Orbital Separation of Charge Order and Superconductivity in La$_{2-x}$Sr$_{x}$CuO$_4$

Abstract

We report a combined x-ray absorption (XAS) and oxygen $K$-edge resonant inelastic x-ray scattering (RIXS) study of charge order in underdoped La$_{2-x}$Sr$_x$CuO$_4$ ($x=0.125$) under uniaxial $c$-axis pressure. We find that compressive $c$-axis strain modifies the charge order only within the superconducting state, with a striking polarization dependence: suppression in the $d_{x^2-y^2}$ channel and enhancement in the $d_{z^2}$ channel. X-ray absorption spectra reveal concomitant strain-induced modifications of the oxygen pre-edge and upper Hubbard band, consistent with increased $d_{z^2}$ orbital admixture. Our results suggest that $c$-axis pressure drives an orbital separation between superconductivity, rooted in $d_{x^2-y^2}$ states, and charge order, which gradually shifts to the $d_{z^2}$ channel. This orbital separation reveals a way for superconductivity and charge order to coexist in the cuprates with minimal competition. Furthermore, it suggests that the multi-order phase diagram of La$_{2-x}$Sr$_{x}$CuO$_4$ cannot be realistically described within single band models usually used to describe cuprate physics.

Figures (7)

• Figure 1: (a) Schematic representation of the uniaxial strain device. The sample is mounted with the crystallographic c-axis aligned within the scattering plane. The scattering angle $\theta_{SC}$ is controlled by the $\theta$ manipulator rotation angle. Uniaxial strain is tuned by the screw rotation $\omega$. (b) Orientation of p oxygen and d copper orbitals with respect to the polarization of incident x-ray beam (LH - horizontal, LV - vertical). (c-f) Oxygen $K$-edge x-ray absorption of strained and unstrained LSCO $x=0.125$ at 18 K. (e,f) The oxygen $K$-edge features specific for LSCO chen_electronic_1991 are shown in details for LV (e) and LH polarization (f) and marked with corresponding dashed lines: blue - apical oxygen excitation, violet - planar oxygen, grey - upper Hubbard band.
• Figure 2: RIXS spectra at oxygen K-edge under c-axis strain application, at $T<T_c$. (a) RIXS intensity versus in-plane momentum map collected with LV light polarization for unstrained condition. The vertical dashed line marks $Q_{CO}=(0,0.24)$. (b) RIXS spectra collected with LV light polarization, at $Q=(0,0.30)$ -- away from the charge ordering vector. (c-d) RIXS spectra at $Q_{CO}$. Insets schematically present the polarization of incident beam and the symmetry of the corresponding Cu $d$ orbitals, probed indirectly through hybridization with oxygen. The shaded areas demonstrate the difference within elastic signal induced by c-axis strain application.
• Figure 3: (a-c) Difference in RIXS intensity ($\Delta I$) between spectra taken with and without applied maximum strain (0.13%). Temperature and polarization conditions are indicated in the corresponding panels below. (d-f) Elastic $Q$-scans through the charge ordering vector. Intensity of charge order for unstrained (green) and maximally strained sample (red) measured below (18 K) and above $T_c$ (40 K). Insets schematically represent the polarization of incident beam and the symmetry of probed copper orbitals.
• Figure 4: Temperature dependence of charge order under uniaxial $c$-axis strain. (a) Integrated intensity of charge order ($I_{co}$) under uniaxial strain as a function of temperature, overlaid with unstrained x-ray diffraction (XRD) data adapted from Ref. kuspert_engineering_2024. Filled squares (triangles) denote high-resolution (medium-resolution) RIXS measurements performed with LV-polarized light, while filled circles correspond to high-resolution data collected with LH polarization. Black arrows schematically indicate the evolution of charge order under strain, depending on the incident light polarization. Data are normalized to unstrained values at 18 K. (b) Integrated intensity of charge order as a function of strain, measured with different light polarizations, both within and outside the superconducting state, as indicated. Data are normalized to the corresponding unstrained value.
• Figure 5: Orbital separation of superconductivity and charge order with uniaxial strain. c-axis strain deforms copper - oxygen octahedra, reducing the energy split between $d_{x^2-y^2}$ and $d_{z^2}$ orbitals. As a result, the carriers involved in charge order (CO) formation shift to $d_{z^2}$ states to avoid competition with superconductivity (SC).