Energy Band Calculation of Spiral Single-Walled Carbon Nanotubes

On the base of the electron energy band structure of graphene obtained by the tight-binding method, the quantized wave vector equation along the circumferential director of the spiral single-walled carbon nanotubes was established through coordinate transformation and periodic boundary condition, and an analytical expression of the electron energy band was derived. MATLAB is used to calculate the energy band curve of spiral single-walled carbon nanotubes with different structural parameters. The characteristic of the energy band curves was analyzed and discussed. The results shows that single-walled carbon nanotubes (n, m) can be identified as metallic with no band gap nearly which satisfies n-m=3q(q is integer), otherwise, the nanotubes is semiconducting and there are band gaps between conduction band and valence band. And the band gap is inversely proportional to diameter approximately for semiconducting tubes.