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Recent advances have attracted attention to non-standard Josephson junctionsin which a supercurrent can flow despite zero phase difference between theconstituent superconducting leads. Here, we propose a zero-phase-differencenanoelectromechanical junction which, in contrast to other considered systems,exhibits symmetry between leftward and rightward tunneling through thejunction. We show that a supercurrent is nevertheless possible as a result ofspontaneous symmetry breaking. In the suggested junction, the supercurrent ismediated by tunneling via a superconducting Cooper-pair box on a bendablecantilever. An alternating electric potential parametrically excites mechanicaloscillations which are synchronized with charge oscillations of the box. Thisleads to coherent transfer of Cooper pairs through the junction. The directionof the supercurrent is a result of spontaneous symmetry breaking and thus itcan be reversed without changing the parameters.

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