Localized and Itinerant States in Lanthanide Oxides United by $GW@\mathrm{LDA}+U$

Many-body perturbation theory in the $GW$ approach is applied to lanthanide oxides, using the local-density approximation plus a Hubbard $U$ correction ($\mathrm{LDA}+U$) as the starting point. Good agreement between the $G_0{W}_0$ density of states and experimental spectra is observed for ${\mathrm{CeO}}_2$ and ${\mathrm{Ce}}_2{\mathrm{O}}_3$. Unlike the $\mathrm{LDA}+U$ method $G_0{W}_0$ exhibits only a weak dependence on $U$ in a physically meaningful range of $U$ values. For the whole lanthanide sesquioxide (${\mathrm{Ln}}_2{\mathrm{O}}_3$) series $G_0{W}_0@\mathrm{LDA}+U$ reproduces the main features found for the optical experimental band gaps. The relative positions of the occupied and unoccupied $f$ states predicted by $G_0{W}_0$ confirm the experimental conjecture derived from phenomenological arguments.

Figure 1

The DOS of ${\mathrm{CeO}}_2$ (left) and ${\mathrm{Ce}}_2{\mathrm{O}}_3$ (right) from LDA, $\mathrm{LDA}+U$ and $G_0{W}_0@\mathrm{LDA}+U$ with $U=5.4\mathrm{eV}$ are compared to experimental data ($\mathrm{XPS}+\mathrm{BIS}$ and $\mathrm{XPS}+\mathrm{XAS}$) [38]. The LDA and $\mathrm{LDA}+U$ curves have been offset vertically for clarity.

Figure 2

Band gaps of ${\mathrm{CeO}}_2$ ($p\mathrm{\text{−}}f$ and $p\mathrm{\text{−}}d$, upper row) and ${\mathrm{Ce}}_2{\mathrm{O}}_3$ ($f\mathrm{\text{−}}d$ and $p\mathrm{\text{−}}d$, lower row) from $\mathrm{LDA}+U$ and $G_0{W}_0@\mathrm{LDA}+U$ as a function of $U$. The dashed rectangles in the lower panel indicate the range of physically meaningful values of $U$ (see text).

Figure 3

Band gaps of the ${\mathrm{Ln}}_2{\mathrm{O}}_3$ series from $\mathrm{LDA}+U$ and $G_0{W}_0$ ($U=5.4\mathrm{eV}$) are compared to SIC-LDA results [10] and experimental optical gaps [8]. The schematic in the upper part of the figure illustrates the position of the $f^{\mathrm{occ}}$ and $f^{\mathrm{un}}$ states extracted from the $G_0{W}_0@\mathrm{LDA}+U$ calculations in relation to the valence and conduction band edge (VB and CB).