Electronic properties of lanthanide oxides from the GW perspective

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.