Zero-Phase-Difference Josephson Current Based on Spontaneous Symmetry Breaking via Parametric Excitation of a Movable Superconducting Dot

Recent advances have attracted attention to nonstandard 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 mechanical resonator. 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.

Figure 1

(a) Schematic illustration of the system. A superconducting quantum dot (gray sphere) can mechanically oscillate in the gap between two superconducting leads (gray blocks). Cooper pairs can tunnel to and from the quantum dot from both sides of the gap. An alternating voltage applied to the gate (yellow) modulates the charge on the dot, leading to a parametric excitation of mechanical vibrations. The mechanical oscillator can be realized by, e.g., (b) a bendable nanowire with a superconducting seed (gray sphere), or (c) a superconducting quantum dot (gray rectangle) on a suspended nanobeam which can oscillate laterally. (Brown components are insulating.)

Figure 2

The dynamics in charge ($q$) and position ($x$) space are automatically synchronized by the parametric excitation. The charge oscillations follow the driving field. The position has two possible oscillatory solutions which are out of phase with the driving field by approximately $\pm \pi /2$. Therefore, the time evolution in charge-position space is (a) clockwise or (b) counterclockwise. These “chiral states” coherently transfer Cooper pairs across the junction, leading to a supercurrent (a) to the right ($J_{+}$) or (b) to the left ($J_{-}$).

Figure 3

The effective mechanical-energy landscape in the frame rotating with the electric driving field. Small damping will drag the system down to one of the two stable states ${\rho }_{\pm }$. In these states, the system performs synchronized electronic and mechanical oscillations which generate a supercurrent. The direction of the supercurrent is opposite for ${\rho }_{+}$ and ${\rho }_{-}$. Stochastic fluctuations may therefore reverse the supercurrent by inducing transitions between the two states. The landscape is plotted for $\mu =0.2$. Note that $g(P,X)=g(-P,X)$.