Activated hopping transport in anisotropic systems at low temperatures

TL;DR

This paper investigates how anisotropy affects low-temperature hopping transport in disordered systems, revealing a transition from variable-range to nearest-neighbor hopping due to anisotropic wave functions.

Contribution

It provides a numerical analysis of anisotropic hopping transport showing the transition in conduction mechanisms and temperature dependence based on wave function anisotropy.

Findings

Conductivity follows a stretched exponential with exponents from 1/4 to 1.

Strong anisotropy leads to nearest-neighbor hopping in the transport direction.

Perpendicular transport exhibits variable-range hopping consistent with experiments.

Abstract

Numerical calculations of anisotropic hopping transport based on the resistor network model are presented. Conductivity is shown to follow the stretched exponential dependence on temperature with exponents changing from 1/4 to 1 as the wave functions become anisotropic and their localization length in the direction of charge transport decreases. For sufficiently strong anisotropy, this results in nearest-neighbor hopping at low temperatures due to the formation of a single conduction path, which adjusts in the planes where the wave functions overlap strongly. In the perpendicular direction, charge transport follows variable-range hopping, a behavior that agrees with experimental data on organic semiconductors.