Frequency Scales for Current Statistics of Mesoscopic Conductors

We calculate the third cumulant of current in a chaotic cavity with contacts of arbitrary transparency as a function of frequency. Its frequency dependence drastically differs from that of the conventional noise. In addition to a dispersion at the inverse $RC$ time characteristic of charge relaxation, it has a low-frequency dispersion at the inverse dwell time of electrons in the cavity. This effect is suppressed if both contacts have either large or small transparencies.

Figure 1

Left panel: A chaotic cavity is biased from two leads and capacitively coupled to a gate. Right panel: Charged fluctuations of the distribution function $f$ decay at the short $RC$ time and contribute to the current noise. Uncharged fluctuations decay at a much longer time ${\tau }_D$ and do not contribute directly to the current noise but result in a low-frequency dispersion of the third cumulant of current.

Figure 2

A 3D plot of $\mathrm{Re}{P}_3({\omega }_1,{\omega }_2)$ for $G_L/G_R=1/2$, ${\Gamma }_L={\Gamma }_R=3/4$, ${\tau }_Q=1/3$, and ${\tau }_D=10$ (dimensionless units).

Figure 3

$P_3(\omega ,0)$ as a function of $\omega$ for $G_L/G_R=1$, ${\Gamma }_L=1$, ${\Gamma }_R=0$, and ${\tau }_D=10$ (dimensionless units). The solid, dashed, and dash-dotted curves correspond to ${\tau }_Q=1/2$, ${\tau }_Q=3$, and to weak electrostatic coupling ${\tau }_Q={\tau }_D$ ($C=\infty$).

Figure 4

Charge neutral process leading to the low-frequency dispersion of the third cumulant.