Fate of charge order in overdoped La-based cuprates

Abstract

In high-temperature cuprate superconductors, stripe order refers broadly to a coupled spin and charge modulation with a commensuration of eight and four lattice units, respectively. How this stripe order evolves across optimal doping remains a controversial question. Here we present a systematic resonant inelastic x-ray scattering study of weak charge correlations in La_2-xSr_xCuO₄ and La_1.8-xEu_0.2Sr_xCuO₄. Ultra high energy resolution experiments demonstrate the importance of the separation of inelastic and elastic scattering processes. Long-range temperature-dependent stripe order is only found below optimal doping. At higher doping, short-range temperature-independent correlations are present up to the highest doping measured. This transformation is distinct from and preempts the pseudogap critical doping. We argue that the doping and temperature-independent short-range correlations originate from unresolved electron-phonon coupling that broadly peaks at the stripe ordering vector. In La_2-xSr_xCuO₄, long-range static stripe order vanishes around optimal doping and we discuss both quantum critical and crossover scenarios.

Keywords: Electronic properties and materials; Phase transitions and critical phenomena; Superconducting properties and materials.

Fig. 1. X-ray absorption and resonant inelastic x-ray scattering spectra recorded on La_2−xSr_xCuO₄ as a function of energy loss and momentum.

a, b High-resolution RIXS spectra recorded on LSCO x = 0.145 and 0.16 at the charge ordering vector for different temperatures as indicated. Vertical dashed lines indicate the energy resolution and with that the integration window of elastic scattering. The intensity is given in arbitrary units (a. u.). The inset shows XAS spectra featuring the copper L-edge for LSCO with doping concentrations as indicated. c–f RIXS spectra probed in longitudinal (h) and transverse (k) directions on LSCO x = 0.145. Data in c, e are recorded with an energy resolution of 129 meV, whereas d, f show spectra recorded at a high-resolution beamline with a total resolution of 33 meV. Horizontal dashed lines in c, e illustrate the energy range in d, f. The improved resolution allows for resolving the phonon branch. The black circles mark the phonon dispersion determined from fitting the spectra. Error bars are set by standard deviation from fitting. High-resolution data were taken at 37 K, all other data at base temperature, see the “Methods” section.

Fig. 2. Doping evolution of the charge order in LSCO and LESCO at base temperature.

a–d Longitudinal scans along (h, 0) for the compounds and compositions as indicated. e, g Transverse scans through the longitudinal peak position (δ, k) for doping concentrations as indicated. f Circular arc scan through two charge order reflections, with ϕ = 0 at (h, 0). Panels for LSCO x = 0.145 and 0.16 compare high- and medium- resolution data. Solid lines are Gaussian fits. Error bars are set by counting statistics. See text for further explanations. Insets display sketches of the charge order reflections in reciprocal space and the scan trajectories. Data in a, e are adapted from ref. .

Fig. 3. Charge order temperature and doping dependence.

a–e Transverse and longitudinal scans through the charge ordering vector (δ, 0) recorded as a function of temperature, as indicated, on LSCO x = 0.138, 0.145, 0.16, and 0.20. Data in b, c were recorded with high energy resolution, whereas in a, d, e medium resolution was applied, see text for further information. Solid lines are fits using a Gaussian lineshape. All intensities have been normalized to the integrated dd-excitation intensity. Error bars are set by counting statistics. Insets in a, d, e display the longitudinal and transverse scan direction.

Fig. 4. Charge order parameters and phase diagram.

a–c Charge order incommensurability δ, correlation length ξ (defined as the inverse half-width-half-maximum) and integrated diffracted intensity (amplitude I divided by ξ²) versus hole doping for LSCO (circles) and LESCO (squares) at base temperature. The parameters were extracted from fits to elastic scans, see Supplementary Fig. 4. Error bars reflect the standard deviation obtained from the fits. Data for LSCO x = 0.12 are from ref. and for LESCO x = 0.125 from ref. . All colored lines are guides to the eye. Vertical dashed line in a–c marks the critical doping separating long- from short-range correlations. d Schematic charge order phase diagram: temperature versus hole doping/Sr content x. Superconducting dome and pseudogap onset of LSCO are illustrated by respectively solid violet and dashed black line^,,. Red and blue phases indicate respectively long-range and short-range charge correlations. Solid squares indicate the doping compositions studied in this work.