Coulomb zero bias anomaly for fractal geometry and conductivity of granular systems near the percolation threshold

TL;DR

This paper investigates how fractal geometry influences Coulomb zero bias anomalies and conductivity in granular systems near the percolation threshold, revealing enhanced effects across dimensions.

Contribution

It introduces a theoretical framework linking fractal cluster structures to Coulomb zero bias anomalies and conductivity behavior in granular systems.

Findings

Coulomb zero bias anomaly is significantly enhanced by fractal cluster structures.

The temperature dependence of conductivity follows a stretched exponential law.

The effects are observed not only in low dimensions but also in three-dimensional systems.

Abstract

A granular system slightly below the percolation threshold is a collection of finite metallic clusters, characterized by wide spectrum of sizes, resistances, and charging energies. Electrons hop from cluster to clusters via short insulating "links" of high resistance. At low temperatures all clusters are Coulomb blockaded and the dc-conductivity is exponentially suppressed. At lowest T the leading transport mechanism is variable range cotunneling via largest (critical) clusters, leading to the modified Efros-Shklovsky law. At intermediate temperatures the principal suppression of the conductivity originates from the Coulomb zero bias anomaly occurring, when electron tunnels between adjacent large clusters with large resistances. Such clusters are essentially extended objects and their internal dynamics should be taken into account. In this regime the T-dependence of conductivity is stretched exponential with a nontrivial index, expressed through the indices of percolation theory. Due to the fractal structure of large clusters the anomaly is strongly enhanced: it arises not only in low dimensions, but also in d=3 case.