Coexistence of superconductivity with quadrupole order in a Γ₃ system

Superconductivity in a model on a cubic lattice for a Γ₃ non-Kramers system is discussed. In our previous studies, we have found that d-wave superconductivity with E_g symmetry occurs in a wide parameter range in a Γ₃ system. In such an anisotropic superconducting state, the cubic symmetry of the system can be broken. Since the quadrupole degrees of freedom is active in a Γ₃ system, the effect of cubic symmetry breaking should be important. In d_x²-y² or d_3z²-r² superconducting state, a ferroquadrupole moment of O₂⁰ = 3z² - r² becomes finite. In this study, we investigate the coexisting states of the superconductivity and ferroquadrupole order of O₂⁰ by a mean-field theory. Then, we find that superconducting transition temperature can be increased by the quadrupole ordering. (author)