Low-energy electronic properties of carbon nanotubes

Low-energy electronic properties of carbon nanotubes are studied by the tight-binding model. When the bond symmetry of neighboring carbon atoms is broken, the transfer integrals will vary along the different directions. We attempt to develop a general formulation to include the effects of curvature, strain, and magnetic field. Analytic expressions for energy gap and electron effective mass are derived for achiral zigzag and armchair nanotubes. The ratio of electron effective mass to energy gap can be expressed simply as a constant. There are significant differences among (3I+1,0), (3I-1,0), and (3I,0) zigzag nanotubes regarding the effects of strain on the semiconductor-metal transition. The critical magnetic flux of the narrow-gap zigzag nanotubes is inversely proportional to the nanotube radius. The dependence of the electronic properties on the chiral angle is strong.