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Most resonant inelastic x-ray scattering (RIXS) studies of dynamic charge order correlations in the cuprates have focused on the high-symmetry directions of the copper oxide plane. However, scattering along other in-plane directions should not be ignored as it may help understand, for example, the origin of charge order correlations or the isotropic scattering resulting in strange metal behavior. Our RIXS experiments reveal dynamic charge correlations over theq_x-q_yscattering plane in underdoped Bi₂Sr₂CaCu₂O_8+δ. Tracking the softening of the RIXS-measured bond-stretching phonon, we show that these dynamic correlations exist at energies below approximately 70 meV and are centered around a quasi-circular manifold in theq_x-q_yscattering plane with radius equal to the magnitude of the charge order wave vector,q_CO. This phonon-tracking procedure also allows us to rule out fluctuations of short-range directional charge order (i.e., centered around [q_x= ±q_CO,q_y= 0] and [q_x= 0,q_y= ±q_CO]) as the origin of the observed correlations. 

Abstract The shape of 3d-orbitals often governs the electronic and magnetic properties of correlated transition metal oxides. In the superconducting cuprates, the planar confinement of the$${d}_{{x}^{2}-{y}^{2}}$$ $d_{x^2-y^2}$orbital dictates the two-dimensional nature of the unconventional superconductivity and a competing charge order. Achieving orbital-specific control of the electronic structure to allow coupling pathways across adjacent planes would enable direct assessment of the role of dimensionality in the intertwined orders. Using CuL₃and PrM₅resonant x-ray scattering and first-principles calculations, we report a highly correlated three-dimensional charge order in Pr-substituted YBa₂Cu₃O₇, where the Prf-electrons create a direct orbital bridge between CuO₂planes. With this we demonstrate that interplanar orbital engineering can be used to surgically control electronic phases in correlated oxides and other layered materials.