Role of Spatial Amplitude Fluctuations in Highly Disordered s-Wave   Superconductors
  The effect of non-magnetic 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 break up 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 in the highly inhomogeneous BdG state is shown to lead to a transition to a non-superconducting state. 
Amit Ghosal, Mohit Randeria and Nandini Trivedi (Tata Institute of   Fundamental Research)