Polaronic effects and thermally enhanced weak superconductivity

We theoretically analyze the d.c Josephson current between two superconductors connected by a vibrating weak link. Assuming the weak link to be a “quantum dot” we predict that the critical current is thermally enhanced at low temperatures if the electron-vibron interaction is strong and has an anomalous temperature dependence in a large temperature interval. We estimate that this unusual behavior, which occurs because the current through the weak link is carried by “polaronic” Andreev states, is measurable in experiments on, e.g., carbon-nanotube based Josephson junctions.