invasion percolation cluster, explaining the universality of conductivity and the accuracy of effective-medium approximations.

Contribution

It identifies the bond invasion percolation cluster as the key structure for ac conduction in extreme disorder, clarifying universality and modeling accuracy.

Findings

AC conduction occurs on the bond invasion percolation cluster.

Universal behavior of rescaled ac conductivity is explained.

Effective-medium approximation accurately predicts conductivity.

Abstract

It has been suggested that ac conduction in extremely disordered solids occurs on the critical percolation cluster. In this note, we argue that in fact the transport process takes place on the bond invasion percolation cluster (BIPC). The structure of the BIPC is universal independent of the conductances of the bonds, which explains why the rescaled ac conductivity is a universal function of the rescaled frequency. It also explains why the effective-medium approximation provides quantitatively accurate predictions for the effective conductivity.