Full counting statistics of nano-electromechanical systems

– We develop a theory for the full counting statistics (FCS) for a class of nanoelectromechanical systems (NEMS), describable by a Markovian generalized master equation. The theory is applied to two specific examples of current interest: vibrating C60 molecules and quantum shuttles. We report a numerical evaluation of the first three cumulants for the C60-setup; for the quantum shuttle we use the third cumulant to substantiate that the giant enhancement in noise observed at the shuttling transition is due to a slow switching between two competing conduction channels. Especially the last example illustrates the power of the FCS. Introduction. – The full counting statistics (FCS) of charge transport in mesoscopic systems is an active topic of recent research [1–5]. Calculation and measurement of the whole probability distribution of transmitted charge is motivated by the fact that FCS provides more information about a particular system than just the mean current or current noise which are the first two cumulants of the large-time asymptotics of the probability distribution. Very recently, a measurement of the third cumulant, which quantifies the skewness of the distribution, was reported [6]. The detailed nature of charge transport in nanoelectromechanical systems (NEMS), another modern field in mesoscopics, poses many challenges both to experiments and theory, and the computation of FCS for NEMS is an important task that needs to be addressed. The first steps were taken recently with a calculation of FCS for a driven, classical shuttle [7]. In this Letter, we present a theory for the evaluation of cumulants in a wide class of NEMS encompassing the majority of systems considered thus far, namely those which can be described by a Markovian generalized master equation (GME). The current cumulants turn out to be fully determined by an extremal eigenvalue of the system evolution superoperator (Liouvillean) in analogy with previous studies [4, 5]. Their evaluation is, however, more complicated since in NEMS there are generally many relevant states which need to be taken into account. We solve the problem by formulating a systematic perturbation theory, and using this derive explicit formulas for the first three cumulants. The method is illustrated by (∗) E-mail: [email protected]