Onsager approach to the universal cross-over in variable-range hopping with Coulomb interactions

A model describing low-temperature dc conductivity in a disordered hopping system is formulated. The model considers one-particle excitations as a variable range hopping with a constant density of states near the Fermi level and accounts for Coulomb interaction of charge carriers on the basis of Onsager dissociation probability. The resulting temperature dependence of the conductivity reveals a universal crossover from Mottʹs T−1/4 to Efros–Shklovskiiʹs T−1/2 laws with decreasing temperature and increasing density of localized states.