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arXiv:2501.10287 · Physical Review X

Beyond-Hubbard Pairing in a Cuprate Ladder

Hari Padma, Jinu Thomas, Sophia F. R. TenHuisen, Wei He, Ziqiang Guan, Jiemin Li, Byungjune Lee, Yu Wang, Seng Huat Lee, Zhiqiang Q. Mao, Hoyoung Jang, Valentina Bisogni, Jonathan Pelliciari, M. P. M. Dean, Steven Johnston, Matteo Mitrano

Published May 12, 2025• 10 citations
arXivHTMLPDF

Abstract

The Hubbard model is believed to capture the essential physics of cuprate superconductors. However, recent theoretical studies suggest that it fails to reproduce a robust and homogeneous superconducting ground state. Here, using resonant inelastic x-ray scattering and density matrix renormalization group calculations, we show that magnetic excitations in the prototypical cuprate ladder Sr 14 Cu 24 O 41 are inconsistent with those of a simple Hubbard model. The magnetic response of hole carriers, contributing to an emergent branch of spin-flip excitations, is strongly suppressed. This effect is the consequence of strong d -wavelike pairing, enhanced by nearly an order of magnitude through a large nearest-neighbor attractive interaction and persisting up to at least 260 K. The close connection between the physics of cuprate ladders and that of the two-dimensional compounds suggests that such an enhanced hole pairing may be a universal feature of superconducting cuprates.

DOI
10.1103/physrevx.15.021049

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The Hubbard model is believed to capture the essential physics of cuprate superconductors. However, recent theoretical studies suggest that it fails to reproduce a robust and homogeneous superconducting ground state. Here, using resonant inelastic x-ray scattering and density matrix renormalization group calculations, we show that magnetic excitations in the prototypical cuprate ladder Sr 14 Cu 24 O 41 are inconsistent with those of a simple Hubbard model. The magnetic response of hole carriers, contributing to an emergent branch of spin-flip excitations, is strongly suppressed. This effect is the consequence of strong d -wavelike pairing, enhanced by nearly an order of magnitude through a large nearest-neighbor attractive interaction and persisting up to at least 260 K. The close connection between the physics of cuprate ladders and that of the two-dimensional compounds suggests that such an enhanced hole pairing may be a universal feature of superconducting cuprates.
We investigate the spin dynamics of the cuprate ladder Sr2.5_{2.5}2.5​Ca11.5_{11.5}11.5​Cu24_{24}24​O41_{41}41​ to elucidate the behavior of its intrinsically doped holes. Combining high-resolution neutron spectroscopy and density matrix renormalization group calculations enables a comprehensive analysis of the collective magnetic dynamics. We find a general absence of magnetic signatures from unpaired charges, indicating holes within the system form strongly bound localized Cooper pairs. A one-band Hubbard model fails to match the spectral features but a straightforward extension to a large attractive nearest-neighbor interaction quantitatively explains our results. Our finding shows the significance of additional interactions beyond the long-predicted quantum spin pairing in the (ddd-wave) charge pairing process. Considering the parallels between ladders and two-dimensional cuprates, these results are potentially relevant for square lattices as well.
Magnetic interactions are widely believed to play a crucial role in the microscopic mechanism leading to high critical temperature superconductivity. It is therefore important to study the signatures of pairing in the magnetic excitation spectrum of simple models known to show unconventional superconducting tendencies. Using the density matrix renormalization group technique, we calculate the dynamical spin structure factor $S(\mathbf{k},\ensuremath{\omega})$ of a generalized $t\ensuremath{-}U\ensuremath{-}J$ Hubbard model away from half filling in a two-leg ladder geometry. The addition of JJJ enhances pairing tendencies. We analyze quantitatively the signatures of pairing in the magnetic excitation spectra. We found that the superconducting pair-correlation strength, that can be estimated independently from ground state properties, is closely correlated with the integrated low-energy magnetic spectral weight in the vicinity of $(\ensuremath{\pi},\ensuremath{\pi})$. In this wave-vector region, robust spin incommensurate features develop with increasing doping. The branch of the spectrum with rung direction wave vector krung=0{k}_{\mathrm{rung}}=0krung​=0 does not change substantially with doping where pairing dominates and thus plays a minor role. We discuss the implications of our results for neutron scattering experiments, where the spin excitation dynamics of hole-doped quasi-one-dimensional magnetic materials can be measured and also address implications for recent resonant inelastic x-ray scattering experiments.
Magnetic interactions are widely believed to play a crucial role in the microscopic mechanism leading to high critical temperature superconductivity. It is therefore important to study the signatures of pairing in the magnetic excitation spectrum of simple models known to show unconventional superconducting tendencies. Using the density matrix renormalization group technique, we calculate the dynamical spin structure factor $S(\mathbf{k},\ensuremath{\omega})$ of a generalized $t\ensuremath{-}U\ensuremath{-}J$ Hubbard model away from half filling in a two-leg ladder geometry. The addition of JJJ enhances pairing tendencies. We analyze quantitatively the signatures of pairing in the magnetic excitation spectra. We found that the superconducting pair-correlation strength, that can be estimated independently from ground state properties, is closely correlated with the integrated low-energy magnetic spectral weight in the vicinity of $(\ensuremath{\pi},\ensuremath{\pi})$. In this wave-vector region, robust spin incommensurate features develop with increasing doping. The branch of the spectrum with rung direction wave vector krung=0{k}_{\mathrm{rung}}=0krung​=0 does not change substantially with doping where pairing dominates and thus plays a minor role. We discuss the implications of our results for neutron scattering experiments, where the spin excitation dynamics of hole-doped quasi-one-dimensional magnetic materials can be measured and also address implications for recent resonant inelastic x-ray scattering experiments.
The Hubbard and closely related t-J models are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extended t-J model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure t-J model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( δ = 0.1 to 0.2 ), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping t 2 suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates the t-J model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.
Understanding which minimal effective model captures the essential physics of cuprates is a key step towards unraveling the mechanism behind high- T c superconductivity. Recent measurements of the dynamical spin structure factor (DSF) in cuprate ladder compounds have indicated the presence of an additional, attractive term in the single-band Hubbard model, potentially originating from electron-phonon interactions. Here, we demonstrate that similar DSF features can also be captured by t − J descriptions with a smaller attractive term. Motivated by this observation, we systematically investigate the strength and origin of different contributions to the single-band Hamiltonians by downfolding either from the three-band Emery model or the electron-phonon coupled Hubbard-Holstein model. For one-dimensional systems, we find that the extended versions of both single-band descriptions can reproduce the experimentally observed DSF signatures. Finally, we extend our analysis to two dimensions by comparing two-hole correlation functions for the different single-band models. Our results provide new insights into the long-standing question of which single-band Hamiltonian can capture the essential physics of cuprates.
The Hubbard and related models serve as a fundamental starting point in understanding the novel experimental phenomena in correlated electron materials, such as superconductivity, Mott insulator, magnetism. Recent numerical simulations demonstrate that the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ plays a key role for the superconductivity. However, the impacts of long-range intersite interactions in such a ${t}^{\ensuremath{'}}$-Hubbard model are less explored. Using the state-of-art density-matrix renormalization group method, we investigate the ${t}^{\ensuremath{'}}$-Hubbard model on a two-leg ladder with the intersite interactions extended to the fourth neighbors. The numerical results show that the quasi-long-range superconducting correlation remains stable under the repulsive intersite interactions and these long-range repulsive interactions only change the ground state quantitatively. In addition, inspired by recent experiments on one-dimensional cuprate chain ${\mathrm{Ba}}_{2\ensuremath{-}\mathrm{x}}{\mathrm{Sr}}_{\mathrm{x}}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$, we find that the nearest-neighbor attractive interaction significantly enhances the superconducting correlation when it is comparable to the nearest-neighbor hopping ttt. Stronger attraction drives the system into an electron-hole phase separation. Finally, we discuss the effects of the on-site interaction on superconductivity.