Influence of thermal phase fluctuations on the spectral density function in a 2D d-wave superconductor

We present the study of the spectral density for a two-dimensional superconductor in a regime of strong phase fluctuations. The focus of the talk is on $d$-wave superconductors. We obtain analytical expressions for the Green function below the transition temperature and have worked out a way to extrapolate it for a finite temperatures above $T_c$. The quasi-classical approximation is inapplicable in the vicinity of the nodes of the order parameter. We have summed the most singular terms of the perturbation theory in pairing potential. Along with analytical expressions we present the qualitative features of the spectral function.