Statistics of Current Fluctuations and Electron-Electron Interactions in Mesoscopic Coherent Conductors

TL;DR

This paper develops a path integral method to analyze current fluctuation statistics in mesoscopic conductors, revealing how electron-electron interactions influence noise and cumulants across frequencies and voltages.

Contribution

It introduces a general approach for current fluctuation statistics in mesoscopic conductors, including interactions, and provides explicit universal formulas for noise behavior.

Findings

Coulomb interactions decrease Nyquist noise.

Frequency dispersion of the third cumulant can cause sign changes.

Interaction corrections to shot noise depend on transmission coefficients.

Abstract

We formulate a general path integral approach which describes statistics of current fluctuations in mesoscopic coherent conductors at arbitrary frequencies and in the presence of interactions. Applying this approach to the non-interacting case, we analyze the frequency dispersion of the third cumulant of the current operator ${\cal S}_3$ at frequencies well below both the inverse charge relaxation time and the inverse electron dwell time. This dispersion turns out to be important in the frequency range comparable to applied voltages. For comparatively transparent conductors it may lead to the sign change of ${\cal S}_3$. We also analyze the behavior of the second cumulant of the current operator ${\cal S}_2$ (current noise) in the presence of electron-electron interactions. In a wide range of parameters we obtain explicit universal dependencies of ${\cal S}_2$ on temperature, voltage and frequency. We demonstrate that Coulomb interaction decreases the Nyquist noise. In this case the interaction correction to the noise spectrum is governed by the combination $\sum_nT_n(T_n-1)$, where $T_n$ is the transmission of the $n$-th conducting mode. The effect of electron-electron interactions on the shot noise is more complicated. At sufficiently large voltages we recover two different interaction corrections entering with opposite signs. The net result is proportional to $\sum_nT_n(T_n-1)(1-2T_n)$, i.e. Coulomb interaction decreases the shot noise at low transmissions and increases it at high transmissions.