Interplay of D-wave Superconductivity and Antiferromagnetism in the Cuprate Superconductors.pdf

a r X i v : c o n d - m a t / 0 5 0 8 4 2 6 v 1 [ c o n d - m a t .s u p r - c o n ] 1 8 A u g 2 0 0 5 Interplay of D-wave Superconductivity and Antiferromagnetism in the Cuprate Superconductors: Phase Separation and the Pseudogap Phase Diagram W. P. Su Department of Physics and Texas Center for Superconductivity, University of Houston, Houston, Texas 77204 Abstract To understand the interplay of d-wave superconductivity and antiferro- magnetism in the cuprates, we consider a two-dimensional extended Hubbard model with nearest neighbor attractive interaction. Free energy of the homo- geneous (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 up- per crossover curve can be identified with the phase separation boundary. At zero temperature, the boundary constitutes a critical point. The inhomogene- ity 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. PACS numbers: 74.20.-z, 74.72.-h, 74.25.Ha Typeset using REVTEX 1 I. Introduction The phase diagram1,2 of the cuprates highlights the unusual physics of the cuprates, as such it constitutes a touchstone of high-Tc theory. Particularly intriguing is the mystery surrounding the nature of the pseudogap phase. How is that phase related to the unusual superconducting phase with the characteristic inhomogeneities3? How are all those related to the antiferromagnetic correlation which seems to coexist4,5 with superconducitivty? To address those questions, we consider an effective model for antiferromagnetism and d-wave superconductivity: the t-U-V-W model. This model6,7 is a slight extension