Late transition-metal oxides with infinite-layer structure: Nickelates versus cuprates

The correlated electronic structure of the infinite-layer compounds NdNiO$_2$ and SrCuO$_2$ at stoichiometry and with finite hole doping is compared. Key differences are elucidated from an advanced first-principles many-body perspective. Contrary to the charge-transfer insulating cuprate, the self-doped nickelate remains non-insulating even for large interaction strength, though the Ni-$d_{x^2-y^2}$ spectral weight is also gapped in that limit. Hybridization between Ni$(3d)$ and Nd$(5d)$ is crucial for the appearance of the self-doping band. Upon realistic hole doping, Sr$_{1-y}$CuO$_2$ shows the expected mixed oxygen-Cu-$d_{x^2-y^2}$ (Zhang-Rice) states at low-energy. In the case of Nd$_{1-x}$Sr$_x$NiO$_2$, the self-doping band is shifted to higher energies and a doping-dependent $d_{z^2}$-versus-$d_{x^2-y^2}$ competition on Ni is revealed. The absence of prominent Zhang-Rice physics in infinite-layer nickelates might be relevant to understand the notable difference in the superconducting $T_{\rm c}$'s.