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.
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.
Evolution from intralayer to interlayer superconductivity in a bilayer t-J model
Motivated by the bilayer cuprate superconductors and nickelate superconductor La3Ni2O7, we investigate the evolution from intralayer to interlayer superconductivity based on a bilayer two-leg t-J-J⊥ model, where t is the in-plane electron hopping, J is the in-plane spin interaction, and J⊥ is the inter-plane spin interaction. By means of the density matrix renormalization group calculations, we obtain the quantum phase diagram of the system by tuning J⊥ in a large doping range δ=1/8−1/2. We find that a large J⊥ can always drive an interlayer superconductivity by coupling the two layers in both the Luther-Emery liquid and Luttinger liquid states. By coupling two Luther-Emery liquid states, the in-plane superconductivity evolves to inter-plane superconductivity either through an intermediate charge density wave (CDW) phase or directly, depending on doping ratio. This emergent CDW phase, which exists over a finite doping range, appears to develop from the CDW state of the two-leg ladder at δ=1/4. By coupling two Luttinger liquids, the in-plane Luttinger liquids show a transition to the inter-plane superconducting phase at large J⊥, as reported in previous literature. Interestingly, in the intermediate J⊥ regime we find that while the in-plane Luttinger-liquid features remain stable, the inter-plane superconductivity can develop an enhanced quasi-long-range order with the power exponent KSCzz∼1. At last, we show that the interlayer superconductivity is also stable by coupling the bilayer three-leg t-J ladders by a strong J⊥ interaction, from both the Luther-Emery liquid and Luttinger-liquid states.
In this work, we propose and study a double Kondo lattice model which hosts robust superconductivity. The system consists of two identical Kondo lattice model, each with Kondo coupling JK within each layer, while the localized spin moments are coupled together via an inter-layer on-site antiferromagnetic spin coupling J⊥. We consider the strong J⊥ limit, wherein the local moments tend to form rung singlets and are thus gapped. However, the Kondo coupling JK transmits the inter-layer entanglement between the local moments to the itinerant electrons. Consequently, the itinerant electrons experience a strong inter-layer antiferromangetic spin coupling and form strong inter-layer pairing, which is confirmed through numerical simulation in one dimensional system. Experimentally, the JK→−∞ limits of the model describes the recently found bilayer nickelate La3Ni2O7, while the JK>0 side can be realized in tetralayer optical lattice of cold atoms. Two extreme limits, JK→−∞ and JK→+∞ 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 JK. We highlight both the qualitative similarity and the quantitative difference in the two sides of JK. 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.
Inspired by the recent discovery of superconductivity in the nickelate ${\mathrm{Nd}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Ni}{\mathrm{O}}_{2}$, we study a generalized $t\text{\ensuremath{-}}J$ model to investigate the correlated phases induced by doping spin-1 Ni2+ into a spin-1/2 Mott insulator formed by Ni1+. Based on a three-fermion parton mean-field analysis, we identify a robust fractional Fermi liquid (FL*) phase for almost every doping level. The FL* state is characterized by a small Fermi pocket on top of a spin liquid, which violates the Luttinger theorem of a conventional Fermi liquid and is an example of a symmetric pseudogap metal. Furthermore, we verify our theory in one dimension through density matrix renormalization group simulations on both the generalized $t\text{\ensuremath{-}}J$ model and a two-orbital Hubbard model. The fractional Fermi liquid reduces to a fractional Luttinger liquid (LL*) in one dimension, which is connected to the conventional Luttinger liquid through a continuous quantum phase transition by tuning interaction strength. Our findings offer insights into correlated electron phenomena in nickelate superconductors and other multiorbital transition-metal oxides with a spin-triplet d8 state.
Superconductivity is usually assumed to arise from attractive interaction. In this work we show that strong pairing is possible soley from kinetic energy even without a net attraction. We demonstrate a high-temperature kinetic superconductor in a simple lattice model with nearest-neighbor hopping (t) projected onto a constrained Hilbert space, analogous to the t-J model with J=0, where kinetic magnetism has been previously studied. Using density matrix renormalization group (DMRG) on cylinders up to width Ly=8, we find a superconducting ground state exhibiting a key difference from high-Tc cuprates: both the pairing gap and phase stiffness \textit{increase} with doping (x). We find pairing gaps, determined from spin and single-electron charge gaps, exceeding 1.5t. This model can be realized within the double Kondo lattice model, relevant to bilayer nickelates, in the limit of strong inter-layer spin coupling (J⊥/t→+∞) and a balancing inter-layer repulsion (V). Importantly, the double Kondo model does not fundamentally restrict J⊥/t, suggesting the potential for high critical temperatures (Tc) approaching 0.5t. While this idealized limit predicts large pairing gaps, we show a smooth connection to the more realistic regime with J⊥∼t, albeit with a reduced pairing gap of approximately 0.1t. Assuming t∼103 K in typical solid state systems, our model suggests the exciting possibility of achieving Tc of hundreds of Kelvin. We propose searching for bilayer materials with reduced out-of-plane lattice constants to better approximate the conditions of our ideal model.
We report the numerical discovery of a Luther-Emery liquid with pair-density-wave (PDW) correlations from doping either (i) a spin-one Haldane chain or (ii) a two-leg ladder in the rung-singlet phase in which the doped charges occupy a single leg. We model these systems using a generalized Kondo model. The itinerant electrons are correlated and described by the $t\text{\ensuremath{-}}J$ model, and are further coupled to a spin-1/2 Heisenberg model through the Kondo coupling JK. When the density of electrons x is one, the Mott insulator is in a Haldane phase or in a rung-singlet phase depending on whether JK is negative or positive. Upon doping, a pair-density-wave with $\mathbf{Q}=\ensuremath{\pi}$ can emerge for both signs of JK. In the ${J}_{K}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ limit, the model reduces to the recently proposed type II $t\ensuremath{-}J$ model. We also identify a composite order parameter for the superconductor, which can be understood as a Cooper pair formed by two nearby fermionic spin-polarons. Our model and the predicted PDW phase can be experimentally realized by doping S=1 chains formed by Ni2+ in a solid-state system or a two-leg ladder of fermionic cold atoms with a potential bias between legs, which preferentially dopes carriers into a single leg. Long-range order of the PDW can be achieved in quasi-one-dimensional system with finite interwire coupling.
Symmetric pseudogap metal in a generalized t−J model
In this article we study a generalized t−J model in which we dope spin-one doublons into a spin 1/2 Mott insulator. We generalize this model to SU(N) case and obtain the ground state based on a three-fermion parton mean field calculation. Surprisingly, for almost every doping we find a fractional Fermi liquid (FL*) phase , which is a symmetric pseudogap metal in the sense that the total Fermi volume is equal to x, instead of 1+x as required by Luttinger constraint of a Fermi liquid. We then verify our theory in one dimension through DMRG simulation of the t−J model. Indeed we find that the doped doublon forms a small Fermi on top of the spinon Fermi surface (SU(2)1 CFT) inherited from the Mott insulator. This phase is clearly a one dimension analog of the FL* phase and we dub it as fractional Luttinger liquid (LL*). We also discover a continuous quantum phase transition from this LL* phase with small Fermi to conventional Luttinger liquid phase with large Fermi by tuning interaction strength in a two-orbital Hubbard model at fixed density. Lastly we discuss the experimental realizations of this generalized t−J model and comment on possible connection to the recently discovered nickelate superconductor Nd1−xSrxNiO2.