Stabilization of singlet hole-doped state in infinite-layer nickelate superconductors

Motivated by the recent x-ray absorption spectroscopy and resonant inelastic x-ray scattering (RIXS) experiments, we use a detailed impurity model to explore the nature of the parent compound and hole-doped states of (La, Nd, $\mathrm{Pr}){\mathrm{NiO}}₂$ by including the crystal field splitting, the $\mathrm{Ni}\text{\ensuremath{-}}3d$ multiplet structure, and the hybridization between $\mathrm{Ni}\text{\ensuremath{-}}3d, \mathrm{O}\text{\ensuremath{-}}2p$, and $\mathrm{Nd}\text{\ensuremath{-}}5d$ orbitals. For simplicity and stimulated by the recent electronic structure calculations, the latter are formally replaced with symmetric orbitals centered at the missing O sites in the Nd layer, forming a two-dimensional band strongly hybridizing with the $\mathrm{Ni}\text{\ensuremath{-}}3{d}_{{z}²}⁹$ state. This hybridization pushes the main part of the $3{d}_{{z}²}⁹$ spectral function up in energy by several eV and stabilizes the singlet with considerable ${d}_{{z}²}⁹$ and other configurational components. For the parent compound, we find that states of $\mathrm{Ni}\text{\ensuremath{-}}3{d}_{{z}²}⁹$ character spread over a large energy range in the spectra, and cannot and should not be represented by a single orbital energy, as suggested in other approximations. This is qualitatively consistent with the RIXS measurements showing a broad distribution of the $\mathrm{Ni}\text{\ensuremath{-}}3{d}_{{z}²}⁹$ hole state, although the shape of the $\mathrm{Ni}\text{\ensuremath{-}}3{d}_{{z}²}⁹$ related structure is much more complicated requiring reinterpretations of the RIXS data. For the hole-doped systems, we show that adding these additional ingredients can still result in the lowest-energy hole-doped state having a singlet character.