Nearest-neighbor attraction between doped holes in a cuprate ladder

The Hubbard model, long considered a paradigmatic model to describe high-T_C superconductivity, is now known to exhibit a non-superconducting ground state. Recent experiments on quasi-1D cuprate chains show that an additional nearest-neighbor attraction beyond the pure Hubbard model is necessary to describe the phenomenology of doped holes. However, its relevance beyond the quasi-1D scenario, and particularly in the context of quasi-2D superconducting cuprates remains unknown. Here, we investigate spin fluctuations in Sr₁₄Cu₂₄O₄₁, parent compound of an archetypal family of cuprate ladders that exhibits superconductivity and competing charge order, and a structure intermediate between 1D and 2D. Combining high-resolution resonant inelastic X-ray scattering with numerically exact DMRG calculations, we extract the parameters of the underlying Hubbard Hamiltonian. Our measurements reveal a strong suppression of scattering from holes, which is at odds with predictions based on the pure Hubbard model. We find that an additional nearest-neighbor attraction that favors pairing of doped holes is necessary to reproduce this suppression. Furthermore, we find that this attractive interaction competes with static charge order, allowing us to establish an upper bound on its magnitude. Our work highlights the crucial role of nearest-neighbor attraction beyond the Hubbard model in describing the behavior of doped holes, in a model system that directly pertains to quasi-2D high-T_C superconductivity.