A Numerical Study of Transport and Shot Noise at 2D Hopping

TL;DR

This study uses large-scale Monte Carlo simulations to analyze transport and shot noise in 2D hopping conductors, revealing the absence of 1/f noise and characterizing the Fano factor's dependence on sample length and electric field.

Contribution

It provides the first detailed numerical analysis of shot noise and transport properties in 2D hopping conductors across various electric fields and temperatures, including the scaling behavior of the Fano factor.

Findings

Fano factor scales with length as (L_c/L)^α with α≈0.76

No evidence of 1/f noise within the model accuracy

L_c depends on electric field as E^{-0.911}

Abstract

We have used modern supercomputer facilities to carry out extensive Monte Carlo simulations of 2D hopping (at negligible Coulomb interaction) in conductors with the 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 $(L_c/L)^{\alpha}$, where $\alpha=0.76\pm 0.08 < 1$, 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 $L_c\propto E^{-0.911}$ which follows from directed percolation theory arguments.