Universality of ac-conduction in anisotropic disordered systems: An effective medium approximation study

TL;DR

This paper investigates the universal ac-conduction behavior in anisotropic disordered systems using an effective medium approximation, demonstrating that the isotropic universal law applies when scaled variables are used.

Contribution

It extends the understanding of ac-conduction universality to anisotropic systems within the random barrier model framework.

Findings

Universal ac-conduction law is recovered in anisotropic systems with proper scaling.

Effective medium approximation effectively models frequency-dependent conductivity.

Anisotropic disordered systems exhibit the same universal behavior as isotropic ones under certain conditions.

Abstract

Anisotropic disordered system are studied in this work within the random barrier model. In such systems the transition probabilities in different directions have different probability density functions. The frequency-dependent conductivity at low temperatures is obtained using an effective medium approximation. It is shown that the isotropic universal ac-conduction law, $\sigma \ln \sigma=u$, is recovered if properly scaled conductivity ($\sigma$) and frequency ($u$) variables are used.