Recently, the bulk nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ is reported to show a signature of high-temperature superconductivity under high pressure above 14 GPa [H. Sun et al., Nature (London) 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-unit-cell intraorbital components with antiphase between the on-site 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.

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• Pairing mechanisms
• Superconducting gap
• Unconventional superconductors
• Functional renormalization group
• Gutzwiller approximation