Gossamer Superconductor Ground State Phase Diagram

Within the t-J-U mode and Gutzwiller mean-field approximation,the ground state phase diagram and the influence of the additional second-neighbor hopping t' on the phase diagram of the copper oxide materials are studied systemically.The paper is organized as follows.In ChapterⅠ,a brief review of the development of cuprate material is given.Then we introduce the t-J-U model which is able to describe the essential low-energy physics of cuprates and the GutzwiUer mean-field approximation which can treat the strong correlation between the electrons properly.Within the t-J-U mode and Gutzwiller mean-field approximation,the phase diagrams of gossamer superconductors are studied in ChapterⅡ:firstly,we study the d-wave superconductivity(dSC) and antiferromagnetism(AF) in a renormalized mean field theory. The phase diagrams as functions of dopingδand U are studied.Using the standard value of t/J=3.0 and in the large U limit,we find that the AF order emerges and coexists with the dSC in the underdoped region below the doping 0.1.The dSC order parameter increases from zero as the doping increases and reaches a maximum near the optimal doping 0.15.In the small U limit,only the dSC order survives while the AF order disappears.As U increases up to a critical value,the AF order shows up and coexists with the dSC in the underdoped regime.At half filling,the system is in the dSC state for small U and becomes an AF insulator for large U.Finally we study the influence of the additional second-neighbor hopping t' on the phase diagram in ChapterⅢ.We find that for the small values of t',the qualitative feature of the ground state phase diagram in the t-t'-J-U model is the same as in the case of the t-J-U model,where the AF order coexists with the dSC in the underdoped region, while the dSC order parameter is slightly suppressed in the underdoped regions,and greatly enhanced in the optimal and overdoped regions with the increasing of the t'.As a result,the coexistence region of the AF and dSC is extended to higher doping and the dSC order persists for a larger doping.Our results are agreement with the recent numerical calculations.