Large-voltage behavior of charge transport characteristics in nanosystems with weak electron-vibration coupling

We study analytically the Full Counting Statistics of the charge transport through a nanosystem consisting of a few electronic levels weakly coupled to a discrete vibrational mode. In the limit of large transport voltage bias the cumulant generating function can be evaluated explicitly based solely on the intuitive physical arguments and classical master equation description of the vibration mode. We find that for the undamped vibrational modes mutual dynamical interplay between electronic and vibronic degrees of freedom leads to strongly nonlinear (in voltage) transport characteristics of the nanosystem. In particular, we find that for large voltages the k-th cumulant of the current grows as V (2k) to be contrasted with the linear dependence in case of more strongly externally damped and thus thermalized vibrational modes.