Junctions created by coupling two superconductors via a semiconductor nanowire in the presence of high magnetic fields are the basis for the potential detection, fusion, and braiding of Majorana bound states. We study NbTiN/InSb nanowire/NbTiN Josephson junctions and find that the dependence of the critical current on the magnetic field exhibits gate-tunable nodes. This is in contrast with a well-known Fraunhofer effect, under which critical current nodes form a regular pattern with a period fixed by the junction area. Based on a realistic numerical model we conclude that the Zeeman effect induced by the magnetic field and the spin-orbit interaction in the nanowire are insufficient to explain the observed evolution of the Josephson effect. We find the interference between the few occupied one-dimensional modes in the nanowire to be the dominant mechanism responsible for the critical current behavior. We also report a strong suppression of critical currents at finite magnetic fields that should be taken into account when designing circuits based on Majorana bound states.

The Josephson effect describes supercurrent flowing through a junction connecting two superconducting leads by a thin barrier. This current is driven by a superconducting phase difference φbetween the leads. In the presence of chiral and time-reversal symmetry of the Cooper pair tunnelling process, the current is strictly zero when φvanishes. Only if these underlying symmetries are broken can the supercurrent for φ= 0 be finite. This corresponds to a ground state of the junction being offset by a phase φ0, different from 0 or π. Here, we report such a Josephson φ0 -junction based on a nanowire quantum dot. We use a quantum interferometer device to investigate phase offsets and demonstrate that φ0 can be controlled by electrostatic gating. Our results may have far-reaching implications for superconducting flux- and phase-defined quantum bits as well as for exploring topological superconductivity in quantum dot systems.