Self-consistent full counting statistics of inelastic transport

We consider the full counting statistics (FCS) of inelastic transport through a molecular junction. A self-consistent procedure for FCS within the nonequilibrium Green function method is introduced. We show that in the case of FCS the self-consistent treatment provides a conserving approximation. The importance of renormalizing the molecular vibration for the counting statistics of electron transport is discussed within a generic two-level model. We consider weak electron-vibration coupling, and report that heating the molecular vibration may lead to either an increase or a decrease in the current through the junction depending on the model parameters. Super-Poissonian noise induced by the nonequilibrium vibration is observed at resonance. We argue that the origin of the effect is the avalanche transport previously discussed in the literature for a system with a strong electron-vibration interaction.