Origin of the deep band-gap state in TiO2 (110): ddσ bonds between Ti-Ti pairs

Abstract

Defects play crucial roles in the photonic and chemical activities of ${\mathrm{TiO}}_{2}$. The origin of the deep band-gap defect state ${S}_{bg}$ in the rutile ${\mathrm{TiO}}_{2}$(110) surface has remained controversial for quite a long time. Using many-body Green's function theory, we believe that ${S}_{bg}$ can be attributed only to $\ensuremath{\sigma}$ bonds formed between $3d$ orbitals at the Ti interstitial, while the nonbonded Ti $3d$ defect states from the oxygen vacancy and polaron, which are held to be responsible for ${S}_{bg}$ by the present prevailing view, are shallow regardless of their spatial distribution. Especially, we discover the defect-induced appreciable downshift of unoccupied Ti $3d$ bands which should be the key for accurately describing the electronic structure of ${\mathrm{TiO}}_{2}$ but was missed in previous studies based on density functional theory. Our model could more consistently and more reasonably account for various experimental phenomena on rutile (110) than the current model based on the oxygen vacancy and polaron.