ABSTRACT
We have used modern supercomputer facilities to carry out extensive Monte Carlo simulations of 2D hopping (at negligible Coulomb interaction) in conductors with a completely random distribution of localized sites in both space and energy, within a broad range of the applied electric field E and temperature T, both within and beyond the variable-range hopping region. The calculated properties include not only dc current and statistics of localized site occupation and hop lengths, but also the current fluctuation spectrum. Within the calculation accuracy, the model does not exhibit 1/f noise, so that the low-frequency noise at low temperatures may be characterized by the Fano factor F. For sufficiently large samples, F scales with conductor length L as (L(c)/L)(α), where α = 0.76 ± 0.08<1, and parameter L(c) is interpreted as the average percolation cluster length. At relatively low E, the electric field dependence of parameter L(c) is compatible with the law [Formula: see text] which follows from directed percolation theory arguments.
ABSTRACT
We have extended our supercomputer-enabled Monte Carlo simulations of hopping transport in completely disordered 2D conductors to the case of substantial electron-electron Coulomb interaction. Such interaction may not only suppress the average value of hopping current, but also affect its fluctuations rather substantially. In particular, the spectral density S(I)(f) of current fluctuations exhibits, at sufficiently low frequencies, a 1/f-like increase which approximately follows the Hooge scaling, even at vanishing temperature. At higher f, there is a crossover to a broad range of frequencies in which S(I)(f) is nearly constant, hence allowing characterization of the current noise by the effective Fano factor [Formula: see text]. For sufficiently large conductor samples and low temperatures, the Fano factor is suppressed below the Schottky value (F = 1), scaling with the length L of the conductor as F = (L(c)/L)(α). The exponent α is significantly affected by the Coulomb interaction effects, changing from α = 0.76 ± 0.08 when such effects are negligible to virtually unity when they are substantial. The scaling parameter L(c), interpreted as the average percolation cluster length along the electric field direction, scales as [Formula: see text] when Coulomb interaction effects are negligible and [Formula: see text] when such effects are substantial, in good agreement with estimates based on the theory of directed percolation.
