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

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${7-δ}$ 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.

💡 Research Summary

In this work the authors investigate how electron‑phonon coupling (EPC) evolves across the phase diagram of the cuprate superconductor YBa₂Cu₃O₇₋δ (YBCO) and how it relates to superconducting properties. Using Cu L₃‑edge resonant inelastic X‑ray scattering (RIXS) they simultaneously probe the bond‑stretching (breathing) phonon branch and the charge excitations that manifest as dynamic charge‑density fluctuations (CDF). Thin YBCO films (≈100 nm) with hole dopings p = 0, 0.06, 0.13, 0.19, and 0.23 were measured over a wide momentum range (0.14–0.48 r.l.u.) along (H, 0), at temperatures from 20 K to room temperature, and for selected dopings also as a function of azimuthal angle up to 45°. The experimental geometry (σ‑polarized incident beam, fixed 2θ = 149.5°, ≈40 meV energy resolution) maximizes the charge‑response cross‑section.

The key observations are: (i) a pronounced softening of the breathing phonon at a characteristic wave vector q_c ≈ 0.32 r.l.u.; (ii) a concurrent quasi‑elastic intensity peak in the same q‑region, which the authors attribute to CDF rather than to the quasi‑static charge‑density wave (CDW) that is known to appear in underdoped YBCO. The phonon softening is strongest at low temperature (20 K) and diminishes linearly with increasing temperature, yet remains detectable well above the CDW onset temperature, indicating a different origin. By defining a reference phonon energy from the undoped sample (where no softening occurs) they quantify the softening ΔE(p,T) = Ē₀ – Ē(p,T). ΔE reaches its maximum at p ≈ 0.19, precisely where previous studies have shown the CDF intensity to peak and where superconducting parameters (critical temperature, superfluid density, critical current, upper critical field) are optimal.

The intensity of the breathing phonon itself shows a similar doping dependence: starting from a sin²(πq)‑like behavior in the insulating sample, the integrated intensity over high‑q (q > 0.3 r.l.u.) grows by more than a factor of two, peaks at p ≈ 0.19, and then declines at higher doping. This intensity trend mirrors both the CDF strength and the phonon softening, establishing a direct correlation between EPC strength and CDF. Azimuthal‑angle scans reveal that the CDF‑related features are nearly isotropic, persisting up to ϕ = 45°, whereas the CDW signal in the underdoped sample disappears already at ϕ ≈ 15°, confirming that the phonon anomalies are governed by the more isotropic, short‑range CDF rather than the anisotropic, quasi‑static CDW.

The authors discuss how these findings reconcile with earlier inelastic neutron scattering (INS) results, noting that their twinned thin films average the response of the a‑ and b‑axes, whereas INS on untwinned crystals reported anisotropic softening. They also cite strain‑dependent studies showing that CDW intensity is highly strain‑sensitive while the phonon softening is not, consistent with the strain‑insensitivity of CDF.

Overall, the study demonstrates that EPC in cuprates is not a fixed material constant but an emergent property that is strongly enhanced by dynamic charge fluctuations. The EPC strength follows a dome‑like dependence on hole doping, peaking at the same doping where superconductivity is most robust. This provides compelling experimental evidence that EPC, in cooperation with CDF, plays an active role in the mechanism of high‑temperature superconductivity, and suggests that similar cooperative EPC‑CDF physics may be a unifying theme across other families of unconventional superconductors such as transition‑metal dichalcogenides and kagome metals.