Short-time counting statistics of charge transfer in Coulomb-blockade systems

TL;DR

This paper investigates short-time charge transfer statistics in Coulomb-blockade systems, emphasizing the use of factorial cumulants to detect correlations among tunneling events, demonstrated through models like sequential and Andreev tunneling.

Contribution

It introduces the use of factorial cumulants for analyzing short-time charge transfer statistics to identify correlations in Coulomb-blockade systems.

Findings

Factorial cumulants reveal correlations through sign and power law deviations.

Short-time behavior of factorial cumulants differs in correlated vs. uncorrelated systems.

Application to models shows practical detection of tunneling correlations.

Abstract

We study full counting statistics of electron tunneling in Coulomb-blockade systems in the limit of short measuring-time intervals. This limit is particularly suited to identify correlations among tunneling events, but only when analyzing the charge-transfer statistics in terms of factorial cumulants $C_{{\rm F}, m}(t)$ rather than ordinary ones commonly used in literature. In the absence of correlations, the short-time behavior of the factorial cumulants is given by $C_{{\rm F}, m}(t) \propto (-1)^{m-1}t^m$. A different sign and/or a different power law of the time dependence indicates correlations. We illustrate this for sequential and Andreev tunneling in a metallic single-electron box.