Fluctuating-time and full counting statistics for quantum transport in a system with internal telegraphic noise

Many molecular junctions display stochastic telegraphic switching between two distinct current values, which is an important source of fluctuations in nanoscale quantum transport. Using Markovian master equations, we investigate electronic fluctuations and identify regions of nonrenewal behavior arising from telegraphic switching. Nonrenewal behavior is characterized by the emergence of correlations between successive first-passage times of detection in one of the leads. Our method of including telegraphic switching is general for any source-molecule-drain setup, but we consider three specific cases. In the first, we model stochastic transitions between an Anderson impurity with and without an applied magnetic field B. The other two scenarios couple the electronic level to a single vibrational mode via the Holstein model. We then stochastically switch between two vibrational conformations, with different electron-phonon coupling lambda and vibrational frequency omega, which corresponds to different molecular conformations. Finally, we model the molecule attaching and detaching from an electrode by switching between two different molecule-electrode coupling strengths gamma. We find, for all three cases, that including the telegraph process in the master equation induces relatively strong positive correlations between successive first-passage times, with Pearson coefficient p approximate to 0.5. These correlations only appear, however, when there is telegraphic switching between two significantly different transport scenarios, and we show that it arises from the underlying physics of the model. We also find that, in order for correlations to appear, the switching rate. must be much smaller than gamma.