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

We report an analysis of low-temperature measurements of the conductance of partially disordered reduced graphene oxide, finding that the data follow a simple crossover scenario. At room temperature, the 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(−E0/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 E0 and Ea 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.