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Electronic Phase Separation Transition as the Origin of the Superconductivity and the Pseudogap Phase of Cuprates

We propose a new phase of matter, an electronic phase separation transition that starts near the upper pseudogap and segregates the holes into high and low density domains. The Cahn-Hilliard approach is used to follow quantitatively this second order transition. The resulting grain boundary potential confines the charge in domains and favors the development of intragrain superconducting amplitudes. The zero resistivity transition arises only when the intergrain Josephson coupling $E_J$ is of the order of the thermal energy and phase locking among the superconducting grains takes place. We show that this approach explains the pseudogap and superconducting phases in a natural way and reproduces some recent scanning tunneling microscopy data