We study the spectral function of a two-dimensional superconductor in a regime of strong phase fluctuations. Although the developed approach is valid for any symmetry, we concentrate on
d-wave superconductors. We obtain analytical expressions for the single electron Green's function below the transition temperature and have worked out a way to extrapolate it for a finite temperatures above
Tc. The suggested approach is easily generalizable for other models with critical fluctuations.
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.