Calculations of the mean width of the Coulomb gap in disordered systems by two simple methods

Abstract

Two simple models, a dielectric model and a Thomas-Fermi model, are used to calculate the Coulomb gap E _g in disordered systems, and hopping excitation energies in the presence of Coulomb interactions. An important approximation in both methods is that the mean width of the Coulomb gap is obtained by assuming that the response to the presence of an electron at any location is the average response.

A very important element in the determination of E _g is the inability of the electronic system to sustain short-range screening. This is quantified in dielectric theory by a cut-off wave-vector for the dielectric function, and in the Thomas-Fermi theory by a saturation charge. The latter is easier to relate to known properties of the system; this is one reason why the Thomas-Fermi method is deemed more reliable.

Although more sophisticated methods for calculating E_g exist in the literature, the advantages of the present method are its simplicity and ready applicability to complex situations. One such application considered here is the Coulomb gap in the vicinity of a metallic electrode, a configuration which occurs in transport experiments on inversion layers and in tunnelling experiments.