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arXiv:2501.10296 · Physical review. B./Physical review. B

Cooper-pair localization in the magnetic dynamics of a cuprate ladder

Allen O. Scheie, Pontus Laurell, Jinu Thomas, V. K. Sharma, Alexander I. Kolesnikov, Garrett E. Granroth, Qiang Zhang, B. Lake, Marián Mihalik, Robert Bewley, R. S. Eccleston, J. Akimitsu, Elbio R. Dagotto, Cristian D. Batista, Gonzalo Álvarez, Steven Johnston, D. M. Tennant

Published Apr 27, 2026• 0 citations
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Abstract

We investigate the spin dynamics of the cuprate ladder Sr$_{2.5}$Ca$_{11.5}$Cu$_{24}$O$_{41}$ 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 ($d$-wave) charge pairing process. Considering the parallels between ladders and two-dimensional cuprates, these results are potentially relevant for square lattices as well.

DOI
10.1103/1s7m-xkby

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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.
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.
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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.
Cooper pairing instability in a Fermi liquid is well understood by the BCS theory, but pairing mechanism for doped Mott insulators still remains elusive. Previously it has been shown by density matrix renormalization group (DMRG) method that a single doped hole is always self-localized due to the quantum destructive interference of the phase string signs hidden in the t-J ladders. Here we report a DMRG investigation of hole binding in the same model, where a novel pairing-glue scheme beyond the BCS realm is discovered. Specifically, we show that, in addition to spin pairing due to superexchange interaction, the strong frustration of the phase string signs on the kinetic energy gets effectively removed by pairing the charges, which results in strong binding of two holes. By contrast, if the phase string signs are "switched off" artificially, the pairing strength diminishes significantly even if the superexchange coupling remains the same. In the latter, unpaired holes behave like coherent quasiparticles with pairing drastically weakened, whose sole origin may be attributed to the resonating-valence-bond (RVB) pairing of spins. Such non-BCS pairing mechanism is therefore beyond the RVB picture and may shed important light on the high-T(c) cuprate superconductors.
Holes doped within the square CuO2\mathrm{Cu}{\mathrm{O}}_{2}CuO2​ network specific to the cuprate superconducting materials have oxygen 2p2p2p character. We investigate the basic properties of such oxygen holes by wave-function-based quantum chemical calculations on large embedded clusters. We find that a 2p2p2p hole induces ferromagnetic correlations among the nearest-neighbor Cu3d\mathrm{Cu}\phantom{\rule{0.2em}{0ex}}3dCu3d spins. When moving through the antiferromagnetic background, the hole must bring along this spin-polarization cloud at nearby Cu sites, which gives rise to a substantial reduction of the effective hopping parameters. Such interactions can explain the relatively low values inferred for the effective hoppings by fitting the angle-resolved photoemission data. The effect of the background antiferromagnetic couplings of renormalizing the effective nearest-neighbor hopping is also confirmed by density-matrix renormalization-group model-Hamiltonian calculations for chains and ladders of CuO4\mathrm{Cu}{\mathrm{O}}_{4}CuO4​ plaquettes.
The ground state of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ ladder with four legs favors a striped charge distribution for the parameters corresponding to hole-doped cuprate superconductors. We investigate the dynamical spin and charge structure factors of the model by using the dynamical density matrix renormalization group (DMRG) and clarify the influence of the stripe on the structure factors. The dynamical charge structure factor along the momentum direction from q=(0,0)\mathbf{q}=(0,0)q=(0,0) to $(\ensuremath{\pi},0)$ clearly shows low-energy excitations corresponding to the stripe order in hole doping. On the other hand, the stripe order weakens in electron doping, resulting in fewer low-energy excitations in the charge channel. In the spin channel, we find incommensurate spin excitations near $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$ forming an hourglass behavior in hole doping, while in electron doping we find clearly spin-wave-like dispersions starting from $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$. Along the $(0,0)\text{\ensuremath{-}}(\ensuremath{\pi},0)$ direction, the spin excitations are strongly influenced by the stripes in hole doping, resulting in two branches that form a discontinuous behavior in the dispersion. In contrast, the electron-doped systems show a downward shift in energy toward $(\ensuremath{\pi},0)$. These behaviors along the $(0,0)\text{\ensuremath{-}}(\ensuremath{\pi},0)$ direction are qualitatively similar to momentum-dependent spin excitations recently observed by resonant inelastic x-ray scattering experiments in hole- and electron-doped cuprate superconductors.