Electronic properties of lanthanide oxides from theGWperspective

A first-principles understanding of the electronic properties of $f$-electron systems is currently regarded as a great challenge in condensed-matter physics because of the difficulty in treating both localized and itinerant states on the same footing by the current theoretical approaches, most notably density-functional theory (DFT) in the local-density or generalized gradient approximation (LDA/GGA). Lanthanide sesquioxides (Ln${}_{2}$O${}_{3}$) are typical $f$-electron systems for which the highly localized $f$ states play an important role in determining their chemical and physical properties. In this paper, we present a systematic investigation of the performance of many-body perturbation theory in the $GW$ approach for the electronic structure of the whole Ln${}_{2}$O${}_{3}$ series. To overcome the major failure of LDA/GGA, the traditional starting point for $GW$, for $f$-electron systems, we base our $GW$ calculations on Hubbard $U$ corrected LDA calculations (LDA+$U$). The influence of the crystal structure, the magnetic ordering, and the existence of metastable states on the electronic band structures are studied at both the LDA+$U$ and the $GW$ level. The evolution of the band structure with increasing number of $f$ electrons is shown to be the origin for the characteristic structure of the band gap across the lanthanide sesquioxide series. A comparison is then made to dynamical mean-field theory (DMFT) combined with LDA or hybrid functionals to elucidate the pros and cons of these different approaches.