Cooper pairs without "glue" in high-T_c superconductors: A universal phase diagram

The phase diagram of high-T _c cuprates can be understood, without resorting to a boson mode, in terms of a single energy scale $\sim J$, the antiferromagnetic (AF) exchange energy at the metal-insulator transition. As a result, holes form a new quantum object, the "pairon", i.e., a pair of holes localized within their local antiferromagnetic environment on the scale of the finite AF correlation length, ${\xi }_{AF}$. In the incoherent pseudogap phase, above T _c or within the vortex core, the pairon binding energies are distributed statistically, forming a "Cooper-pair glass". Contrary to conventional superconductors it is the mutual pair-pair interaction that is responsable for their condensation. We give a natural explanation for the ergodic rigidity of the excitation gap, the latter being constant with respect to a perturbation such as temperature or magnetic field, and determined only by the carrier concentration p and J. (letter)