单壁纳米碳管的声子谱研究

Phonon spectrum of single-walled carbon nanotubes

通过五步旋转操作方便地得到了不同位置原子间的力常数矩阵 ,从而可以使对各种不同类型管的声子谱的计算变得简便 .计算表明 ,非螺旋的扶手椅型 (n ,n)管与锯齿型 (n ,0 )管的非简并和二重简并模式数分别为 12和6 (n- 1) ,这与从群论等方法所得结果相符 .

The phonon spectra are calculated within the frame of force constant model. By virtue of five rotation operations determined by the coordinates of carbon atoms, it is convenient for us to obtain the force matrix. The calculations show that there are only 12 non-degenerate phonon branches and 6(n - 1) degenerate branches for armchair (n, n) tube and zigzag (n, 0) tube.