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We propose a new phase of matter, an electronic phase separation transitionthat starts near the upper pseudogap and segregates the holes into high and lowdensity domains. The Cahn-Hilliard approach is used to follow quantitativelythis second order transition. The resulting grain boundary potential confinesthe charge in domains and favors the development of intragrain superconductingamplitudes. The zero resistivity transition arises only when the intergrainJosephson coupling $E_J$ is of the order of the thermal energy and phaselocking among the superconducting grains takes place. We show that thisapproach explains the pseudogap and superconducting phases in a natural way andreproduces some recent scanning tunneling microscopy data

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