Current Fluctuations in an Interacting Quantum Dot

We calculate the counting statistics of electron transfer through an open quantum dot with charging interaction. A dot that is connected to leads by two single-channel quantum point contacts in an in-plane magnetic field is described by a Luttinger liquid with impurity at the Toulouse point. We find that the fluctuations of the current through this conductor exhibit distinctive interaction effects. Fluctuations saturate at high voltages, while the mean current increases linearly with the bias voltage. All cumulants higher than the second one reach at large bias a temperature independent limit.

Figure 1

QD connected to two leads by single-channel point contacts QPC 1 and QPC 2. QPC 2 introduces backscattering. The current $I$ of charge transferred from lead 1 to lead 2 is measured.

Figure 2

${\mathcal{C}}_3$ is plotted in units of $e{G}_0{T}_B$ versus $eV/T_B$ for different temperatures. For large voltages, ${\mathcal{C}}_3$ saturates at the temperature independent value ${\mathcal{C}}_3^{\infty }=-(\pi e/8)G_0{T}_B$. The inset shows that, at zero temperature, ${\mathcal{C}}_3$ changes sign at an effective transmission ${\Gamma }_{\mathrm{eff}}\approx 0.26$.