We investigate on the same footing the time-dependent electronic transport properties and vibrational dynamics of a molecular junction. We show that fluctuations of both the molecular vibron displacement and the electronic current across the junction undergo damped oscillations toward the steady state. We assign the former to the onset of electron tunneling events assisted by vibron emission. The time-dependent buildup of electron-hole correlations is revealed as a departure of the charge-transfer statistics from the generalized-binomial one after a critical time $t_c$. The phonon backaction on the tunneling electrons is shown to amplify and accelerate this buildup mechanism.

• Received 30 December 2018

DOI:https://doi.org/10.1103/PhysRevB.99.121403