Mean-field simulation of hopping resistivity in a model with Coulomb interactions and current correlations

Simulations of hopping resistivity by mean-field methods rely on randomly generated site energies. Thus such effects as the presence of the Coulomb gap and electron current correlations have been simulated using predominantly Monte Carlo methods. This paper presents a method of mean-field calculation of hopping resistivity in a wide range of temperatures and electric fields. This method considers the long-range Coulomb interactions and at least partially accounts for the electron current correlations. Resulting curves reproduce the Mott law in the form predicted by Efros and Shklovskii and the experimentally observed electric field dependencies. Based on the results, a decrease of hopping energy is predicted with increasing temperature in the nearest-neighbor hopping regime. The report analyses the differences between the mean-field and the Monte Carlo approaches. •Simulation of hopping resistivity in wide range of temperatures and electric fields.•Mean filed simulation method is described and the source code is published.•Method accounts for the Coulomb gap in the DOS and its evolution with temperature.•Hubbard current correlations and Coulomb correlations are considered.•Advantages and disadvantages of mean field and Monte Carlo approaches are discussed.