Possible $S_\pm$-wave superconductivity in La$_3$Ni$_2$O$_7$

Recently, the bulk nickelate La$_3$Ni$_2$O$_7$ is reported to show signature of high-temperature superconductivity under high pressure above $14$GPa [H. Sun et al., Nature 621, 493 (2023)]. We analyze the pairing mechanism and pairing symmetry in a bilayer Hubbard model with two orbitals in the $E_g$ multiplet. In the weak to moderate interaction regime, our functional renormalization group (FRG) calculations yield $S_\pm$-wave Cooper pairing triggered by leading spin fluctuations. The gap function changes sign across the Fermi pockets, and in real space the pairing is dominated by intra-unitcell intra-orbital components with antiphase between the onsite ones. In the strong coupling limit, we develop a low-energy effective theory in terms of atomic one- and two-electron states in the $E_g$ multiplet. The variational treatment of the effective theory produces results consistent with the FRG ones, suggesting the robustness of such a pairing function. The driving force for superconductivity in the strong coupling limit can be attributed to the local pair-hopping term and the spin-exchange on vertical bonds. We also discuss a possible scenario for the weak insulating behavior under low pressures in terms of the tendency toward the formation of charge order in the strong coupling limit.