Approximate thermodynamical treatment of the Coulomb gap

Abstract In disordered systems, in which transport occurs by hopping between localized states, both Pollak and Efros and Shklovskii have pointed out that conduction could be greatly affected by the electron-electron repulsion, opening the so-called Coulomb gap in the one-electron density of states, N(E). The aim of this paper is to represent the effect of the Coulomb gap on the free energy, F. F is expressed in terms of an unknown correlation length, r0. Minimization of F with respect to r0 yields r 0 ∝ T −1, divergent at zero temperature, T. Owing to this singularity in the correlation length, models for transport must be based on finite temperature structure, as finite temperature conditions are not representable as small departures from those at zero temperature. The density of states at the Fermi level obtained by this treatment is in agreement with Efros and with recently published results of Mogilyanski.