Electronic Properties of TiO$_2$ Nanotubes
  quasi-one-dimensional (1D) titania nanostructures - single-walled nanotubes formed by rolling [101] planes of TiO$_2$ (anatase phase) are modeled and their electronic properties and bond orders indices are studied using the tight-binding band theory. We show that all zigzag (n,0)- and armchair (n,n)-like nanotubes are uniformly semiconducting, and the band gap trends to vanish as the tube diameters decrease. It was established that the zigzag (n,0) nanotubes configurations are more likely to form when the diameters are larger 1 nm. The Ti-O covalent bonds were found to be the strongest interactions in TiO$_2$ tubes, whereas Ti-Ti bonds proved to be much weaker. 
V.V. Ivanovskaya, A.N. Enyashin, N.I. Medvedeva and A.L. Ivanovskii