Strong pairing and symmetric pseudogap metal in a double Kondo lattice model: From a nickelate superconductor to a tetralayer optical lattice

In this work, we propose and study a double Kondo lattice model which hosts robust superconductivity. The system consists of two identical Kondo lattice models in two separate layers, with Kondo coupling ${J}_{K}$ within each layer, while the localized spin moments are coupled together via an interlayer on-site antiferromagnetic spin coupling ${J}_{\ensuremath{\perp}}$. We consider the strong ${J}_{\ensuremath{\perp}}$ limit, wherein the local moments tend to form rung singlets and are thus gapped. However, the Kondo coupling ${J}_{K}$ transmits the interlayer entanglement between the local moments to the itinerant electrons. Consequently, the itinerant electrons experience a strong interlayer antiferromangetic spin coupling and form strong interlayer pairing, which is confirmed through numerical simulation in one dimensional system. Experimentally, the ${J}_{K}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ limits of the model describes the recently found bilayer nickelate ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$, while the ${J}_{K}>0$ side can be realized in tetralayer optical lattice of cold atoms. Two extreme limits, ${J}_{K}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ and ${J}_{K}\ensuremath{\rightarrow}+\ensuremath{\infty}$ limit are shown to be simplified to a bilayer type II t-J model and a bilayer one-orbital t-J model, respectively. Thus, our double Kondo lattice model offers a unified framework for nickelate superconductor and tetralayer optical lattice quantum simulator upon changing the sign of ${J}_{K}$. We highlight both the qualitative similarity and the quantitative difference in the two sides of ${J}_{K}$. Finally, we discuss the possibility of a symmetric Kondo breakdown transition in the model with a symmetric pseudogap metal corresponding to the usual heavy Fermi liquid.