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There has been considerable effort expended toward understanding high temperature superconductors (HTSC), and more specifically the cuprate phase diagram as a function of doping level. Yet, the only agreement seems to be that HTSC is an example of a strongly correlated material where Coulomb repulsion plays a major role. This manuscript proposes a model based on a Feshbach resonance pairing mechanism and competing orders. An initial BCS‐type superconductivity at high doping is suppressed in the two particle channel by a localized preformed pair (PP) (Nozieres and Schmitt‐Rink, J Low Temp Phys, 1985, 59, 980) (circular density wave) creating a quantum critical point. As doping continues to diminish, the PP then participates in a Feshbach resonance complex that creates a new electron (hole) pair that delocalizes and constitutes HTSC and the characteristic dome (Squire and March, Int J Quantum Chem, 2007, 107, 3013; 2008, 108, 2819). The resonant nature of the new pair contributes to its short coherence length. The model we propose also suggests an explanation (and necessity) for an experimentally observed correlated lattice that could restrict energy dissipation to enable the resonant Cooper pair to move over several correlation lengths, or essentially free. The PP density wave is responsible for the pseudogap as it appears as a “localized superconductor” since its density of states and quasiparticle spectrum are similar to those of a superconductor (Peierls–Fröhlich theory), but with no phase coherence between the PP. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

international journal of quantum chemistry

HTSC cuprate phase diagram using a modified Boson–Fermion–Gossamer model describing competing orders, a quantum critical point and possible resonance complex