The calculation of energy gaps in small single-walled carbon nanotubes within a symmetry-adapted tight-binding model

This paper studies in detail the electronic properties of the semimetallic single-walled carbon nanotubes by applying the symmetry-adapted tight-binding model. It is found that the hybridization of π-σ states caused by the curvature produces an energy gap at the vicinity of the Fermi level. Such effects are obvious for the small zigzag and chiral single-walled carbon nanotubes. The energy gaps decrease as the diameters and the chiral angles of the tubes increase, while the top of the valence band and the bottom of the conduction band of armchair tubes cross at the Fermi level. The numeral results agree well with the experimental results.