The recent discovery of high-temperature superconductivity in the bilayer nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ has spurred intense interest in exploring analogous mechanisms in other transition metal oxides. This raises a pivotal question: can cuprates, as neighbors to nickelates in the periodic table, host similar two-orbital superconductivity? Here, we systematically investigate the electronic structure of a series of designed Ruddlesden-Popper cuprates. Our calculations reveal that the parent compound ${\mathrm{La}}_3{\mathrm{Cu}}_2{\mathrm{O}}_7$ is a weakly correlated metal, and hole doping fails to induce strong correlation. We find that the actual valence of the copper cations becomes strikingly pinned around $+2.3$, far away from the targeted $d^8$ configuration. This valence pinning is attributed to the in- herent charge-transfer nature of cuprates. We propose this mechanism as a general principle explaining the robust single-orbital physics consistently observed in the cuprate family, holding true even in materials like the high-$T_c$ superconductor ${\mathrm{Ba}}_2{\mathrm{CuO}}_{3+\delta }$ that appear structurally primed for two-orbital activity. Our results therefore conclude that the route towards two-orbital superconductivity is fundamentally obstructed in cuprates, providing a crucial constraint for the future design of high-temperature superconductors.

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• Multiband superconductivity
• Cuprates
• Nickelates
• Strongly correlated systems
• Density functional theory
• Dynamical mean field theory