Quasiparticle band structures of the 4d perovskite oxides SrZrO3 and BaZr

Although the challenge of GW calculations of the quasiparticle properties of $3d$ transition metal oxides (TMOs) is well recognized, TMOs involving $4d$ electrons may be considered borderline systems and have received less attention. Here we present the quasiparticle band structures of $\mathrm{SrZr}{\mathrm{O}}_{3}$ and $\mathrm{BaZr}{\mathrm{O}}_{3}$, two relatively simple wide band gap oxides for which accurate calculations of the electronic structure are scarce despite their technological importance. We show that fully converged GW calculations can accurately predict the quasiparticle properties of $4d$ TMO perovskites $\mathrm{SrZr}{\mathrm{O}}_{3}$ and $\mathrm{BaZr}{\mathrm{O}}_{3}$, regardless of the starting mean-field solution being calculated within straightforward density functional theory (DFT) or the $\mathrm{DFT}\text{+}U$ method. This is in contrast to the cases of $3d$ TMO perovskites $\mathrm{SrTi}{\mathrm{O}}_{3}$ and $\mathrm{BaTi}{\mathrm{O}}_{3}$, for which the $\mathrm{DFT}\text{+}U$ method is shown to provide a much better starting point for subsequent GW calculations. Compared with the fairly localized $3d$ states, the more extended $4d$ orbitals seem to be well described within DFT using local or semilocal functionals. Our results reaffirm the accuracy and robustness of the GW method provided that faithful zeroth-order mean-field solutions are available, and that the results are adequately converged.