The theory of local superconductivity and phase separation applied to cuprates

In this paper we present a theory of the high critical temperature superconductors (HTSC). As has been shown directly by Scanning Tunneling Microscopy (STM) and indirectly by neutron diffraction, these materials are not homogeneous. We suppose that, at temperatures detected by some experiments, these compounds go through a phase separation which essentially creates regions with low and large doping around the average doping level. Using a Bogoliubov-deGennes local theory, we calculate the superconducting local gap as function of the density, for islands with 10-14 lattice parameters on average. We argue that this procedure is suitable to explain many HTSC properties and their universal phase diagram.