Doping a spin-one Mott insulator: possible application to bilayer nickelate

Abstract In this article, we review some recent theoretical developments on potential high-temperature superconductors and unconventional metallic states that can arise from doping a spin-one Mott insulator in the d 8 valence. These studies are particularly relevant—though not limited—to the recently discovered bilayer nickelate superconductor La 3 Ni 2 O 7 . We focus on a ferromagnetic Kondo lattice model with mobile electrons in the d x 2 − y 2 orbital coupled to the localized spin moments in d z 2 orbital through a large Hund’s coupling J H . In the large J H limit, the model reduces to the type II t − J model with a mixture of spin-half singlon states and spin-one doublon states. We summarize density matrix renormalization group results on the Luther-Emery liquid in one dimensional chain and two-leg ladder. Then we mainly focus on bilayer square lattice and show that a large inter-layer coupling J ⊥ of d z 2 orbital can induce strong inter-layer pairing of d x 2 − y 2 orbital. In the strong J ⊥ limit, a kinetic-energy driven high T c superconductivity is demonstrated in an ideal model with only a single hopping term. Furthermore, the model predicts a symmetric pseudogap metal—dubbed ‘second Fermi liquid (FL)’—in the underdoped regime, yielding a phase diagram analogous to that of hole-doped cuprates. The bilayer Kondo model therefore presents a promising platform for both realizing higher- T c superconductors and exploring non-FL physics. We also comment on the possible limitations of the current models for the bilayer nickelate material and point out some future directions.