Role of Spatial Amplitude Fluctuations in Highly Disordereds-Wave Superconductors

The effect of nonmagnetic impurities on 2D $s$-wave superconductors is studied beyond the weak disorder regime. Within the Bogoliubov–de Gennes (BdG) framework, the local pairing amplitude develops a broad distribution with significant weight near zero with increasing disorder. Surprisingly, the density of states continues to show a finite spectral gap. The persistence of the spectral gap at large disorder is shown to arise from the breakup of the system into superconducting “islands.” Superfluid density and off-diagonal correlations show a substantial reduction at high disorder. A simple analysis of phase fluctuations about the highly inhomogeneous BdG state is shown to lead to a transition to a nonsuperconducting state.