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arXiv:2307.16873 · Physical Review Letters

Bilayer t − J − J ⊥ Model and Magnetically Mediated Pairing in the Pressurized Nickelate La 3 Ni 2 O 7

Xing-Zhou Qu, Dai-Wei Qu, Jialin Chen, Congjun Wu, Fan Yang, Wei Li, Gang Su

Published Jan 19, 2024• 187 citations
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Abstract

The recently discovered nickelate superconductor ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ has a high transition temperature near 80 K under pressure, providing an additional avenue for exploring unconventional superconductivity. Here, with state-of-the-art tensor-network methods, we study a bilayer ${t\text{\ensuremath{-}}J\text{\ensuremath{-}}J}_{\ensuremath{\perp}}$ model for ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ and find a robust $s$-wave superconductive (SC) order mediated by interlayer magnetic couplings. Large-scale density matrix renormalization group calculations find algebraic pairing correlations with Luttinger parameter ${K}_{\mathrm{SC}}\ensuremath{\lesssim}1$. Infinite projected entangled-pair state method obtains a nonzero SC order directly in the thermodynamic limit, and estimates a strong pairing strength ${\overline{\mathrm{\ensuremath{\Delta}}}}_{z}\ensuremath{\sim}\mathcal{O}(0.1)$. Tangent-space tensor renormalization group simulations elucidate the temperature evolution of SC pairing and further determine a high SC temperature ${T}_{c}^{*}/J\ensuremath{\sim}\mathcal{O}(0.1)$. Because of the intriguing orbital selective behaviors and strong Hund's rule coupling in the compound, ${t\text{\ensuremath{-}}J\text{\ensuremath{-}}J}_{\ensuremath{\perp}}$ model has strong interlayer spin exchange (while negligible interlayer hopping), which greatly enhances the SC pairing in the bilayer system. Such a magnetically mediated pairing has also been observed recently in the optical lattice of ultracold atoms. Our accurate and comprehensive tensor-network calculations reveal a robust SC order in the bilayer ${t\text{\ensuremath{-}}J\text{\ensuremath{-}}J}_{\ensuremath{\perp}}$ model and shed light on the pairing mechanism of the high-${T}_{c}$ nickelate superconductor.

DOI
10.1103/physrevlett.132.036502

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Abstract Ever since the discovery of high-temperature superconductivity in cuprates, gaining microscopic insights into the nature of pairing in strongly correlated systems has remained one of the greatest challenges in modern condensed matter physics. Following recent experiments reporting superconductivity in the bilayer nickelate La3Ni2O7 (LNO) with remarkably high critical temperatures of Tc = 80 K, it has been argued that the low-energy physics of LNO can be described by the strongly correlated, mixed-dimensional bilayer t–J model. Here we investigate this bilayer system and utilize density matrix renormalization group techniques to establish a thorough understanding of the model and the magnetically induced pairing through comparison to the perturbative limit of dominating inter-layer spin couplings. In particular, this allows us to explain appearing finite-size effects, firmly establishing the existence of long-range superconducting order in the thermodynamic limit. By analyzing binding energies, we predict a BEC–BCS crossover as a function of the Hamiltonian parameters. We find large binding energies of the order of the inter-layer coupling that suggest strikingly high critical temperatures of the Berezinskii–Kosterlitz–Thouless transition, raising the question of whether (mixD) bilayer superconductors possibly facilitate critical temperatures above room temperature.
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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.
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