  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.
