Implications of XY-Critical Point Behavior for the Properties of High-Tc Cuprates

The analysis presented here affords a new perspective on the implications of the phase diagram and the nature of the superconducting state in cuprate superconductors. We invoke the mapping of this state onto the anisotropic three-dimensional (3D)-XY model, supplemented by the experimental doping dependence, the effective mass anisotropy parameter and the fact that the cuprates undergo an insulator-to-superconductor and superconductor-to-normal-state transition at zero temperature. On this basis we show that the materials undergo at zero temperature a crossover from Bose-Einstein condensation to BCS-type behavior as the hole concentration increases from the underdoped to the overdoped limit, combined with a dimensional crossover from 2D-XY to anisotropic 3D-XY critical behavior. Moreover, using the critical properties and the phase transition line, we estimate the doping dependence of the penetration depth lambda, transverse correlation length, and specific heat singularity, in remarkable agreement with the available experimental data. The resulting relation between transition temperature and lambda**(-2) reveals the generic significance of this scenario.