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

Abstract

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 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 ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}\ifmmode\pm\else\textpm\fi{}i{d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$. With increasing tetragonal distortion, the time-reversal symmetry-breaking phase is suppressed, giving way to only ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ or ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ single-component phases. Based on these results, we propose that a time-reversal symmetry-breaking superconducting state may be found in cubic systems with pairing driven by antiferromagnetic fluctuations.