Hopping conductivity of a suspension of flexible wires in an insulator

TL;DR

This paper investigates the hopping conductivity in a composite of flexible metallic wires in an insulator, revealing how Coulomb interactions and screening effects influence the temperature-dependent conduction laws.

Contribution

It introduces a model for hopping conductivity in flexible wire suspensions, analyzing the transition from Efros-Shklovskii to Mott law due to screening effects at different concentrations.

Findings

Conductivity follows ES law at low temperatures due to Coulomb gap.

At higher concentrations and temperatures, conductivity obeys Mott law.

The characteristic temperatures T_ES and T_M depend on wire concentration and length.

Abstract

We study the hopping conductivity in a composite made of Gaussian coils of flexible metallic wires randomly and isotropically suspended in an insulator at such concentrations that the spheres containing each wire overlap. Uncontrolled donors and acceptors in the insulator lead to random charging of wires and, hence, to a finite density of states (DOS) at the Fermi level. Then the Coulomb interactions between electrons of distant wires result in the soft Coulomb gap. At low temperatures the conductivity is due to variable range hopping of electrons between wires and obeys the Efros-Shklovskii (ES) law $\ln\sigma \propto -(T_{ES}/T)^{1/2}$ with $T_{ES}$ decreasing with concentration and length of the wires. Due to enhanced screening of Coulomb potentials, at large enough wire concentrations and sufficiently high temperatures, the ES law is replaced by the Mott law $\ln\sigma \propto -(T_{M}/T)^{1/4}$.