Dual behavior of excess electrons in rutile TiO₂

The behavior of electrons in the conduction band of TiO2 and other transition-metal oxides is key to the many applications of these materials. Experiments seem to produce conflicting results: optical and spin-resonance techniques reveal strongly localized small polarons, while electrical measurements show high mobilities that can only be explained by delocalized free electrons. By means of hybrid functional calculations we resolve this apparent contradiction and show that small polarons can actually coexist with delocalized electrons in the conduction band of TiO2, the former being energetically only slightly more favorable. We also find that small polarons can form complexes with oxygen vacancies and ionized shallow-donor impurities, explaining the rich spectrum of Ti$^{3+}$ species observed in electron spin resonance experiments.