Role of quantum confinement in semiconductor-superconductor core-shell nanowires

Abstract

This work is motivated by the experimentally observed coherence of the supercurrent in semiconductor nanowires covered by a half-shell metallic superconductor, which leads to flux dependent supercurrent oscillations with period h/2e, as expected for a tubular superconductor, i.e. Little-Parks oscillations. We perform microscopic model calculations and compare the results for full and half metallic shells. We use an effective Hamiltonian derived from the Green's function of the proximitized semiconductor nanowire, where the presence of the superconductor is represented by a self energy. Furthermore, we incorporate the electrostatic band-bending at the metal-semiconductor interface as a rectangular narrow quantum well on the semiconductor side. The properties of the eigenstates of the effective Hamiltonian are determined by the spatial profile of the corresponding transverse modes in the normal state. For half-shell wires, transverse modes with high-enough energy expand outside the interface quantum well and generate eigenstates with mixed electron-hole character that surround the entire circumference of the nanowire, similar to eigenstates of the full-shell system. We identify these states as being responsible for the observed Little-Parks effect.