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SrTiO$_3$, although a wide gap insulator, has long been known to become metallic and superconducting at extremely low doping levels. This has given rise to questions concerning the coexistence or interdependence of metallicity, superconductivity, and the material's polar properties. This issue becomes especially intriguing in conjunction with the observation that filamentary metallicity can be induced by means of resistive switching at conditions well below relevant doping levels for homogeneous metallicity. In this study, we demonstrate that resistive switching can also be employed to generate superconductivity at the superconducting transition temperature of $T_c$ $\approx$ 0.2 K in SrTiO$_3$. By combining local characterization of the conductivity with theoretical analysis, we propose that the superconducting properties are associated with the electro-formation of columnar-like bundles with a diameter of 40-50 nm, consisting of metallic filaments surrounded by polar regions. We provide a theoretical model identifying the coexistence of metallic and polar regions as a prerequisite for the filamentary-like superconductivity observed.

The analysis of the electronic surface properties of transition metal oxides being key materials for future nanoelectronics requires a direct characterization of the conductivity with highest spatial resolution. Using local conductivity atomic force microscopy (LC-AFM) we demonstrate the possibility of recording current maps with true atomic resolution. The application of this technique on surfaces of reduced TiO$_2$ and SrTiO$_3$ reveals that the distribution of surface conductivity has a significant localized nature. Assisted by density functional theory (DFT) we propose that the presence of oxygen vacancies in the surface layer of such materials can introduce short range disturbances of electronic structure with confinement of metallic states on the nanoscale.