Flux-tunable supercurrent in full-shell nanowire Josephson junctions

Full-shell nanowires formed by a semiconducting core fully wrapped by an epitaxial superconducting shell, have recently been introduced as promising hybrid quantum devices. Despite this, however, their properties when forming a Josephson junction (JJ) have not been elucidated yet. We here fill this void by theoretically studying the physics of JJs based on full-shell nanowires. In the hollow-core limit, where the thickness of the semiconducting layer can be ignored, we demonstrate that the critical supercurrent ${I}^{\text{c}}$ can be tuned by an external magnetic flux $\mathrm{\ensuremath{\Phi}}$. Specifically, ${I}^{\text{c}}(\mathrm{\ensuremath{\Phi}})$ does not follow the Little-Parks modulation of the superconducting pairing $\mathrm{\ensuremath{\Delta}}(\mathrm{\ensuremath{\Phi}})$ and exhibits steps for realistic values of nanowire radii. The position of the steps can be understood from the underlying symmetries of the orbital transverse channels contributing to the supercurrent.