Nature of the electronic band gap in lanthanide oxides

Abstract

Accurate electronic structures of the technologically important lanthanide/rare-earth sesquioxides (Ln${}_{2}$O${}_{3}$, with $\text{Ln}=\text{La},\ensuremath{\cdots},$Lu) and CeO${}_{2}$ have been calculated using hybrid density functionals HSE03, HSE06, and screened exchange (sX-LDA). We find that these density functional methods describe the strongly correlated Ln $f$ electrons as well as the recent ${G}_{0}{W}_{0}$@LDA$+U$ results, generally yielding the correct band gaps and trends across the Ln period. For HSE, the band gap between O 2$p$ states and lanthanide 5$d$ states is nearly independent of the lanthanide, while the minimum gap varies as filled or empty Ln 4$f$ states come into this gap. sX-LDA predicts the unoccupied 4$f$ levels at higher energies, which leads to a better agreement with experiments for Sm${}_{2}$O${}_{3}$, Eu${}_{2}$O${}_{3}$, and Yb${}_{2}$O${}_{3}$.