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

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.