Pairing Mechanism in Bilayer Nickelate La$_3$Ni$_2$O$_7$ Superconductors

Abstract

The recent discovery of superconductivity with $T_c \approx 80$~K in bilayer nickelate La$_3$Ni$_2$O$_7$ provides a new setting in which to test the organizing principles of unconventional high-temperature superconductivity. We show that the gene principle and the collaborative Fermi-surface rule which were previously proposed to unify unconventional high temperature superconductors, extend naturally to this bilayer, multi-orbital system. We identify that there are two antiferromagnetic exchange channels that can provide the dominant pairing force: an interlayer intra-orbital nearest-neighbour exchange $J_\perp$ between $d_{z^2}$ orbitals mediated by the inner apical oxygen, and an intralayer inter-orbital nearest-neighbour exchange $J_{xz}$ between $d_{z^2}$ and $d_{x^2-y^2}$ orbitals mediated by the in-plane oxygen. Owing to the bilayer bonding--antibonding splitting and the $B_{1g}$ symmetry of the $d_{x^2-y^2}$ orbital, these two channels cooperate to produce a robust $s^\pm$ superconducting state with an internal sign reversal between mirror-even and mirror-odd Fermi-surface pockets in momentum space. Both pairing channels maximize the superconducting gap on the $\beta$ pocket with a form factor $(cosk_x-cosk_y)^2$ in momentum space. The result places La$_3$Ni$_2$O$_7$ within a unified framework for unconventional superconductivity while revealing a distinct electronic environment for high-$T_c$ pairing.