M. Fedele¹, K. Rongrueangkul², S. Caprara³, Dorothée Colson⁴, G. Merzoni¹, L. Martinelli¹, F. Rosa¹, Alain Sacuto⁵, G. Seibold⁶, N. B. Brookes⁷, F. Lombardi², M. Moretti Sala¹, G. Ghiringhelli¹, Riccardo Arpaia^2,8

¹ Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy
² Department of Microtechnology and Nanoscience, Chalmers University, SE-41296 Göteborg, Sweden
³ Dipartimento di Fisica, Universit`a di Roma “La Sapienza”, P.le Aldo Moro 5, I-00185 Roma, Italy
⁴ Service de Physique de l’Etat Condensé, CEA Saclay, IRAMIS, SPEC (CNRS URA 2464), F-91191, Gif sur Yvette, France
⁵ Universit´e Paris Cit´e, Matériaux et Phénomènes Quantiques, UMR CNRS 7162, Batiment Condorcet, F-75205, Paris Cedex 13, France
⁶ Institut fur Physik, BTU Cottbus-Senftenberg, D-03013 Cottbus, Germany
⁷ ESRF, The European Synchrotron, F-38043 Grenoble, France
⁸ Department of Molecular Sciences and Nanosystems, Ca’ Foscari University, I-30172 Venice, Italy

In the complex phase diagram of high-Tc cuprate superconductors, charge-order phenomena are nearly as ubiquitous as short-range spin correlations. While it is widely accepted that spin fluctuations play a role in Cooper pair formation in these unconventional superconductors, the role of charge order remains less well understood. Resonant inelastic X-ray scattering (RIXS) provides unique insight by enabling the direct and simultaneous observation of charge order, as well as the dispersion of high-energy optical phonons and paramagnons. Moreover, RIXS offers rare experimental access to the momentum (q) dependence of the electron–phonon coupling. Here, we present recent results on several hole-doped cuprates demonstrating that charge order—whether in the form of charge-density waves (CDWs) or charge-density fluctuations (CDFs)—cannot be neglected in the search for a comprehensive understanding of high-temperature superconductivity [1,2]. We investigated YBa₂Cu₃O_7-d (YBCO) across doping and temperature, tracking both charge order and bond-stretching phonons [3]. We observe a phonon softening that peaks at (p = 0.19) (fully oxygenated YBCO), coinciding with maximal CDF intensity and superfluid stiffness. This softening occurs near the charge-order wavevector (q~0.3 rlu), suggesting that (i) the electronic response, modulated by CDFs, significantly affects phonon propagation, and (ii) a substantial electron–phonon coupling is present, with maximum strength near optimal doping. We also investigated the paramagnon dispersion in HgBa₂Ca₂Cu₃O_8+d (Hg1223). In this material, no CDW and only CDFs are observed by RIXS, even at (p = 0.125), where CDWs dominate in other cuprates. We detect an anomaly in the paramagnon dispersion at the charge-order wavevector, indicating a spin–phonon coupling that may be relevant for d-wave pairing [4]. These findings support a central role for charge fluctuations in high-Tc superconductivity and suggest that their interplay with lattice and spin excitations may be key to understanding unconventional superconductivity.

[1] R. Arpaia, et al.: Science 365, 906 (2019).
[2] R. Arpaia, et al.: Nat. Commun. 14, 7198 (2023).
[3] M. Fedele et al., arXiv:2602.18112.
[4] K. Rongrueangkul et al, manuscript in preparation