Variable range hopping and/or phonon-assisted tunneling mechanism of electronic transport in polymers and carbon nanotubes

We review and compare two models recently used to describe electronic transport in polymer fibers/nanotubes and carbon nanotubes including graphene nanoribbons, namely, variable range hopping (VRH) in different versions and their modifications on the one hand and electric-field-induced phonon-assisted tunneling (PhAT) on the other hand. The VRH model is mainly approved on behalf of the results of temperature dependences. However, the field dependencies of the conductivity in the framework of this model remain practically unexplained. At the same time, the PhAT model describes properly not only temperature dependence of conductivity measured in a wide temperature range, but also conductivity/current dependences on field strength using the same set of parameters characterizing the materials