Phase diagram of hole-doped high-T_c superconductors: Effects of Cooper-pair phase fluctuations within fluctuation-exchange theory

Using the Hubbard model Hamiltonian we study spin-fluctuation exchange-induced superconductivity of d-wave symmetry. Results are presented for the characteristic temperature T^* at which a gap appears in the spectral density, for T_c^* at which Cooper-pairs are formed, for T_c at which Cooper pairs become phase coherent, and for the superfluid density n_s. We find that, with increasing doping, for x>0.15 the phase coherence energy becomes larger than the Cooper-pair condensation energy. Accordingly, one has T_c∝n_s for x<0.15 and T_c∝Δ for the overdoped cuprates. We use our results to discuss dynamics and recent dynamical conductivity and ultrafast nonequilibrium measurements.