Hybridization of lattice and charge order excitations in a superconducting cuprate

Abstract

The ubiquitous tendency of superconducting cuprates to form charge density waves (CDWs) has reignited interest in the nature of their electron-phonon interaction and its role in shaping their phase diagrams. While pronounced dispersion anomalies were reported in several phonon branches, their precise connection to charge order and superconductivity remains unresolved. Here, using high-resolution inelastic x-ray scattering under low temperature and high magnetic field, we uncover a striking phonon renormalization in YBa$_2$Cu$_3$O$_{6+x}$. It appears along a reciprocal space trajectory connecting the wave vectors of a short-range 2D-CDW, emerging above the superconducting transition, and a long-range 3D-CDW, appearing only when superconductivity is strongly suppressed. The spectral changes are strongest around the wave vector of the 3D-CDW despite the fact that it is absent in our experimental conditions. Our findings challenge conventional phonon self-energy renormalization models, instead support a scenario in which low-energy phonons hybridize with dispersive CDW excitations and provide insights into the interplay between lattice vibrations and electronic correlations in high-temperature superconductors.

Figures (4)

• Figure 1: Crystal structure, reciprocal space schematics and temperature dependence of the quasielastic peak. (a) Crystal structure of YBa$_{2}$Cu$_{3}$O$_{6.67}$. Some of the O atoms along the Cu-O chains are missing and the chains are ordered in an ortho-VIII pattern along the $a$-axis. (b-c) Schematic representation of the (0 $K$$L$) reciprocal lattice plane of YBa$_{2}$Cu$_{3}$O$_{6.67}$. Reciprocal space regions where signal related to the short-ranged 2D charge-density-wave order was detected at low temperature diffraction experiments are marked by the elongated red satellite peaks LeTacon2014. The satellite peaks corresponding to the long-ranged 3D charge-density-wave order appearing under uniaxial compression are illustrated in purple Kim2018Vinograd2024. The dashed blue rectangles mark the Brillouin zones used for the measurements presented here and the (mostly) longitudinal and (mostly) transverse measurement geometries are indicated by $\bf{Q_{2D}^{long}}$/$\bf{Q_{3D}^{long}}$ and $\bf{Q_{2D}^{trans}}$/$\bf{Q_{3D}^{trans}}$ respectively. The pink x's indicate the reciprocal space positions of the measurements presented in Fig.\ref{['fig3']}-(a,b). (d-g) Temperature dependence of the inelastic x-ray scattering spectra around the central elastic peak at the reciprocal space wave vectors (d) $\bf{Q_{2D}^{trans}}$, (e) $\bf{Q_{2D}^{long}}$, (f) $\bf{Q_{3D}^{trans}}$ and (g) $\bf{Q_{3D}^{long}}$. Note that the intensities in (f) and (g) are multiplied by 6 and 3.5 respectively. (h-i) Temperature dependence of the elastic peak intensity at the reciprocal space wave vectors (h) $\bf{Q}$ = (0 0.315 $L$) with $L$=6.5, 7 and at (i) $\bf{Q}$ = (0 1.685 $L$) with $L$=0, 0.5, 0.75, 1. The gray lines are guides to the eye.
• Figure 2: $L$ dependence of the phonon dispersion and spectra. (a) Phonon dispersion curves of YBa$_2$Cu$_3$O$_7$ along the (0 1.685 $L$) direction calculated by density-functional perturbation theory (lines). The phonon branches are grouped in two categories based on the symmetry operations for their displacement patterns: the first category (colored/grey lines) includes a mirror symmetry operation ($\sigma(x)$, $x$$\rightarrow$${-x}$), while the second category (white lines) does not. Further symmetry operations are restored for the displacement patterns of some of the modes at $L$=1 and 0.5 (see also discussion in the Discussion section). A colormap representation of the calculated structure factors is shown in the background. A zero value is calculated for the structure factors of the branches grouped in the second category. (b,c) $L$ dependence of the experimental $\chi^{\prime \prime}(\bm{Q},\omega)$ measured at (b) 295 K and (c) 12 K. A vertical offset is included for clarity. The thick solid lines correspond to the fits of the experimental data. Details of the fits are included in the lower spectra of (b) and (c) as thin lines. The fitting procedure is described in the Supplementary Note 5. The fitting results of the experimental spectra measured at 295 K are included as red open symbols in panel (a).
• Figure 3: Temperature dependence of the phonon spectra at the wave vector of the 3D charge-density-wave order and away from it. Temperature dependence of the experimental $\chi^{\prime \prime}(\bm{Q},\omega)$ measured at the reciprocal space wave vectors (a) $\bm{Q}$ = (0 0.34 7.24), (b) $\bm{Q}$ = (0 1.77 1.02), (c) $\bf{Q_{3D}^{trans}}$ = (0 0.315 7), (d) $\bf{Q_{3D}^{long}}$ = (0 1.685 1), (e) $\bm{Q}$ = (-0.082 0.318 7) and (f) $\bm{Q}$ = (-0.082 1.685 1). The vertical axis scales are common for panels (a), (c) and (e) and for panels (b), (d) and (f).
• Figure 4: Magnetic field dependence of the phonon spectra at the wave vector of the 3D charge-density-wave order. Magnetic field dependence of the experimental $\chi^{\prime \prime}(\bm{Q},\omega)$ from inelastic x-ray scattering spectra recorded at the reciprocal space wave vector $\bm{Q}$ = $\bf{Q_{3D}^{long}}$ =(0 1.685 1) at (a) 295 (150) K, (b) 65 K, (c) 47 K and (d) 30 K. The open symbols correspond to the data measured under zero field and the color-filled symbols correspond to those taken under 7 T. The intensities have been normalized to the intensity of the $\sim$11 meV peak. The error bars correspond to the statistical error.