Percolation with excluded small clusters and Coulomb blockade in a granular system

TL;DR

This paper investigates how the dc-conductivity in a granular system near the percolation threshold is affected by Coulomb blockade and the exclusion of small clusters, revealing a power-law temperature dependence.

Contribution

It introduces a percolation model with excluded small clusters and Coulomb blockade effects, deriving a power-law relation for conductivity with temperature.

Findings

Conductivity decreases as a power law of excluded cluster size.

Power-law temperature dependence of conductivity in an intermediate range.

Analytical and numerical confirmation of the relation between critical indices and conductivity.

Abstract

We consider dc-conductivity $\sigma$ of a mixture of small conducting and insulating grains slightly below the percolation threshold, where finite clusters of conducting grains are characterized by a wide spectrum of sizes. The charge transport is controlled by tunneling of carriers between neighboring conducting clusters via short ``links'' consisting of one insulating grain. Upon lowering temperature small clusters (up to some $T$-dependent size) become Coulomb blockaded, and are avoided, if possible, by relevant hopping paths. We introduce a relevant percolational problem of next-nearest-neighbors (NNN) conductivity with excluded small clusters and demonstrate (both numerically and analytically) that $\sigma$ decreases as power law of the size of excluded clusters. As a physical consequence, the conductivity is a power-law function of temperature in a wide intermediate temperature range. We express the corresponding index through known critical indices of the percolation theory and confirm this relation numerically.