A Numerical Study of Coulomb Interaction Effects on 2D Hopping Transport

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 $F\equiv S_I(f)/2e⟨I⟩$. 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 $F=(L_c/L{)}^{\alpha }$. The exponent $\alpha$ is significantly affected by the Coulomb interaction effects, changing from $\alpha =0.76\pm 0.08$ 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 $L_c\propto E^{-(0.98\pm 0.08)}$ when Coulomb interaction effects are negligible and $L_c\propto E^{-(1.26\pm 0.15)}$ when such effects are substantial, in good agreement with estimates based on the theory of directed percolation.

19 pages, 7 figures. Fixed minor typos and updated references

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