The superconducting phase diagram in a model for tetragonal and cubic systems with strong antiferromagnetic correlations

We calculate the superconducting phase diagram as a function of temperature and z-axis anisotropy in a model for tetragonal and cubic systems having strong antiferromagnetic fluctuations. The formal basis for our calculations is the fluctuation exchange approximation (FLEX) applied to the single-band Hubbard model near half-filling. For nearly cubic lattices, two superconducting phase transitions are observed as a function of temperature with the low-temperature state having the time-reversal symmetry-breaking form, $d_{x^2 - y^2} \pm id_{3z^2 -r^2}$. With increasing tetragonal distortion the time-reversal-symmetry-breaking phase is suppressed giving way to only $d_{x^2 - y^2}$ or $d_{3z^2 -r^2}$ single-component phases. Based on these results, we propose that CeIn$_3$ is a candidate for exhibiting a time-reversal symmetry-breaking superconducting state.