Transient electron dynamics in a vibrating quantum dot in the Kondo regime

We employ the time-dependent non-crossing approximation to investigate the joint effect of strong electron–electron and electron–phonon interaction on the instantaneous conductance of a single-molecule transistor which is abruptly moved into the Kondo regime by means of a gate voltage. We find that the instantaneous conductance exhibits decaying sinusoidal oscillations on the long timescale for infinitesimal bias. The ambient temperature and electron–phonon coupling strength influence the amplitude of these oscillations. The frequency of the oscillations is found to be equal to the phonon frequency. We argue that the origin of these oscillations can be attributed to the interference between the emerging Kondo resonance and its phonon sidebands. We discuss the effect of finite bias on these oscillations.