Unconventional Pressure Dependent Interorbital and Interlayer Doping in Superconducting Nickelates

The discovery of nickelate superconductivity provided the first example of a non-copper-based material with superconductivity strongly analogous to the cuprates, but recent findings raise questions and inconsistencies around the electron counts and doping phase diagrams. We show using superconducting La$_4$Ni$_3$O$_{10}$ that there are unconventional interlayer and interorbital intrinsic doping effects that render the $d_{x^2-y^2}$ orbital occupation similar to the cuprates. The results enable a consistent framework for nickelate superconductivity, while maintaining the connection between cuprate and nickelate superconductors.