Position-dependent effect of non-magnetic impurities on superconducting properties of nanowires

Anderson's theorem states that non-magnetic impurities do not change the bulk properties of conventional superconductors. However, as the dimensionality is reduced, the effect of impurities becomes more significant. Here we investigate superconducting nanowires with diameter less than the superconducting coherence length by using a microscopic description based on the Bogoliubov-de Gennes method. We find that: 1) impurities strongly affect the superconducting properties, 2) the effect is impurity position-dependent, and 3) it exhibits opposite behavior for resonant and off-resonant wire widths. We show that this is due to the interplay between the shape resonances of the order parameter and the sub-band energy spectrum induced by the lateral quantum confinement. These effects can be used to manipulate the Josephson current, filter electrons by subband and investigate the symmetries of the superconducting subbands.