Non-Ohmic variable-range hopping transport in one-dimensional conductors

TL;DR

This paper provides a theoretical analysis of how finite electric fields influence resistivity in disordered one-dimensional conductors within the variable-range hopping regime, revealing complex field-dependent behaviors.

Contribution

It introduces a detailed theoretical model describing the non-Ohmic transport behavior and resistance scaling laws under varying electric fields in 1D disordered systems.

Findings

Resistivity is initially dominated by rare high-resistance breaks.

Increasing the field reduces the resistance exponentially at first.

At high fields, the resistance follows an inverse square-root dependence.

Abstract

We investigate theoretically the effect of a finite electric field on the resistivity of a disordered one-dimensional system in the variable-range hopping regime. We find that at low fields the transport is inhibited by rare fluctuations in the random distribution of localized states that create high-resistance ``breaks'' in the hopping network. As the field increases, the breaks become less resistive. In strong fields the breaks are overrun and the electron distribution function is driven far from equilibrum. The logarithm of the resistance initially shows a simple exponential drop with the field, followed by a logarithmic dependence, and finally, by an inverse square-root law.