Transient dynamics and steady state behavior of the Anderson–Holstein model with a superconducting lead

Author-Highlights•We calculate the transient current of an Anderson model with a superconducting lead.•We compare an analytical and Monte Carlo approach. •We include electron–phonon interaction.•We make predictions for the behavior in the deep Kondo limit.

We analyze the nonequilibrium dynamics and steady-state behavior of the two-terminal Anderson–Holstein model with a superconducting and a normal conducting lead. In the deep Kondo limit we develop an analytical description if no phonons are included and a rate equation approach when phonons are present. Both cases are compared with the numerically exact diagrammatic Monte Carlo method obtaining a good agreement. For small voltages we find a pronounced enhancement of phonon sidebands due to the SC DOS.