First-principles study of electron and hole doping effects in perovskite nickelates

Rare-earth nickelates ${R}^{3+}{\mathrm{Ni}}^{3+}{\mathrm{O}}_{3}$ ($R=\mathrm{Lu}\text{\ensuremath{-}}\mathrm{Pr}$, Y) show a striking metal-insulator transition in their bulk phase whose temperature can be tuned by the rare-earth radius. These compounds are also the parent phases of the newly identified infinite layer $R\mathrm{Ni}{\mathrm{O}}_{2}$ superconductors. Although intensive theoretical works have been devoted to understand the origin of the metal-insulator transition in the bulk, there have only been a few studies on the role of hole and electron doping by rare-earth substitutions in $R\mathrm{Ni}{\mathrm{O}}_{3}$ materials. Using first-principles calculations based on density functional theory (DFT) we study the effect of hole and electron doping in a prototypical nickelate $\mathrm{SmNi}{\mathrm{O}}_{3}$. We perform calculations without Hubbard-like $U$ potential on Ni $3d$ levels but with a meta--generalized gradient approximation better amending self-interaction errors. We find that at low doping, polarons form with intermediate localized states in the band gap resulting in a semiconducting behavior. At larger doping, the intermediate states spread more and more in the band gap until they merge either with the valence (hole doping) or the conduction (electron doping) band, ultimately resulting in a metallic state at 25% of $R$ cation substitution. These results are reminiscent of experimental data available in the literature and demonstrate that DFT simulations without any empirical parameter are qualified for studying doping effects in correlated oxides and exploring the mechanisms underlying the superconducting phase of rare-earth nickelates.