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A model for high-temperature superconductors incorporatingantiferromagnetism, d-wave superconductivity, and no double lattice-siteoccupancy can give energy surfaces exquisitely balanced betweenantiferromagnetic and superconducting order for specific ranges of doping andtemperature. The resulting properties can reconcile a universal cuprate phasediagram with rich inhomogeneity, relate that inhomogeneity to pseudogaps, givea fundamental rationale for giant proximity effects and other emergentbehavior, and provide an objective framework for separating essential fromperipheral in the superconducting mechanism.

Inhomogeneity, dynamical symmetry, and complexity in high-temperature superconductors: Reconciling a universal phase diagram with rich local disorder