The role of disorder symmetry in a dirty superconductor: a Bogoliubov-deGennes (BdG) study

We study the effect of disorder symmetry in a disordered s-wave superconductor. We begin with an attractive Hubbard model on a two-dimensional square lattice in the presence of diagonal- and off-diagonal disorder. The model is studied numerically using Bogoliubov-deGennes mean-field approach. We find that the off-diagonal disorder is much more efficient in destroying superconducting order. A detailed analysis brings out very distinct qualitative pictures in the two cases: diagonal disorder leads to formation of small scale isolated superconducting islands separated by large region of normal metal, whereas off-diagonal disorder leads to a connected network of superconducting region. Naively, it seems that the connected network of superconducting regions should have a large average value for superconducting order parameter, but this does not hold true for large disorder, as we demonstrate explicitly. Our qualititive picture is supported by real-space data on local order parameters.