Oscillations of the band gap of single-walled carbon nanotubes in the range of very small diameters

The electronic properties of carbon nanotubes with controllable chirality indices are studied in the range of very small diameters (0.3–2.0 nm) of semiconductor single-walled carbon nanotubes. The density functional theory (DFT) in the local density approximation (LDA) (DFT-LDA) method and Gaussian and TubeGen software are used in the study. An unsteady oscillatory variation in the band gap is established. Such behavior is due to the small chirality indices that define the symmetry and curvature of nanotubes. It is found that, for semiconductor nanotubes with very small diameters and (0, 4) and (0, 5) chirality indices, the band structure is degenerate and this degeneracy is responsible for the metal properties and violation of the rule of the 3 k classification of single-walled nanotubes according to their electrical properties.