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

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.