A comprehensive model for high-$T_c$ based on pair-pair interactions.

The superconducting (SC) state of cuprates is characterized by a dome-shaped $T_c$ versus carrier density and an unconventional {\it pseudogap} (PG) state above $T_c$ - basic properties remain highly debated. We have recently proposed a mechanism [1] based on the mutual interaction between incoherent Cooper pairs existing above $T_c$. At the critical temperature, this interaction induces a Bose-like condensation leading to the coherent SC state. \\ Absent in the conventional BCS case, the mutual pair-pair interaction is proportional to the condensate density $n_{oc}(T)$ but is also related to the quasiparticle excitations. It gives an excellent fit to the DOS as measured by electron tunneling for a wide range of samples and carrier concentration. We conclude that long-range order is achieved by a direct quasiparticle - Cooper-pair coupling. \\ We then focus on the {\it temperature dependence} of the thermodynamic functions (condensation energy, entropy, etc.) and of the quasiparticle DOS. We show that these quantities depend on the unique combination of pair (boson) and quasiparticle (fermion) excitations, allowing a qualitative understanding of the phase diagram.\\ [1] W. Sacks, A. Mauger, Y. Noat, Superconduct. Sci.Technol. {\bf 28} 105014, 2015