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.

Review paper submitted to Focus Issue in New Journal of Physics (https://iopscience.iop.org/collections/njp-241206-740); 17 pages, 10 figures