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arXiv:2312.04304 · Physical review. B./Physical review. B

Pair correlations of the hybridized orbitals in a ladder model for the bilayer nickelate La 3 Ni 2 O 7

Masataka Kakoi, Tatsuya Kaneko, Hirofumi Sakakibara, Masayuki Ochi, Kazuhiko Kuroki

Published May 24, 2024• 38 citations
arXivHTMLPDF

Abstract

To clarify the nature of high-temperature superconductivity in the bilayer nickelate ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ 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.

DOI
10.1103/physrevb.109.l201124

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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\ensuremath-Jt\text{\ensuremath{-}}Jt\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.
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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 ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbital in La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​.
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​.
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Simulating superconductivity in mixed-dimensional t∥t_\parallelt∥​-J∥{J}_\parallelJ∥​-J⊥{J}_\perpJ⊥​ bilayers with neural quantum states
Motivated by the recent discovery of superconductivity in the bilayer nickelate La3_33​Ni2_22​O7_77​ (LNO) under pressure, we study a mixed-dimensional (mixD) bilayer t∥t_\parallelt∥​-J∥J_\parallelJ∥​-J⊥J_\perpJ⊥​ model, which has been proposed as an effective low-energy description of LNO. Using neural quantum states (NQS), and in particular Gutzwiller-projected Hidden Fermion Pfaffian State, we access the ground-state properties on large lattices up to 8×8×28\times 8\times 28×8×2 sites. We show that this model exhibits superconductivity across a wide range of dopings and couplings, and analyze the pairing behavior in detail. We identify a crossover from tightly bound, Bose-Einstein-condensed interlayer pairs at strong interlayer exchange to more spatially extended Bardeen-Cooper-Schrieffer-like pairs as the interlayer exchange is decreased. Furthermore, upon tuning the intralayer exchange, we observe a sharp transition from interlayer sss-wave pairing to intralayer ddd-wave pairing, consistent with a first-order change in the pairing symmetry. We verify that our simulations are accurate by comparing with matrix product state simulations on coupled ladders. Our results represent the first simulation of a fermionic multi-orbital system with NQS, and provide the first evidence for superconductivity in two-dimensonal bilayers using high-precision numerics. These findings provide insight into superconductivity in bilayer nickelates and cold atom quantum simulation platforms.
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.