Non-Markovian waiting-time distribution for electron transport through a vibrating molecular junction

A thorough understanding of electronic transport through molecular junctions in the presence of molecular vibrations is crucial for the technical progress of molecular electronics. In this work, we first develop a non-Markovian formalism to predict the waiting-time distribution (WTD) in terms of a generalized quantum master equation, which is valid for finite bias and temperatures. This formalism is applied to the investigation of electron transport through a vibrating molecule for different parameters, where the WTDs are analyzed to explore non-Markovian dynamics induced by the coupling between the molecule and the electrodes in the presence of mechanical dampings. This analysis reveals that the WTDs exhibit prominent damped oscillations for a small damping, indicating that electron transport is directly modulated by the periodic motion of the molecular vibration for both Markovian and non-Markovian couplings to the electrodes. However, the periodic oscillations are sustained for a much longer time in the presence of non-Markovian dynamics. This intriguing non-Markovian characteristic is gradually washed out by increasing either the bias or the tunneling length because both decrease the electronic correlation time, leading to an effective reduction of the coupling between molecules and electrodes. In contrast, an increasing tunneling rate gives rise to enhanced non-Markovian signatures in the WTD, which feature a strong first peak as more energy is pumped into the molecular vibrations by frequent electron tunneling events.