Phase separation and the phase diagram of cuprate superconductors

We show that the main features of the cuprate superconductor phase diagram can be derived considering the disorder as a key property of these materials. Our basic point is that the high pseudogap line is an onset of phase separation which generates compounds made up of regions with distinct doping levels. We calculate how this continuous temperature dependent phase separation process occurs in high critical temperature superconductors (HTSC) using the Cahn-Hilliard approach, originally applied to study alloys. Since the level of phase separation varies for different cuprates, it is possible that different systems with average doping level pm exhibit different degrees of charge and spin segregation. Calculations on inhomogeneous charge distributions in the form of stripes on finite clusters performed by the Bogoliubov-de Gennes superconducting approach yield good agreement between the onset of local pairing amplitude and the pseudogap temperature T*(pm). Assuming that the local order parameters generated at these clusters have their phase locked, we can follow how the superconducting phase develops at Tc(pm) by possible percolation or Josephson coupling.