Full Current Statistics of Incoherent "Cold Electrons"

TL;DR

This paper analyzes the full current statistics in low-dimensional diffusive conductors under incoherent conditions, revealing how Coulomb interactions and temperature influence current fluctuations and distribution tails.

Contribution

It provides a detailed evaluation of FCS in 1D and 2D conductors, highlighting Coulomb interaction effects and conditions for strong fluctuations, including the hot electron regime.

Findings

Coulomb interactions significantly increase large current fluctuation probabilities.

Exponential tails appear in the current distribution due to Coulomb effects.

Current fluctuations are strongest at low temperatures under specific Thouless energy conditions.

Abstract

We evaluate the full current statistics (FCS) in the low dimensional (1D and 2D) diffusive conductors in the incoherent regime, $eV\gg E_{\rm Th}=D/L^2$, $E_{\rm Th}$ being the Thouless energy. It is shown that Coulomb interaction substantially enhances the probability of big current fluctuations for short conductors with $E_{\rm Th}\gg1/\tau_E$, $\tau_E$ being the energy relaxation time, leading to the exponential tails in the current distribution. The current fluctuations are most strong for low temperatures, provided $E_{\rm Th}\sim [(eV)^2/D\nu_1^2\bigr]^{1/3}$ for 1D and $E_{\rm Th}\sim (eV/g)\ln g$ for 2D, where $g$ is a dimensionless conductance and $\nu_1$ is a 1D density of states. The FCS in the "hot electron" regime is also discussed.