title: The effect of correlations on the non-ohmic behavior of the small-polaron hopping conductivity in 1D and 3D disordered systems.
abstract: According to percolation theory the investigation of charge transport in disordered systems is equivalent to the study of the possibility of the passage of the carriers through a random network of impedances which interconnect the different lattice sites. When the site energies are not the same, the energy of a site affects the incoming as well as the outgoing impedances connected to the given site and this gives rise to correlations between neighboring impedances. This new condition characterizes the transport process and imposes the evaluation of the average number of sites accessible by a bond from a given site for all possible configurations of sites that satisfy the percolation condition. The generalized molecular crystal model, appropriate for the study of small-polaron hopping transport in disordered systems, and the Kubo formula permit the evaluation of these impedances. Taking correlations into account, theoretical percolation considerations applicable to one-dimensional and three-dimensional disordered systems, lead to analytical expressions for the temperature and electric field dependence of the DC conductivity at high (multi-phonon-assisted hopping) and low (few-phonon-assisted hopping) temperatures. The theoretical analysis reveals the effect of correlations on the non-ohmic behavior of the small-polaron hopping conductivity and permits the evaluation of the maximum hopping distance. Quantitative estimates of this effect are presented comparing the theoretical results, including correlations with those ignoring them, previously reported, applying them to recent experimental data for a wide temperature range and from low up to moderate electric fields.
authors.affiliation: Solid State Section, Physics Department, University of Athens, Panepistimiopolis, GR-15784 Zografos, Athens, Greece.
authors.forename: M
authors.initials: M
authors.lastname: Dimakogianni
authors.forename: G P
authors.initials: GP
authors.lastname: Triberis