Plaquette Valence Bond Theory of Cuprate High-Temperature Superconductivity

We investigate the phenomenon of high-temperature superconductivity within a strong coupling perspective. The occurence is traced to a quantum critical point that is in the phase diagram of the plaquette's t; t0-Hubbard model. We develop a bottom-up approach combining several methods, i.e. exact diagonalization of an isolated plaquette, the Lanczos-method for a plaquette within a bath and cluster dynamical Mean-Field theory with continuous time quantum Monte-Carlo solver to embedd the plaquette in a lattice environment. The quantum critical point is located where the N = 2; 3; 4-sectors of the plaquette cross. This point is also found to show optimal doping. The wave order turns out to be largest at the localized-itinerant transition of the electrons. Furthermore, we present an explenation for the pseudo-gap phenomenon, that is explained by a soft mode related to local singlets of the plaquette. The theory presented here is similar to the resonating valence bond theory, but stresses the importance of local singlets.