Full Current Statistics of Incoherent “Cold Electrons”

We evaluate the full current statistics (FCS) in the low-dimensional (1D and 2D) diffusive conductors in the incoherent regime $eV\gg E_{\mathrm{T}\mathrm{h}}=D/L^2$, $E_{\mathrm{T}\mathrm{h}}$ being the Thouless energy. It is shown that the Coulomb interaction substantially enhances the probability of big current fluctuations for short conductors with $E_{\mathrm{T}\mathrm{h}}\gg 1/{\tau }_E$, ${\tau }_E$ being the energy relaxation time, leading to the exponential tails in the current distribution. The current fluctuations are most strong for low temperatures, provided $E_{\mathrm{T}\mathrm{h}}\sim [(eV{)}^2/D{\nu }_1^2{]}^{1/3}$ for 1D and $E_{\mathrm{T}\mathrm{h}}\sim (eV/g)\ln g$ 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.

Figure 1

The sketch of voltage dependence of the 6th cumulant of charge transfer. Left plot: 1D, conductance $g=100$; right plot: 2D, $g={10}^3$. The temperature changes from up to down, $T/E_{\mathrm{T}\mathrm{h}}=1,2,4,8$.

Figure 2

The log of probability to measure the big nonequilibrium current fluctuations ($eV\gg T$). Curve (1), coherent regime; curve (2), incoherent “cold electron” regime, $\gamma =0.2$; curve (3), “hot electron” regime.