Theoretical investigation of the superconducting pairing symmetry in a bilayer two-orbital model of pressurized La${}_3$Ni${}_2$O${}_7$

We investigate the superconducting pairing symmetry in pressurized La${}_3$Ni${}_2$O${}_7$ based on a bilayer two-orbital model. There are two symmetric bands $\alpha$ and $\gamma$, as well as two antisymmetric ones $\beta$ and $\delta$. It is found that the $\gamma$ band induces considerable ferromagnetic spin fluctuation and prefers an odd-frequency, $s$-wave spin triplet pairing state. The addition of the other bands gradually suppresses the ferromagnetic spin fluctuation and enhances the antiferromagnetic ones. The superconducting pairing then evolves from a spin triplet into a $d$-wave spin singlet, and finally into an $s_{\pm }$-wave one. The competition between the $d$-wave and $s_{\pm }$-wave pairings relies on whether the ferromagnetic spin fluctuation is suppressed completely or not.