Decoupling of Static and Dynamic Charge Correlations revealed by Uniaxial Strain in a Cuprate Superconductor

We use uniaxial strain in combination with ultra-high-resolution Resonant Inelastic X-ray Scattering (RIXS) at the oxygen K- and copper L3-edges to study the excitations stemming from the charge ordering wave vector in La1.875Sr0.125CuO4. By detwinning stripe ordering, we demonstrate that the optical phonon anomalies do not show any stripe anisotropy. The low-energy charge excitations also retain an in-plane four-fold symmetry. As such, we find that both phonon and charge excitations are decoupled entirely from the strength of static charge ordering. The almost isotropic character of charge excitations is indicative of a quantum critical behaviour and remains a possible source for the strange metal properties found in the normal state of cuprate superconductors.

💡 Research Summary

In this work the authors investigate the relationship between static charge order (CO) and dynamic charge fluctuations in the prototypical cuprate La₂₋ₓSrₓCuO₄ at the 1/8 doping level (x = 0.125). By applying in‑situ uniaxial compressive strain along the crystallographic b‑axis, they achieve a near‑perfect detwinning of the stripe domains, as quantified by the domain population factor η, which rises from near zero to values close to one. Resonant inelastic X‑ray scattering (RIXS) with ultra‑high energy resolution is performed simultaneously at the oxygen K‑edge (23 meV resolution) and the copper L₃‑edge (43 meV resolution) while the sample is held at ≈ 28 K, the temperature at which CO is maximized.

The static CO peaks at wave vectors q = (δ, 0) and (0, δ) with δ ≈ 0.235 r.l.u. show a clear strain dependence: the intensity along the a‑axis (I_H) grows roughly linearly with increasing compressive strain, whereas the intensity along the b‑axis (I_K) is suppressed. The a‑axis correlation length modestly increases from about nine to twelve unit cells, while the b‑axis correlation length remains unchanged. These observations confirm that the applied strain efficiently selects one stripe orientation, effectively detwinning the sample.

Despite this dramatic change in the static order, the low‑energy excitations probed by RIXS remain remarkably isotropic. Three inelastic modes are identified in the 0–100 meV range: a bond‑bending phonon at ~50 meV, a bond‑stretching (BS) phonon at ~70 meV, and a low‑energy (LE) mode near 20 meV. The BS phonon exhibits a pronounced softening of ~10 meV near the CO wave vector, a feature that has been widely reported in cuprates and often interpreted as a Kohn anomaly linked to the static stripe order. However, in the present study the magnitude and momentum dependence of the BS softening are completely independent of strain, and identical for both (H, 0) and (0, K) directions. The LE mode shows a peak in intensity at q ≈ q_CO, a short real‑space correlation length (~6 a), and a modest dispersion of ~5 meV; its intensity and dispersion also do not change with strain.

Because the electron‑phonon coupling strength g(q) is directly proportional to the RIXS phonon intensity, the identical phonon intensities along a and b directions imply that g(q) is unchanged even when the static CO amplitude varies by a factor of two. This finding rules out a conventional Kohn‑type scenario where the phonon self‑energy is proportional to the static charge susceptibility χ(q, 0). Instead, the authors argue that the observed phonon softening must be driven by a sea of dynamic charge fluctuations that exist independently of the static order.

The LE mode’s isotropy and short correlation length are interpreted as signatures of quantum critical fluctuations associated with the charge‑ordering instability. Within a Landau free‑energy framework, such fluctuations acquire the stripe symmetry only below a characteristic energy scale ω_c, which vanishes at a putative quantum critical point (QCP). Above ω_c the excitations are expected to be scale‑invariant and thus display the same spectral weight on both sides of the QCP. The experimental observation that the LE mode is four‑fold symmetric and insensitive to the detwinning suggests that ω_c lies well below the current experimental resolution (~20 meV). Consequently, the system appears to be in the quantum‑critical regime, where dynamic fluctuations dominate the low‑energy physics and may provide the quasi‑isotropic scattering needed to explain the strange‑metal transport observed in the normal state of cuprates.

In summary, the paper demonstrates that (i) static stripe order and dynamic charge fluctuations are decoupled in symmetry, (ii) phonon anomalies are not driven by electron‑phonon coupling to the static order but rather by the underlying quantum‑critical charge fluctuations, and (iii) these fluctuations retain tetragonal symmetry even when the static order is strongly anisotropic. The results challenge conventional interpretations based on Kohn anomalies and highlight the importance of quantum critical charge dynamics for understanding the enigmatic normal‑state properties of high‑T_c cuprates. Future work with improved energy resolution and broader doping/strain parameter space will be essential to map the full critical spectrum and its connection to superconductivity.