Ti-Ti σ bond at oxygen vacancy inducing the deep defect level in anatase TiO2 (101) surface

Using the GW method within many-body perturbation theory, we investigate the quasiparticle structures of defects, including oxygen vacancy, Ti interstitial, and hydroxyl groups, in the anatase TiO2 (101) surface. We find that the deep defect state in this surface observed experimentally, which is 1 eV below the Fermi level, originates from the sigma bond formed between 3d orbitals of the two under-coordinated Ti atoms at the surface oxygen vacancy. Different from the density functional theory modified with on-site Coulomb terms (DFT + U), the GW method predicts that the localized polaron in anatase (101) is a shallow defect state close to the conduction band bottom. Polaronic states play the role in pinning the Fermi level of anatase near the conduction band bottom. Our GW calculations can explain satisfactorily the coexistence of shallow and deep defect states in anatase as observed in experiments. We also find that the conduction band edge of anatase is drawn down greatly after the filling of original empty Ti 3d orbitals by excess electrons, making the calculated bandgap of the reduced anatase agree well with the experiments. This significant difference in the bandgap between the intact and the reduced anatase is missed in DFT + U.