Orbital Josephson interference in a nanowire proximity-effect junction

Abstract

A semiconductor nanowire based superconductor-normal-superconductor (SN S) junction is modeled theoretically. A magnetic field is applied along the nanowire axis, parallel to the current. The Bogoliubov-de Gennes equations for Andreev bound states are solved while considering the electronic subbands due to radial confinement in the N -section. The energy-versus-phase curves of the Andreev bound states shift in phase as the N -section quasiparticles with orbital angular momentum couple to the axial field. A similar phase shift is observed in the continuum current of the junction. The quantum mechanical result is shown to reduce to an intuitive, semi-classical model when the Andreev approximation holds. Numerical calculations of the critical current versus axial field reveal flux-aperiodic oscillations that we identify as a novel form of Josephson interference due to this orbital subband effect. This behavior is studied as a function of junction length and chemical potential. Finally, we discuss extensions to the model that may be useful for describing realistic devices.The Josephson effect is characterized by a currentphase relationship (CPR) linking macroscopic current flow to the phase gradient of the superconducting order parameter1 . The precise form of the CPR for a superconducting weak link depends on intrinsic factors such as junction geometry, material properties, coherence lengths, etc., in addition to extrinsic variables like temperature and magnetic field. In superconductor-normalsuperconductor (SN S) junctions in which the N -section is long enough to suppress direct tunnelling of Cooper pairs, but shorter than the N -section phase coherence length, a supercurrent may be carried by quasiparticles undergoing Andreev reflection at the S-N interfaces 2-5 . Planar SN S junctions of width large compared to the S-section superconducting coherence length have been studied in great detail 6 (width refers to the dimension perpendicular to the current). These have revealed, for example, Fraunhofer oscillations of the critical current I c with respect to an externally applied out-of-plane magnetic field 7-9 . For junction widths comparable to the S-section coherence length, i.e. the narrow junction limit, this becomes a quasi-Gaussian, monotonic decay of the critical current 7,10,11 . Recently, attention has been given to nanoscale, quasi one-dimensional (1D) SN S junctions, such as those readily engineered by contacting semiconductor nanowires with superconducting leads [12][13][14][15][16] . Gating the semiconducting N -section allows for modulating the supercurrent by controlling the chemical potential 12,15 . The oscillations of the magnetoresistance of a nanowire SN S junction in the voltage-biased state (i.e. no dc supercurrent) versus an axial magnetic field have been studied 16 . Efforts to realize Majorana fermion quasiparticles in 1D semiconductors with strong spin-orbit interaction and proximity coupling to a superconductor 17-20 have further raised interest in this type of junction. Theoretical resul...

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