Spin-orbit Josephson $\phi_{\mathrm{0}}$-junction in nanowire quantum dots

The Josephson effect describes supercurrent flowing through a junction connecting two superconducting leads by a thin barrier[1]. This current is driven by a superconducting phase difference $\phi $ between the leads and it is strictly zero when $\phi $ vanishes, due to the chiral and time reversal symmetry of the Cooper pair tunneling process[2]. Only if these underlying symmetries are broken the supercurrent for $\phi \quad =$ 0 may be finite[3]. This corresponds to a ground state of the junction being offset by a phase $\phi_{\mathrm{0}}$. Here, for the first time, we report such Josephson $\phi_{\mathrm{0}}$-junction. Our realization is based on a nanowire quantum dot. We use a quantum interferometer device in order to investigate phase offsets and demonstrate that $\phi_{\mathrm{0}}$ can be controlled by electrostatic gating. Our results have possible far reaching implications for superconducting flux and phase defined quantum bits as well as for exploring topological superconductivity in quantum dot systems. 1. Josephson, \textit{Phys. Lett.} \textbf{1,} 251--253 (1962). 2. Yip, S.-K., De Alcantara Bonfim, O. F. {\&} Kumar, P., \textit{Phys. Rev. B} \textbf{41,} 11214--11228 (1990). 3. Zazunov, A., Egger, R., Jonckheere, T. {\&} Martin, T.,\textit{Phys. Rev. Lett.} \textbf{103,} 147004 (2009).