Abstract
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.
Highlights
After 30 years history of extremely intensive experimental [1,2,3,4] and theoretical [5,6,7,8,9,10] studies of the hightemperature superconductivity (HTSC) in copper oxides we are still far from understanding the basic mechanism of this fascinating phenomenon
We developed a picture of HTSC based on the existence of a quantum critical point at the crossing of the ground state energies in the N = 2, 3, 4 sectors within the plaquette for parameters close to the optimal doping, t being of crucial importance
Contrary to the original resonating valence bond (RVB) theory of Anderson [6], we start with the local valence bond formation in the doped plaquette
Summary
After 30 years history of extremely intensive experimental [1,2,3,4] and theoretical [5,6,7,8,9,10] studies of the hightemperature superconductivity (HTSC) in copper oxides we are still far from understanding the basic mechanism of this fascinating phenomenon. The main aim of this work is to present a simple and transparent strong coupling theory of the dx2−y2 -wave superconductivity, i.e. a minimal consistent many-body model, based on the plaquette energy spectrum peculiarity, namely the “quantum critical point”, that merges two singlets and two doublets. These states of the doped plaquette are different from those discussed in the resonating valence-bond theory [6, 12].
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