Conductance of partially disordered graphene: Crossover from temperature-dependent to field-dependent variable-range hopping

TL;DR

This study investigates the conductance behavior of partially disordered graphene oxide at low temperatures, revealing a crossover from temperature-dependent to electric field-dependent variable-range hopping, with implications for disordered carbon networks.

Contribution

It introduces a unified crossover model explaining conductance in disordered graphene, bridging temperature-driven and field-driven VRH regimes with experimental validation.

Findings

Conductance follows a crossover from thermally-driven to field-driven VRH.

The crossover field E_C(T) is quantitatively determined by material parameters.

The model explains data from various disordered carbon systems.

Abstract

We report and analyze low-temperature measurements of the conductance of partially disordered reduced graphene oxide, finding that the data follow a simple crossover scenario. At room temperature, conductance is dominated by two-dimensional (2D) electric field-assisted, thermally-driven (Pollak-Riess) variable-range hopping (VRH) through highly-disordered regions. However, at lower temperatures T, we find a smooth crossover to follow the exp(-E_0/E)^(1/3) field-driven (Shklovskii) 2D VRH conductance behaviour when the electric field E exceeds a specific crossover value E_C (T)_2D = (E_a E_0^(1/3) /3)^(3/4) determined by the scale factors E_0 and E_a for the high-field and intermediate field regimes respectively. Our crossover scenario also accounts well for experimental data reported by other authors for three-dimensional disordered carbon networks, suggesting wide applicability.