Proximity-induced gap in nanowires with a thin superconducting shell

Coupling a normal-metal wire to a superconductor induces an excitation gap Δ_(ind) in the normal metal. In the absence of disorder, the induced excitation gap is strongly suppressed by finite-size effects if the thickness D_S of the superconductor is much smaller than the thickness D_N of the normal metal and the superconducting coherence length ξ. We show that the presence of disorder, either in the bulk or at the exposed surface of the superconductor, significantly enhances the magnitude of Δ_(ind), such that Δ_(ind) approaches the superconducting gap Δ in the limit of strong disorder. We also discuss the shift of energy bands inside the normal-metal wire as a result of the coupling to the superconducting shell.