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

TL;DR

This study uses advanced Monte Carlo simulations to analyze how Coulomb interactions influence hopping transport and current noise in disordered 2D conductors, revealing significant effects on noise suppression and scaling behavior.

Contribution

It provides the first detailed numerical analysis of Coulomb interaction effects on 2D hopping transport and noise characteristics, extending previous models.

Findings

Coulomb interactions suppress the Fano factor below 1.

The Fano factor scales with conductor length as (L_c / L)^α, with α affected by Coulomb effects.

The percolation cluster length L_c scales with electric field E, with different exponents depending on Coulomb interaction presence.

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 $F\equiv S_I(f)/2e \left< I\right>$. 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.