Properties of the electron glass

We have carried out numerical calculations on two- and three-dimensional models of highly localized electrons interacting by an unscreened Coulomb potential. A Coulomb gap was found in the density of states for bare single-particle excitations. This "soft" gap was deeper than the power-law gap seen in earlier simulations, but for three-dimensional systems it was fitted well by an exponential form proposed by Efros. The gap fills as the temperature is raised. We also found an unexpected clustering of states with the same occupation and energies close to the chemical potential. The density of states for dressed single-particle excitations ("electronic polarons") showed a Coulomb gap too, but a narrower one than that for the bare excitations. There is a clear analogy between this model of interacting electrons and an Ising spin-glass with $\frac{1}{r}$ antiferromagnetic interactions and a random field on each site. We have exploited this analogy to search for a glass transition in the electronic system by calculating the specific heat, susceptibility, and a modified Edwards-Anderson order parameter.