Coulomb gap in two- and three-dimensional systems: Simulation results for large samples

Computer experiments have been performed to study the single-particle density of states, g(E), in the Coulomb gap. This gap occurs in disordered insulating systems as an effect of the long-range tail of the Coulomb interaction. In order to compare these numerical results with the analytical theory on a broader energy scale than previous authors, very large samples have been considered, up to 40 000 and 125 000 sites for dimensions d=2 and 3, respectively. Special algorithms have been developed for this aim. Our numerical results contradict the analytical theory from the literature in two main points: As E→μ, the numerical values for g(E) are considerably smaller than the analytical predictions, and universality with respect to disorder is not present. It could not be decided finally whether or not g(E→μ) follows a power law, g(E)∼‖E-μ${\mathrm{\Vert }}^{\nu }$. Provided it does, the simulation results, ν=1.2±0.1 and 2.6±0.2 for d=2 and 3, respectively, deviate from the analytical prediction, ν=d-1. Moreover, as a first approach to the polaronic transport problem, the influence of relaxation down to stability with respect to all simultaneous two-electron hops is studied. In this case, g(E) is diminished, but not changed qualitatively. In particular, the exponential behavior analytically predicted is not observed.