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 La2CuO4 and compare them to the isostructural single-layer nickelate La2NiO4. A key difference in the low-energy electronic structure leads to very different excitonic behavior. Excitons in La2CuO4 are delocalized and can freely move in the CuO2 plane without disturbing the antiferromagnetic order. In contrast, in La2NiO4, 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-d, and charge-transfer. The implication of these excitations to the high-T-c pairing mechanism is also discussed.