Hopping conductivity of a suspension of nanowires in an insulator

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.