Small Polaron Formation on the Nb-doped SrTiO$_\textbf{3}$(001) Surface
The cubic perovsike strontium titanate SrTiO$_3$ (STO) is one of the most studied, polarizable transition metal oxides. When excess charge is introduced to this material, e.g., through doping or atomic defects, STO tends to host polarons: Quasi-particles formed by excess charge carriers coupling with the crystal phonon field. Their presence alters the materials properties, and is a key for many applications. Considering that polarons form preferentially on or near surfaces, we study small polaron formation at the TiO$_2$ termination of the STO(001) surface via density functional theory calculations. We model several supercell slabs of Nb-doped and undoped STO(001) surfaces with increasing size, also considering the recently observed as-cleaved TiO$_2$ terminated surface hosting Sr-adatoms. Our findings suggest that small polarons become less stable at low concentrations of Nb-doping, in analogy with polarons localized in the bulk. Further, we inspect the stability of different polaron configurations with respect to Nb- and Sr-impurities, and discuss their spectroscopic properties.