Josephson Interference due to Orbital States in Nanowire Proximity Effect Junctions

The Josephson effect in a nanowire-based superconductor-normal-superconductor ($SNS$) junction is studied theoretically and experimentally, focusing on the effects of nanoscale confinement on the current-phase relationship of the junction. An axial external magnetic field is applied. The theory of a previously unstudied type of Josephson interference is described, based on the coupling between the axial flux and $N$-section Andreev quasiparticles (continuum states or bound states) occupying subbands of non-zero orbital angular momentum. The Bogoliubov-de Gennes equations are solved while considering the transverse subbands in the $N$-section, yielding energy-versus-phase curves that are shifted in phase in the presence of the flux. A similar phase shift is observed in the continuum current of the junction. An intuitive, semi-classical version of the theory is presented. The critical current $I_c$ of the junction is numerically calculated, and shown to oscillate versus the axial flux. Experimental observations of the oscillations of $I_c$ in an Nb-InAs nanowire-Nb junction are reported. It is shown that the observed oscillations can be described by the semi-classical picture. The scope and applicability of the theory to experimental devices is discussed.