Time-dependent factorial cumulants in interacting nano-scale systems

We discuss time-dependent factorial cumulants in interacting nano-scale systems. Recent theoretical work has shown that the full counting statistics of non-interacting electrons in a two-terminal conductor is always generalized binomial and the zeros of the generating function are consequently real and negative. However, as interactions are introduced in the transport, the zeros of the generating function may become complex. This has measurable consequences: With the zeros of the generating function moving away from the real-axis, the high-order factorial cumulants of the transport become oscillatory functions of time. Here we demonstrate this phenomenon on a model of charge transport through coherently coupled quantum dots attached to voltage-biased electrodes. Without interactions, the factorial cumulants are monotonic functions of the observation time. In contrast, as interactions are introduced, the factorial cumulants oscillate strongly as functions of time. We comment on possible measurements of oscillating factorial cumulants and outline several avenues for further investigations.Comment: 11 pages, 7 figures, invited contribution to special issue on 'Quantum Transport beyond DC' in the Journal of Computational Electronic

Time-dependent factorial cumulants in interacting nano-scale systems

We discuss time-dependent factorial cumulants in interacting nano-scale systems. Recent theoretical work has shown that the full counting statistics of non-interacting electrons in a two-terminal conductor is always generalized binomial and the zeros of the generating function are consequently real and negative. However, as interactions are introduced in the transport, the zeros of the generating function may become complex. This has measurable consequences: With the zeros of the generating function moving away from the real-axis, the high-order factorial cumulants of the transport become oscillatory functions of time. Here we demonstrate this phenomenon on a model of charge transport through coherently coupled quantum dots attached to voltage-biased electrodes. Without interactions, the factorial cumulants are monotonic functions of the observation time. In contrast, as interactions are introduced, the factorial cumulants oscillate strongly as functions of time. We comment on possible measurements of oscillating factorial cumulants and outline several avenues for further investigation

Full Counting Statistics of Andreev Tunneling

We employ a single-charge counting technique to measure the full counting statistics of Andreev events in which Cooper pairs are either produced from electrons that are reflected as holes at a superconductor–normal-metal interface or annihilated in the reverse process. The full counting statistics consists of quiet periods with no Andreev processes, interrupted by the tunneling of a single electron that triggers an avalanche of Andreev events giving rise to strongly super-Poissonian distributions.Peer reviewe

Factorial cumulants reveal interactions in counting statistics

Full counting statistics concerns the stochastic transport of electrons in mesoscopic structures. Recently it has been shown that the charge transport statistics for non-interacting electrons in a two-terminal system is always generalized binomial: it can be decomposed into independent single-particle events and the zeros of the generating function are real and negative. Here we investigate how the zeros of the generating function move into the complex plane due to interactions and demonstrate that the positions of the zeros can be detected using high-order factorial cumulants. As an illustrative example we consider electron transport through a Coulomb blockade quantum dot for which we show that the interactions on the quantum dot are clearly visible in the high-order factorial cumulants. Our findings are important for understanding the influence of interactions on counting statistics and the characterization in terms of zeros of the generating function provides us with a simple interpretation of recent experiments, where high-order statistics have been measured.Comment: 12 pages, 7 figures, Editors' Suggestion in Phys. Rev.

Counting statistics in interacting nano-scale conductors

Counting statistics investigates the probability P(n,t) that a number n of electrons traverse a nano-scale conductor during a time span t. It is equivalent to consider the zero frequency charge or current correlators, the so-called moments and cumulants, in principle up to infinite order. In this thesis we investigate several aspects of electronic correlations due to interactions. First we investigate the influence of interactions on the counting statistics, considering a generic two-terminal conductor. We show that if the factorial cumulants oscillate as functions of any system parameter or time, then the electrons must be interacting. This statement may be verified in Coulomb blockaded quantum dots, where it is possible to monitor the traversal of electrons in real-time. Moreover, we use a Markovian master equation to describe the first experiment on counting statistics of Andreev events, where two electrons tunnel accross a tunnel barrier between a superconducting lead and a normal metallic island. The statistics are strongly super-Poissonian, reflecting that Andreev events occur in avalanches of different sizes. Finally, we consider finite frequency current noise and show that the noise spectra are in general asymmetric in the applied bias voltage. Using a higher order fluctuation relation, which is an extension of the fluctuation dissipation relation to the non-equilibrium transport regime, we show that this asymmetry is due to a broken electron-hole symmetry, resulting in a finite rectification. We point out that this can occur either due to an asymmetrically applied bias, but more importantly, due to interactions and an inherent chirality of the conductor