Distribution of waiting times between electron cotunneling events

Abstract

In the resonant tunneling regime sequential processes dominate single electron transport through quantum dots or molecules that are weakly coupled to macroscopic electrodes. In the Coulomb blockade regime, however, cotunneling processes dominate. Cotunneling is an inherently quantum phenomenon and thus gives rise to interesting observations, such as an increase in the current shot noise. Since cotunneling processes are inherently fast compared to the sequential processes, it is of interest to examine the short time behaviour of systems where cotunneling plays a role, and whether these systems display nonrenewal statistics. We consider three questions in this paper. Given that an electron has tunneled from the source to the drain via a cotunneling or sequential process, what is the waiting time until another electron cotunnels from the source to the drain? What are the statistical properties of these waiting time intervals? How does cotunneling affect the statistical properties of a system with strong inelastic electron-electron interactions? In answering these questions, we extend the existing formalism for waiting time distributions in single electron transport to include cotunneling processes via an $n$-resolved Markovian master equation. We demonstrate that for a single resonant level the analytic waiting time distribution including cotunneling processes yields information on individual tunneling amplitudes. For both a SRL and an Anderson impurity deep in the Coulomb blockade there is a nonzero probability for two electrons to cotunnel to the drain with zero waiting time inbetween. Furthermore, we show that at high voltages cotunneling processes slightly modify the nonrenewal behaviour of an Anderson impurity with a strong inelastic electron-electron interaction.