Dynamical chiral symmetry breaking and phase transition of cuprate superconductors in QED3

With the coupled Dyson-Schwinger equations in the framework of the unified QED(3) theory, we study the phase transition between the antiferromagnet(AF) and the d-wave superconductor (dSC) of planar cuprates at T=0. By solving the coupled Dyson-Schwinger equations both analytically and numerically in rainbow approximation in Landau gauge and comparing the obtained results with that given in the 1/N expansion, we find that there exists a chiral symmetry breaking from dSC phase to AF phase when the quasi-fermion flavors N less than or similar to 4 in half-filling and the AF phase can possibly coexist with the dSC phase in the underdoped region. By comparing the pressure between the coexistent AF-dSC phase and dSC phase, we find that AF-dSC coexisting phase is the stable phase, the AF phase can then coexist with the dSC phase.