Landscape of coexisting excitonic states in the insulating single-layer cuprates and nickelates

We present an ab initio study of the excitonic states of a prototypical high-temperature superconductor ${\mathrm{La}}₂{\mathrm{CuO}}₄$ and compare them to the isostructural single-layer nickelate ${\mathrm{La}}₂{\mathrm{NiO}}₄$. A key difference in the low-energy electronic structure leads to very different excitonic behavior. Excitons in ${\mathrm{La}}₂{\mathrm{CuO}}₄$ are delocalized and can freely move in the ${\mathrm{CuO}}₂$ plane without disturbing the antiferromagnetic order. In contrast, in ${\mathrm{La}}₂{\mathrm{NiO}}₄$, we find the low-lying excitonic states to be extremely localized, producing a nearly flat dispersion. The theoretically obtained excitonic dispersion and behavior are in excellent agreement with RIXS observations. To classify the excitons, we project the electron-hole coupling onto each atomic site including the full manifold of atomic orbitals. We find the excitons to be composed of a linear combination of exciton classes, including Mott-Hubbard, $d\text{\ensuremath{-}}d$, and charge-transfer. The implication of these excitations to the high-${T}_c$ pairing mechanism is also discussed.