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Correlations turn electronic structure of finite-layer nickelates upside down

Motivated by the recent discovery of superconductivity in the pentalayer nickelate Nd$_6$Ni$_5$O$_{12}$ [Nature Materials 10.1038], we calculate its electronic structure and superconducting critical temperature. We find that electronic correlations are essential for pushing Nd$_6$Ni$_5$O$_{12}$ into the superconducting doping range as they shift the electron pockets above the Fermi energy. As a consequence, Nd$_6$Ni$_5$O$_{12}$ can be described with a single $d_{x^2-y^2}$ orbital per Ni. Instead, for the bilayer nickelate Nd$_3$Ni$_2$O$_6$ we find correlations to drive the system into a three-orbital regime also involving the Ni $d_{xz,yz}$ states. We suggest, however, that single-orbital physics with optimal doping can be restored by substituting 60% of the trivalent Nd or La by tetravalent Zr.