Superconductivity and antiferromagnetism in an extended Gutzwiller approximation for t-J model:: Effect of double-occupancy exclusion

The ground state of two-dimensional t-J model including superconductivity and antiferromagnetism is studied using a new type of analytic estimation of the effect of strong correlation. The method is an extension of the Gutzwiller approximation which gives renormalization of parameters, t and J, due to the Gutzwiller projection operator excluding double occupancies. It is shown that the essential point of the renormalization is its dependence on the expectation values of superconductivity and antiferromagnetic moment. In special the renormalization factor is anisotropic in spin space, which leads to a reliable estimate of antiferromagnetic order parameters in the phase diagram, in contrast to the conventional slave-boson mean-field theory. The obtained phase diagram shows the coexistence of antiferromagnetism and d(x)(-y)(2)(2)-wave superconductivity for the doping rate, delta, less than 10%. At half-filling, the renormalization of the J-term represents some aspects of quantum spin nature. For the finite doping case, there are two kinds of superconducting order parameters. The variational order parameter of the dwave superconductivity increases as the doping rate decreases, which will correspond to the experimentally observed superconducting gap. In contrast, the actual expectation value of superconducting order parameter is proportional to delta in underdoped region and has a maximum near delta = 0.11, which probably determines T-c. We also speculate that the ground-state antiferromagnetic order, being destroyed at finite temperatures, gives the energy and temperature scale of the pseudogap. Applications to the inhomogeneous systems such as the vortex state and stripe state are discussed.