Hopping conductivity of a suspension of nanowires in an insulator

TL;DR

This paper investigates the variable range hopping conductivity in nanowire-insulator composites, revealing how Coulomb interactions and screening effects influence the transition from Efros-Shklovskii to Mott law regimes.

Contribution

It provides a theoretical analysis of hopping conduction in nanowire composites, deriving the dependence of the characteristic temperature on wire concentration and length.

Findings

Conductivity follows Efros-Shklovskii law at low temperatures.

Characteristic temperature T_ES scales as 1/(nL^3)^2.

At high concentrations, the law transitions to Mott law due to screening.

Abstract

We study the hopping conduction in a composite made of straight metallic nanowires randomly and isotropically suspended in an insulator. Uncontrolled donors and acceptors in the insulator lead to random charging of wires and hence finite bare density of states 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 $\ln\sigma \propto -(T_{ES}/T)^{1/2}$. We show that $T_{ES} \propto 1/(nL^3)^2$, where $n$ is the concentration of wires and $L$ is the wire length. Due to enhanced screening of Coulomb potentials, at large enough $nL^3$, the ES law is replaced by the Mott law.