Statistics of current fluctuations and electron-electron interactions in mesoscopic coherent conductors

Abstract

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