Electronic phase separation transition as the origin of the superconductivity and pseudogap phase of cuprates

To deal with the physics of cuprate superconductivity we propose an electronic phase separation transition that segregates the holes into high and low density domains. The calculated grain boundary potential 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 takes place among the superconducting grains. We show that this approach explains the pseudogap and superconducting phases and it also reproduces some recent scanning tunneling microscopy data.