Field and temperature dependence of the small polaron hopping electrical conductivity in 1D disordered systems

Abstract

We investigate the effect of the electric field and the temperature on the electrical conductivity of one-dimensional disordered systems due to phonon assisted hopping of small polarons. The microscopic transport mechanism is treated within the framework of the generalized molecular crystal model and the Kubo formula, while percolation theoretical arguments lead to analytical expressions for the macroscopic behavior of the electrical conductivity at high (multi-phonon assisted hopping) and low (few-phonon assisted hopping) temperatures under the influence of moderate electric fields. The theoretical results are successfully applied to recent experimental findings for a wide temperature range and from low up to moderate electric fields. Comparison is made with other theories.