Effective one-dimensionality of AC hopping conduction in the extreme disorder limit

TL;DR

This paper demonstrates that in extreme disorder, AC hopping conduction is effectively one-dimensional along percolation paths, leading to a universal conductivity expression that aligns well with simulations.

Contribution

It introduces a one-dimensional percolation path model for AC hopping conduction in extreme disorder, improving upon the effective medium approximation.

Findings

Universal AC conductivity expression derived from the model

Model fits computer simulations better than previous approximations

Highlights the dominance of percolation paths in extreme disorder

Abstract

It is argued that in the limit of extreme disorder AC hopping is dominated by "percolation paths". Modelling a percolation path as a one-dimensional path with a sharp jump rate cut-off leads to an expression for the universal AC conductivity, that fits computer simulations in two and three dimensions better than the effective medium approximation.