All-electronGWcalculation of rutileTiO2with and without Nb impurities

Abstract

The all-electron mixed basis $GW$ approach is applied to calculate the electronic structure of rutile ${\mathrm{TiO}}_{2}$ and ${\mathrm{Ti}}_{0.75}{\mathrm{Nb}}_{0.25}{\mathrm{O}}_{2}$. The quasiparticle energies are calculated in fine detail, allowing the accurate determination of electronic structures. Although the valence band maximum (VBM) of the pure rutile ${\mathrm{TiO}}_{2}$ is composed of O $2p$ and Ti $3d$ orbitals, that of ${\mathrm{Ti}}_{0.75}{\mathrm{Nb}}_{0.25}{\mathrm{O}}_{2}$ is composed of Nb $4d$ orbitals and O $2p$ orbitals together with a few Ti $3d$ orbitals, forming an occupied impurity level, while the conduction band minimum is composed of Nb $4d$ and O $2p$ orbitals. In the calculation of ${\mathrm{Ti}}_{0.75}{\mathrm{Nb}}_{0.25}{\mathrm{O}}_{2}$, the energy level of the VBM increases, with finite energy gap, in contrast to the local density approximation calculation showing a metallic band structure. The exchange and correlation contributions to the self-energy drastically change in the VBM. The resulting electronic structure is in reasonable agreement with experiments. Based on our results, the $GW$ approximation seems good in describing a not so strongly correlated transition metal oxide system with impurities.