Factorial cumulants reveal interactions in counting statistics

Dania Kambly, Christian Flindt, Markus Büttiker 

Département de Physique Théorique, Université de Genève

Full counting statistics concerns the stochastic transport of electrons in mesoscopic structures. Recent work has shown that the charge transport statistics for non-interacting electrons in a two-terminal conductor is always generalized binomial: it can be decomposed into independent single-particle events and the zeros of the generating function are real and negative [1]. Here we investigate how the zeros of the generating function may move into the complex plane due to interactions and argue that the positions of the zeros can be experimentally detected using high-order factorial cumulants [2]. Complex zeros of the generating function cause the high-order factorial cumulants to oscillate as functions of basically any system parameter and these oscillations are a clear ngerprint of interactions. Factorial cumulants are as such a useful tool to detect interactions among electrons passing through a nanoscale device. As an illustrative example we consider electron transport through a Coulomb blockade quantum dot, for which we show that the interactions on the dot are clearly visible in the high-order factorial cumulants. Coulomb blockade quantum dots in particular might be used to test our results. 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 [3,4].

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[2] D. Kambly, C. Flindt, and M. Büttiker, Phys. Rev. B 83, 075432 (2011)
[3] C. Flindt, C. Fricke, F. Hohls, T. Novotný, K. Netocný, T. Brandes, and R. J. Haug, Proc. Natl. Acad. Sci. USA 106, 10116 (2009)
[4] C. Fricke, F. Hohls, N. Sethubalasubramanian, L. Fricke, and R. J. Haug, Appl. Phys. Lett. 96, 202103 (2010)