Superconductivity and types of gap in high-Tc cuprates

This paper extends the two-local-spin-mediated interaction from three- to four-band model, gives two T-c formulas using long-range phase coherence condition in quantum and classical XY-models, phase diagram, and types of the gap in Bi2Sr2CaCu2O8+delta (Bi2212). This paper argues that the superconducting gap and the pseudogap are the same gap just at different temperature regions. This paper also argues that the values of T-c versus x should be determined by the long-range phase coherence conditions in the classical and quantum XY-model for underdoped and overdoped regions, respectively.