Instabilities of doped Mott insulators and the properties of high-temperature superconductors

Copper oxides become superconductors rapidly upon doping with electron holes, suggesting a fundamental pair-condensation instability. The Cooper mechanism explains normal superconductivity as an instability of a fermi-liquid state, but high-temperature superconductors derive from a Mott-insulator normal state, not a fermi liquid. We show that competing antiferromagnetism and d-wave pairing on a singly-occupied lattice implies two fundamental instabilities having large implications for superconducting and pseudogap states in the cuprates. The first instability generalizes the Cooper mechanism to doped Mott insulators; the second instability implies that for intermediate ranges of doping the ground states become exquisitely sensitive to external perturbations, permitting rich disorder even for a universal phase diagram.