Fluctuating order parameter in doped cuprate superconductors

We discuss static fluctuations of the d-wave superconducting order parameter $\mathrm{\Delta }$ in CuO${}_2$ planes, due to quasiparticle scattering by charged dopants. The analysis of two-particle anomalous Green functions at $T=0$ permits to estimate the mean-square fluctuation ${\delta }^2=<{\mathrm{\Delta }}^2>-<\mathrm{\Delta }{>}^2$, averaged in random dopant configurations, to the lowest order in doping level $c$. Since $\mathrm{\Delta }$ is found to saturate with growing doping level while $\delta$ remains to grow, this can explain the collapse of $T_c$ at overdoping. Also we consider the spatial correlations $<\mathrm{\Delta }(0)\mathrm{\Delta }(\mathbf{R})>$ for order parameter in different points of the plane.