Effect of Magnetic Field on the Electronic Band Structure of Single Walled Carbon Nanotube

The electronic band structure of Single Walled Carbon Nanotubes (SWCNTs) is shown to vary with mechanical deformation, electric and magnetic fields. The electronic structure is analytically investigated by Saito et al. [1] in 1992. His method is based on π-Tight-Binding (π-TB) model. This method has the advantage of applicability in whole of the Brillouin zone. The effect of magnetic field on the electronic structure is investigated by Ajiki and Ando [2] in 1993 using k.p method. However, there is a limitation for using k.p perturbation theory around the K point, at the corner of the hexagonal Brillouin zone in the case of a CNT, since the k valuestaken in the direction of the tubule circumference can be far from the K point, leading to incorrect values of the energy. In this paper we investigate the energy versus k vector using the π-TB method which is applicable for the whole of Brillouin zone. The magnetic field is taken perpendicular to the tubule’s axis. The frequency of this field must be negligible in comparison with frequency of the lattice vibrations. Furthermore, an analytic formula is driven for high symmetry zig-zag nanotubes