Superconductivity in nickelate and cuprate superconductors with strong bilayer coupling

The discovery of superconductivity at 80 K under high pressure in La_3Ni_2O_7 presents the groundbreaking confirmation that high-T_c superconductivity is a property of strongly correlated materials beyond cuprates. We use density functional theory (DFT) calculations of the band structure of La_3Ni_2O_7 under pressure to verify that the low-energy bands are composed almost exclusively of Ni 3d_x^2-y^2 and O 2p orbitals. We deduce that the Ni 3d_z^2 orbitals are essentially decoupled by the geometry of the high-pressure structure and by the effect of the Ni Hund coupling being strongly suppressed, which results from the enhanced interlayer antiferromagnetic interaction between d_z^2 orbitals and the strong intralayer hybridization of the d_x^2-y^2 orbitals with O 2p. By introducing a tight-binding model for the Fermi surfaces and low-energy dispersions, we arrive at a bilayer t-t_⊥-J model with strong interlayer hopping, which we show is a framework unifying La_3Ni_2O_7 with cuprate materials possessing similar band structures, particularly the compounds La_2CaCu_2O_6, Pb_2Sr_2YCu_3O_8, and EuSr_2Cu_2NbO_8. We use a renormalized mean-field theory to show that these systems should have (d+is)-wave superconductivity, with a dominant d-wave component and the high T_c driven by the near-optimally doped β band, while the α band adds an s-wave component that should lead to clear experimental signatures.