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 (FM) 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 DMRG 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 $J_\perp$ of $d_{z^2}$ orbital can induce strong inter-layer pairing of $d_{x^2-y^2}$ orbital. In the strong $J_\perp$ 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"-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-Tc superconductors and exploring non-Fermi liquid physics. We also comment on the possible limitations of the current models for the bilayer nickelate material and point out some future directions.