Multiterminal counting statistics

TL;DR

This paper reviews calculational schemes for evaluating full current statistics in multi-terminal mesoscopic systems, comparing scattering and master equation approaches, and analyzing the effects of Coulomb interactions on charge transfer fluctuations.

Contribution

It provides a unified framework connecting scattering theory and master equations for FCS in multi-terminal systems, including Coulomb blockade effects.

Findings

Coulomb interactions suppress large current fluctuations.

Scattering and master equation approaches are equivalent for single resonance levels.

Application to three-terminal quantum dots illustrates the methods.

Abstract

The review is given of the calculational schemes that allows for easy evaluation of full current statistics (FCS) in multi-terminal mesoscopic systems. First, the scattering approach by Levitov {\it et.al} to FCS is outlined. Then the multi-terminal FCS of the non-interacting electrons is considered. We show, that this theory appears to be a circuit theory of $2\times 2$ matrices associated with Keldysh Green functions. Further on the FCS in the opposite situation of mesoscopic systems placed in a strong Coulomb blockade limit is discussed. We prove that the theory of FCS in this case turns out to be an elegant extension of the master equation approach. We illustrate both methods by applying them to the various three-terminal circuits. We study the FCS of electron transfer in the three-terminal chaotic quantum dot and compare it with the statistics of charge transfer in the Coulomb blockade island with three leads attached. We demonstrate that Coulomb interaction suppresses the relative probabilities of big current fluctuations. Finally, for the generic case of single resonance level the equivalence of scattering and master equation approach to FCS is established.