Effective model and pairing tendency in bilayer Ni-based superconductor La${}_3$Ni${}_2$O${}_7$

Since the discovery of cuprate, the origin of high-T${}_c$ superconductivity has been an outstanding puzzle. Recently, high-T${}_c$ superconductivity was observed in a bilayer nickelate La${}_3$Ni${}_2$O${}_7$ under pressure, whose structure hosts the apical oxygen between two layers, distinct from multi-layer cuprates. Motivated by this discovery, we investigate its electronic structure using first-principle calculations and superconducting instabilities from both weak-coupling and strong-coupling perspective. Based on the first-principle band structures, we construct a bilayer two-orbital model on a square lattice, consisting of $d_{x^2-y^2}$ and $d_{z^2}$ orbitals, which accurately captures the low-energy electronic properties. Within this model, we study pairing instability using both functional renormalization group approach and multi-orbital t-J model. An $s_{\pm }$-wave pairing with sign-reversal gaps on different Fermi surfaces is revealed, reminiscent of iron based superconductors. The Ni-$d_{z^2}$ orbital and its associated interlayer and intralayer exchange couplings are found to be crucial for the high-T${}_c$ superconductivity. Our study provides valuable insights into unique nature of electronic structure and superconductivity in La${}_3$Ni${}_2$O${}_7$ and contributes to the understanding of unconventional superconductors.