Polaron effects on the dc- and ac-tunneling characteristics of molecular   Josephson junctions
  We study the interplay of polaronic effect and superconductivity in transport through molecular Josephson junctions. The tunneling rates of electrons are dominated by vibronic replicas of the superconducting gap, which show up as prominent features in the differential conductance for the dc and ac current. For relatively large molecule-lead coupling, a features that appears when the Josephson frequency matches the vibron frequency can be identified with an over-the-gap structure observed by Marchenkov et al. [Nat. Nanotech. 2, 481 (2007)]. However, we are more concerned with the weak-coupling limit, where resonant tunneling through the molecular level dominates. We find that certain features involving both Andreev reflection and vibron emission show an unusual shift of the bias voltage V at their maximum with the gate voltage V_g as V ~ (2/3) V_g. Moreover, due to the polaronic effect, the ac Josephson current shows a phase shift of pi when the bias eV is increased by one vibronic energy quantum hbar omega_v. This distinctive even-odd effect is explained in terms of the different sign of the coupling to vibrons of electrons and of Andreev-reflected holes. 
B. H. Wu, J. C. Cao, and C. Timm
cond-mat.mes-hall cond-mat.supr-con