Keywords: electronic transport, variable–range hopping, VRH, crossover model, carbon networks, reduced graphene oxide, highly–doped conducting polymers, electrical conduction, nanotechnology, temperature dependence, electric field dependence, disordered carbon materials, disordered conductors
Variable–range hopping transport: crossovers from temperature dependence to electric field dependence in disordered carbon materials
Variable–range hopping (VRH) is an important conduction mechanism in disordered conductors. One example of such a disordered conductor is reduced graphene oxide in which VRH dominates the temperature dependence of electronic conduction. Electronic transport is generally by electric field–assisted, thermally–driven VRH, following the theory of Mott, and Pollak and Riess. However, with the increase of electric field and decrease of temperature, we identify a surprisingly smooth crossover to solely field–driven VRH described by the theory of Shklovskii. We give the analytic expression for the crossover field E
Cas a function of temperature and coefficients from thermally–driven and field–driven VRH. Besides reduced graphene oxide, we show in this work that our crossover scenario can also account for the experimentally measured conductivity data of three–dimensional (3D) carbon networks as well as that of quasi–1D highly–doped conducting polymers, illustrating the wide validity of our proposed physical scenario. Our crossover scenario has the advantage of combining two distinct regimes of VRH conduction yet remaining within the currently established theoretical framework.