我們再次使用緊束法(tight-binding method)來研究單壁奈米碳管的能帶結構。藉由推廣至第三鄰近原子的Slater-Koster參數表示法，我們考慮了管壁的曲率效應。對於某些小半徑的(n,0)奈米碳管，例如(6,0)，其電子能隙在本計算中大幅地減小。此一符合其他的第一原理(first-principle)計算的結果並不能僅藉由第二鄰近的參數來求得。另外，對於(n,n)奈米碳管，曲率效應並不會改變其金屬特性。因此，第三鄰近原子在奈米碳管的能帶計算中不可忽略，特別是對於小半徑、小角度(chiral angle)的奈米碳管。藉由使用適當的S-K參數，緊束法可以很有效率地產生與第一原理結果相當的能帶結構。

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.

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