Zero-phase-difference Josephson current based on spontaneous symmetry-breaking via parametric excitation of a movable superconducting dot

Recent advances have attracted attention to non-standard Josephson junctions in which a supercurrent can flow despite zero phase difference between the constituent superconducting leads. Here, we propose a zero-phase-difference nanoelectromechanical junction which, in contrast to other considered systems, exhibits symmetry between leftward and rightward tunneling through the junction. We show that a supercurrent is nevertheless possible as a result of spontaneous symmetry breaking. In the suggested junction, the supercurrent is mediated by tunneling via a superconducting Cooper-pair box on a bendable cantilever. An alternating electric potential parametrically excites mechanical oscillations which are synchronized with charge oscillations of the box. This leads to coherent transfer of Cooper pairs through the junction. The direction of the supercurrent is a result of spontaneous symmetry breaking and thus it can be reversed without changing the parameters.