Four-band model for oxygen holes in copper oxide superconductors. II. Phase diagram

Transport in the doped lamellar copper oxides is carried by quasiparticles, composed of holes which move on the oxygen ions on the ${\mathrm{CuO}}_2$ planes, with strong magnetic coupling to the neighboring Cu spins. In the preceding paper, we calculated the bands of these quasiparticles. In the present paper, we use the lowest of these bands to obtain the critical temperature ${\mathit{T}}_{\mathit{c}}$ as a function of the concentration of holes in these planes, using simple BCS equations. We find that the pairing interaction induced by the magnetic frustration model of Aharony et al. yields a phase diagram which is quite similar to the one observed experimentally, provided that one allows hopping between the planes, of order 0.03 eV. We discuss the variation of the phase diagram with the different hopping and interaction parameters. Some features should apply beyond the scope of our specific model.