Theory of the pseudogap state of the cuprates

The phase diagram for a general model for cuprates is derived in a mean-field approximation. A phase-violating time reversal without breaking translational symmetry is possible when both the ionic interactions and the local repulsions are large compared to the energy difference between the Cu and O single-particle levels. It ends at a quantum critical point as the hole or electron doping is increased. Such a phase is necessarily accompanied by singular forward scattering such that, in the stable phase, the density of states at the chemical potential, projected to a particular point-group symmetry of the lattice is zero, producing thereby an anisotropic gap in the single-particle spectrum. It is suggested that this phase occupies the pseudogap region of the phase diagram of the cuprates. The temperature dependence of the single-particle spectra, the density of states, the specific heat, and the magnetic susceptibility are calculated with rather remarkable correspondence with the experimental results. The importance of further direct experimental verification of such a phase in resolving the principal issues in the theory of the cuprate phenomena is pointed out. To this end, some predictions are provided.