Next-Nearest-Neighbor Hopping and Charge-Ordering Tendencies in a Cuprate Ladder

The competing nature of charge-order and superconductivity in the cuprates is an open experimental and theoretical problem in condensed matter physics. Recent theoretical studies on the Hubbard model have revealed that the next-nearest neighbor hopping <i>t’</i> is a key tuning parameter that destabilizes charge-ordered phases in favor of superconductivity¹. However, the influence of <i>t’</i> remains relatively unexplored experimentally. Quasi-1D systems are an ideal platform to study the microscopic physics of the cuprates, owing to the availability of reliable theory that may be rigorously compared to experimental results. Here we consider the quasi-1D cuprate ladder system Sr_14-xCa_xCu₂₄O₄₁, which exhibits a gapped spin singlet ground state² that is charge ordered at ambient pressure³ and superconducting at high pressure⁴ (<i>x</i> &gt; 11, <i>T_C</i> = 9 K at 3.5 GPa). Focusing on the hole self-doped parent compound (<i>x</i> = 0), we map the spectrum of dispersive two-triplon spin fluctuations as a function of temperature across the CO phase transition using high-resolution resonant inelastic X-ray scattering at the Cu <i>L</i>-edge. We identify a substantial downturn in the two-triplon dispersion near the zone boundary, a feature that is at odds with predictions of the Hubbard model with only nearest-neighbor hopping. Furthermore, we observe a dramatic reshaping of the two-triplon spectrum across the CO transition temperature. We fit the experimental two-triplon dispersion measured in the CO ground state using DMRG calculations and unbiased Bayesian optimization to extract the Hubbard model parameters including the exchange anisotropy and <i>t’</i>. We examine the role of <i>t’</i> in the reshaping of the spin fluctuations across the CO transition, in particular identifying signatures of hole pairing and hole-triplon bound states, which have been hypothesized to be precursors to superconductivity in spin ladders^5,6. Our work provides a rigorous experimental quantification of <i>t’</i> in cuprates and clarifies its influence over spin fluctuations and electronic ordering.<br/><br/>1. Jiang, H. C. & Devereaux, T. P. Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping <i>t′</i>. Science 365, 1424–1428 (2019).<br/>2. Notbohm, S. et al. One- and Two-Triplon Spectra of a Cuprate Ladder. Phys Rev Lett 98, 027403 (2007).<br/>3. Abbamonte, P. et al. Crystallization of charge holes in the spin ladder of Sr14Cu24O41. Nature 431, 1078–1081 (2004).<br/>4. Nagata, T. et al. Superconductivity in the ladder compound Sr2.5Ca11.5Cu24O41 (single crystal). Physica C 282–287, 153–156 (1997).<br/>5. Dagotto, E., Riera, J. & Scalapino, D. Superconductivity in ladders and coupled planes. Phys Rev B 45, 5744–5747 (1992).<br/>6. Poilblanc, D., Chiappa, O., Riera, J., White, S. R. & Scalapino, D. J. Evolution of the spin gap upon doping a 2-leg ladder. Phys Rev B 62, R14633–R14636 (2000).<br/><br/>This study was primarily supported by the DOE Office of Science under the Early Career Research Program award no. DE-SC0022883. Support for crystal growth and characterization was provided by the National Science Foundation (NSF) through the Penn State 2D Crystal Consortium-Materials Innovation Platform (2DCC-MIP) under NSF cooperative agreement DMR-1539916 and DMR-2039351.