Electron-phonon coupling revealed by charge density fluctuations in cuprate superconductors

Abstract

Electron-phonon coupling (EPC) governs lattice dynamics, charge transport, and collective electronic phases in quantum materials. In several families of unconventional superconductors, including transition-metal dichalcogenides and kagome metals, growing evidence points to a cooperative role of EPC and dynamic charge-density fluctuations (CDF) in stabilizing superconductivity. However, how the EPC strength evolves across phase diagrams and relates to superconducting properties in strongly correlated systems remains an open question. Here we investigate the interplay between phonons and the CDF recently identified in cuprate superconductors. Using resonant inelastic x-ray scattering, we track the dispersion and intensity of bond-stretching phonons in YBa$_2$Cu$_3$O$_{7-\delta}$ over wide ranges of doping, temperature, and momentum. We find that both the phonon softening at the CDF wave vector and the EPC strength, extracted from a pronounced phonon intensity anomaly, are maximized near $p = 0.19$, where superconducting properties are optimal and CDF intensity is strongest. These results identify dynamic charge-density fluctuations, rather than quasi-static charge density waves, as the dominant source of phonon renormalization in cuprates, and establish a direct correlation between EPC strength and the superconducting dome. More broadly, our measurements highlight EPC as a doping-dependent property of correlated materials, shaped by the electronic environment in which lattice vibrations are embedded.