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Bose-Einstein condensation in the pseudogap phase of cuprate superconductors

We have identified the unscreened Froehlich electron-phonon interaction (EPI) as the most essential for pairing in cuprate superconductors as now confirmed by isotope substitution, recent angle-resolved photoemission (ARPES), and some other experiments. Low-energy physics is that of mobile lattice polarons and bipolarons in the strong EPI regime. Many experimental observations have been predicted or explained in the framework of our "Coulomb-Froehlich" model, which fully takes into account the long-range Coulomb repulsion and the Froehlich EPI. They include pseudo-gaps, unusual isotope effects and upper critical fields, the normal state Nernst effect, diamagnetism, the Hall-Lorenz numbers, and a giant proximity effect (GPE). These experiments along with the parameter-free estimates of the Fermi energy and the critical temperature support a genuine Bose-Einstein condensation of real-space lattice bipolarons in the pseudogap phase of cuprates. On the contrary the phase fluctuation (or vortex) scenario is incompatible with the insulating-like in-plane resistivity and the magnetic-field dependence of orbital magnetization in the resistive state of underdoped cuprates.