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

Abstract

We present an $\text{ab initio}$ study of the excitonic states of a prototypical high-temperature superconductor La${}_2$CuO${}_4$ and compare them to the isostructural single-layer nickelate La${}_2$NiO${}_4$. Key difference in the low-energy electronic structure leads to very different excitonic behavior. Excitons in La${}_2$CuO${}_4$ are delocalized and can freely move in the CuO${}_2$ plane without disturbing the antiferromagnetic order. In contrast, in La${}_2$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, $d-d$, and charge-transfer. The implication of these excitations to the high-$T_c$ pairing mechanism is also discussed.

11 pages, 4 figures