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Pair-pair interactions as a mechanism for high-T$_c$ superconductivity

The mutual interaction between Cooper pairs is proposed as a mechanism for the superconducting state. Above $T_c$, pre-existing but fluctuating Cooper pairs give rise to the unconventional {\it pseudogap} (PG) state, well-characterized by experiment. At the critical temperature, the pair-pair interaction induces a Bose-like condensation of these preformed pairs leading to the superconducting (SC) state. Below $T_c$, both the condensation energy and the pair-pair interaction $β$ are proportional to the condensate density $N_{oc}(T)$, whereas the usual Fermi-level spectral gap $Δ_p$ is independent of temperature. The new order parameter $β(T)$, can be followed as a function of temperature, carrier concentration and disorder - i.e. the phase diagrams. The complexity of the cuprates, revealed by the large number of parameters, is a consequence of the {\it coupling of quasiparticles to Cooper-pair excitations}. The latter interpretation is strongly supported by the observed quasiparticle spectral function.