Hierarchical structure of primary and hybridization-induced superconducting correlations in bilayer nickelates

Abstract: High-pressure superconductivity in the bilayer nickelate La$<em>3$Ni$_2$O$_7$, with a transition temperature approaching 80 K, has stimulated intense debate regarding its microscopic origin. Although an $s</em>{\pm}$ gap symmetry has been widely proposed, the electronic degrees of freedom responsible for pairing remain unsettled. Here we investigate a bilayer two-orbital Hubbard model using the variational Monte Carlo method and reveal a hierarchical pairing structure in bilayer nickelates. The primary pairing interaction originates from the bonding--antibonding splitting of the Ni $3d_{z<sup>2}$ orbitals, while orbital hybridization redistributes superconducting correlations to the $d_{x<sup>2-y<sup>2}$ channel despite its weak intrinsic pairing interaction. This distinction between the origin of pairing and resulting superconducting correlations explains why the two orbital channels exhibit comparable long-range correlations. The resulting $s_{\pm}$ state is robust against changes in Fermi-surface topology. These results reconcile apparently competing theoretical scenarios and provide a comprehensive understanding, highlighting the distinctive role of orbital hybridization in multilayer correlated superconductors.