Detection of confined current paths on oxide surfaces by   local-conductivity atomic force microscopy with atomic resolution
  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. 
C. Rodenb\"ucher, G. Bihlmayer, W. Speier, J. Kubacki, M. Wojtyniak,   M. Rogala, D. Wrana, F. Krok, K. Szot
cond-mat.mes-hall