Interplay of D-wave Superconductivity and Antiferromagnetism in the   Cuprate Superconductors: Phase Separation and the Pseudogap Phase Diagram
  To understand the interplay of d-wave superconductivity and antiferromagnetism in the cuprates, we consider a two-dimensional extended Hubbard model with nearest neighbor attractive interaction. Free energy of the homogeneous (coexisting superconducting and antiferromagnetic) state calculated a s a function of the band filling shows a region of of phase separation. The phase separation caused by the intersite attractive force leads to novel insights into salient features of the pseudogap phase diagram. In particular, the upper crossover curve can be identified with the phase separation boundary. At zero temperature, the boundary constitutes a critical point. The inhomogeneity observed in the underdoped cuprates is a consequence of incomplete phase separation. The disorder (inhomogeneity) brings about the disparity between the high pseudogap temperature and the low bulk superconducting transition temperature. 
W. P. Su