Pairing in disordered s-wave superconductors and the effect of their coupling

Inhomogeneity is introduced through random local interactions (UiUi) in an attractive Hubbard model on a square lattice and studied using mean-field Bogoliubov–de Gennes formalism. Superconductivity is found to be suppressed by the random UiUi contrary to the results of a bimodal distribution of UiUi. The proximity effect of superconductivity is found to be strong, all sites develop non-zero pairing amplitude. The gap in the density of states is always non-zero and does not vanish even for strong disorder. When two such superconductors are coupled via a channel, the effect of one on the other is negligible. The length and width of the connector do not seem to have any noticeable effect on the superconductivity in either system. The superconducting blocks behave as independent entities and the introduction of the channel has no effect on them.