Stabilization of 3-dimensional charge order through interplanar orbital hybridization in Pr$_{x}$Y$_{1-x}$Ba$_{2}$Cu$_{3}$O$_{6+\delta }$

In the copper oxides, two-dimensional (2D) charge order (CO) is a universal phase that competes with superconductivity but is only a short-range phenomenon primarily due to disorder. Three-dimensional (3D) CO can emerge by applying magnetic field or strain, but a 2D CO component remains present and the out-of-plane correlation lengths remain shortened by disorder. We report Cu-L$_{3}$ and Pr-M$_{5}$ resonant x-ray scattering experiments and band structure calculations on Pr$_{x}$Y$_{1-x}$Ba$_{2}$Cu$_{3}$O$_{6+\delta }$ showing that, through the hybridization between the Pr 4$f$ orbital and CuO$_{2}$ electronic states, 3D CO can be stabilized with the highest reported out-of-plane correlation length. Importantly, we do not detect any evidence of 2D CO. These results provide the first observation of a fully stabilized and isolated 3D CO phase that can be achieved by tuning the orbital character of the electronic structure.