Bose-Einstein condensation of interacting Cooper pairs in cuprate superconductors

The Hartree-Fock-Popov theory of interacting Bose particles is generalized to the Cooper-pair system with a screened Coulomb repulsive interaction in high-temperature superconductors. At zero temperature, we find that the condensate density nc(0) of Cooper pairs and the phonon velocity c(0) are dome-shaped functions of the p hole concentration δ. At finite temperature T, we find that the condensate fraction nc(T)/n and the phonon velocity c(T) decrease continuously from nc(0)/n or c(0) to zero as T increases from zero to the transition temperature Tc. The Cooper-pair system undergoes a first-order phase transition from the normal state to the Bose condensed state.