Abstract
The electronic band structures of single-walled carbon nanotubes (SWCNTs) are investigated again within the tight-binding scheme. The curvature effects are considered with the Slater-Koster parameters extended to the 3rd nearest neighbors. For small-diameter zigzag SWCNTs such as the (6,0) case, the energy band gap is significantly reduced. This result which is confirmed with the first-principle studies can not be reproduced when the parameters are only extended to the 2nd nearest neighbors. For armchair SWCNTs, curvature effects do not alter the metallic property because of symmetry. It is concluded that the 3rd nearest neighbors can not be neglected for the band structures of small-diameter and small-chiral-angle SWCNTs. By using appropriate Slater-Koster parameters, the tight-binding method can be efficient to generate the band structures comparable with the first-principle results.