Pseudo-Gap Phase, the Quantum-Critical Point and superconductivity in Copper-Oxide Metals

A systematic solution of a general model for Copper-Oxides reveals a line of transitions T = Tp(x) for x, the doping away from half-filling less than a critical value, to a phase with broken time reversal and rotational symmetry but with translational symmetry preserved. The single-particle spectrum in this phase is calculated to have a gap of dx2−y2 symmetry. The properties in this phase are compared to the properties of the so called ”pseudogap phase” in the Copper-Oxides. The fluctuations towards this phase promote superconductivity which is either of the dx2−y2 or the generalised s-symmetry depending on whether the projected density of states at the chemical potential is larger in the dx2−y2 channel, as in the hole-doped copper-oxides, or in the s-wave channel.