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arXiv:2310.01952 · Physical review. B./Physical review. B

Pair correlations in the two-orbital Hubbard ladder: Implications for superconductivity in the bilayer nickelate La3Ni2O7

Tatsuya Kaneko, Hirofumi Sakakibara, Masayuki Ochi, Kazuhiko Kuroki

Published Jan 31, 2024• 60 citations
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Abstract

Motivated by high-temperature superconductivity in pressurized ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$, we investigate the pair correlations in the two-orbital Hubbard ladder, which consists of the nearly half-filled and nearly quarter-filled orbitals. By employing the density matrix renormalization group method, we demonstrate that the pair correlation exhibits a power-law decay against the distance while the spin correlation decays exponentially. The decay exponent of the pair correlation of the nearly half-filled orbital is comparable to the exponent of the quasi-long-range superconducting correlation in the doped single-orbital Hubbard ladder, which suggests the importance of the ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbital in ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$.

DOI
10.1103/physrevb.109.045154

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Motivated by high-temperature superconductivity in pressurized La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​, we investigate the pair correlations in the two-orbital Hubbard ladder, which consists of the nearly half-filled and nearly quarter-filled orbitals. By employing the density matrix renormalization group method, we demonstrate that the pair correlation exhibits a power-law decay against the distance while the spin correlation decays exponentially. The decay exponent of the pair correlation of the nearly half-filled orbital is comparable to the exponent of the quasi-long-range superconducting correlation in the doped single-orbital Hubbard ladder, which suggests the importance of the d3z2\ensuremath−r2{d}_{3{z}^{2}\ensuremath{-}{r}^{2}}d3z2\ensuremath−r2​ orbital in La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​.
To clarify the nature of high-temperature superconductivity in the bilayer nickelate La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ under pressure, we investigate, using the density-matrix renormalization group method, the pair correlations in the two-orbital $t\text{\ensuremath{-}}J$ ladder model. While the interchain-intraorbital pair correlations exhibit a slow power-law decay in both orbitals, the interorbital pair correlation also develops strongly enough to be comparable with the intraorbital correlations. These intra and interorbital pair correlations are enhanced by Hund's coupling, but more importantly, the interorbital pair correlation develops even when interorbital pairing glue mediated by Hund's coupling is absent. Our finding suggests that the pair correlation in the present system develops as a hybridized two-orbital entity, which may have some implications on the superconductivity in the bilayer nickelate.
While the recent discovery of superconductivity in infinite-layer nickelates has drawn considerable attention, a common ingredient of the fundamental building blocks to describe their ground states has been lacking. A series of experimental and theoretical studies have suggested that an effective two-band Hubbard model with Ni 3dx2−y2d_{x^2-y^2}dx2−y2​ and rare-earth (RRR) 5ddd character may describe the low-energy physics. Here, we study the ground state properties of this two-band model on four-leg cylinders using the density-matrix renormalization group (DMRG). At half-filling, the ground state of the system is consistent with a Luttinger liquid, possessing quasi-long-range charge and spin correlations in the RRR layer, but short-range correlations in the Ni layer. At a hole doping concentration of δ=12.5%\delta=12.5\%δ=12.5%, the RRR layer is nearly empty and the ground state of the system is consistent with a Luther-Emery liquid, where we find power-law superconducting and charge density correlations in the Ni layer, but exponentially decaying spin correlations. The consistency of our results with experimental observations may help to reveal the microscopic mechanism for pairing in these nickelates and other unconventional superconductors.
The recently discovered high-Tc{T}_{c}Tc​ superconductivity in La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ with ${T}_{c}\ensuremath{\approx}80$ K provides another intriguing platform to explore the microscopic mechanism of unconventional superconductivity. In this work, we study a previously proposed bilayer two-orbital model Hamiltonian for La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ [Y. Shen et al., Chin. Phys. Lett. 40, 127401 (2023)] on a plaquette ladder, which is a minimum setup with two-dimensional characteristic. We employ large-scale density matrix renormalization group calculations to accurately determine the ground state of the model. We determine the density, magnetic structure, and the pairing property of the model. We find that with large effective interlayer antiferromagnetic exchange for the 3dz23{d}_{{z}^{2}}3dz2​ orbital, the spin, charge, and pairing correlation display quasi-long-range behavior, which could be viewed as a precursor of possible true long-range order in the two-dimensional limit. Interestingly, sign oscillation for the pairing correlation is observed for both the $3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and 3dz23{d}_{{z}^{2}}3dz2​ orbitals, indicating the presence of a possible pair density wave in the system. Even though we only study the model on a quasi-one-dimensional plaquette ladder geometry due to the computational difficulty, the results for the spin, charge, and pairing correlation provide valuable insight towards the clarification of the properties of La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​.
We investigate the ground-state properties of correlated three-leg ladders near 1/3 filling. We apply the density-matrix renormalization group method to the three-leg t-J ladder with strong interchain couplings and evaluate its pairing nature. When holes are doped into the spin-gapped state at 1/3 filling, we find that pair correlations develop with power-law decays while spin correlations decay exponentially. On the other hand, doping of electrons into the 1/3-filled state does not give rise to substantial pair correlations. We also discuss the hole-doped state in the three-leg Hubbard model to compare it with the pairing state in the t-J model. Our numerical demonstrations provide insights into the electronic properties of trilayer nickelate superconductors.
The recent discovery of superconductivity under high pressure in the ladder compound BaFe2S3{\mathrm{BaFe}}_{2}{\mathrm{S}}_{3}BaFe2​S3​ has opened a new field of research in iron-based superconductors with focus on quasi-one-dimensional geometries. In this publication, using the density matrix renormalization group technique, we study a two-orbital Hubbard model defined in one-dimensional chains. Our main result is the presence of hole binding tendencies at intermediate Hubbard UUU repulsion and robust Hund coupling JH/U=0.25{J}_{H}/U=0.25JH​/U=0.25. Binding does not occur either in weak coupling or at very strong coupling. The pair-pair correlations that are dominant near half-filling, or of similar strength as the charge and spin correlation channels, involve hole-pair operators that are spin singlets, use nearest-neighbor sites, and employ different orbitals for each hole. The Hund coupling strength, presence of robust magnetic moments, and antiferromagnetic correlations among them are important for the binding tendencies found here.
The recently discovered nickelate superconductor La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ 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 La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ and find a robust sss-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-Tc{T}_{c}Tc​ nickelate superconductor.