Temperature-dependent gap equations and their solutions in the SU(4) model of high-temperature superconductivity

Temperature-dependent gap equations in the SU(4) model of high-Tc superconductivity are derived and analytical solutions are obtained. Based on these solutions, a generic gap diagram describing the features of energy gaps as functions of doping P is presented and a phase diagram illustrating the phase structure as a function of temperature T and doping P is sketched. A special doping point P_q occurs naturally in the solutions that separates two phases at temperature T = 0: a pure superconducting phase on one side (P > P_q) and a phase with superconductivity strongly suppressed by antiferromagnetism on the other (P < P_q). We interpret P_q as a quantum phase transition point. Moreover, the pairing gap is found to have two solutions for P < P_q: a small gap that is associated with competition between superconductivity and antiferromagnetism and is responsible for the ground state superconductivity, and a large gap without antiferromagnetic suppression that corresponds to a collective excited state. A pseudogap appears in the solutions that terminates at P_q and originates from the competition between d-wave superconductivity and antiferromagnetism. Nevertheless, this conclusion does not contradict the preformed pair picture conceptually if the preformed pairs are generally defined as any pairs formed before pairing condensation.