Hydrogen-Ti$^{3+}$ Complex as a Possible Origin of Localized Electron Behavior in Hydrogen-Irradiated SrTiO$_3$

A recent muon spin rotation ($\mu^+$SR) study on a paramagnetic defect complex formed upon implantation of $\mu^+$ pseudo-proton into SrTiO$_3$ is reviewed with a specific focus on the relation with experimental signatures of coexisting delocalized and localized electrons in hydrogen-irradiated metallic SrTiO$_3$ films. The paramagnetic defect complex, composed of interstitial $\mu^+$ and Ti$^{3+}$ small polaron, is characterized by a small dissociation energy of about 30 meV. Density functional theory (DFT) calculations in the generalized gradient approximation (GGA) +$U$ scheme for a corresponding hydrogen defect complex reveal that a thermodynamic donor level associated with electron transfer from an H$^+$-Ti$^{3+}$ complex to the conduction band can form just below the conduction band minimum for realistic $U$ values. These findings suggest that the coexistence of delocalized and localized electrons can be realized in hydrogen-irradiated SrTiO$_3$ in electron-rich conditions.