One-dimensionally extended oxygen vacancy states in perovskite oxides

Abstract

We elucidate as-yet-unidentified spatially extended oxygen vacancy states in $\mathit{AB}{\mathrm{O}}_{3}$ perovskite oxides using first-principles calculations. When $B$ sites are occupied with ${d}^{0}$ transition-metal ions, charged oxygen vacancies are found to be long ranged in one direction because of charge transfer accompanied with atomic displacement along a chainlike structure. This finding offers two important results. First, it explains the reason why accurate calculations of oxygen vacancy formation energies necessitate very large supercells in ${d}^{0}$ perovskite and related oxides. It is remarkable especially for ${\mathrm{KNbO}}_{3}$ and ${\mathrm{WO}}_{3}$ on account of their anomalous Born effective charges. Second, such elongated vacancy states tend to show lower formation energies and thereby shallower donor levels. Our discussion is extendable to systems other than perovskites. Since the chainlike structure also appears in anatase ${\mathrm{TiO}}_{2}$ but not in its rutile counterpart, it could be a reason why the oxygen vacancy is a double shallow donor in the former while constructing a deep state in the latter.