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Based on the symmetry adapted tight-binding model, the electronic energy band structures of single wall carbon nanotubes are calculated by considering the spin-orbit coupling interaction. The energy gaps at the Dirac point for the armchair nanotubes are formed due to the spin-orbit coupling interaction and the curvature effect. For the zigzag and chiral carbon nanotubes,the energy band splittings for the lowest unoccupied states and the highest occupied states are also formed by the spin-orbit coupling interaction. The energy splittings are not only dependedent on the diameter and the chiral angle of the carbon nanotubes, but also a symmetric with respect to the Fermi energy level. According to the chiral index (n, m), different tube behaviors are grouped into three families. The numeral results are in good agreement with the experimental results.
[1] Iijima S 1991 Nature (London) 354 56
[2] Mintmire J M, Dunlap B I, White C T 1992 Phys. Rev. Lett. 68 631
[3] Hamada N, Sawada S, Oshiyama A 1992 Phys. Rev. Lett. 68 1579
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[5] Zhang Z H, Peng J C, Chen X H 2001 Acta Phys. Sin. 50 1150 (in Chinese) [张振华、彭景翠、陈小华 2001 物理学报 50 1150]
[6] Ou Y Y, Peng J C, Wang H, Yi S P 2008 Acta Phys. Sin. 57 615 (in Chinese) [欧阳玉、彭景翠、王 慧、易双萍 2008 物理学报 57 615]
[7] Mei L W, Zhang Z H, Ding K H 2009 Acta Phys. Sin. 58 1971 (in Chinese) [梅龙伟、张振华、丁开和 2009 物理学报 58 1971]
[8] Satio R, Fujita M, Dresselhaus G, Dresselhaus M S 1992 Appl. Phys. Lett. 60 2204
[9] Satio R, Fujita M, Dresselhaus G, Dresselhaus M S 1992 Phys. Rev. B 46 1804
[10] Popov V N 2004 New J. Phys. 6 17
[11] Popov V N, Henrard 2004 Phys. Rev. B 70 115407
[12] Ando T 2000 J. Phys. Soc. Jpn. 69 1757
[13] Liang W, Bocktath M, Park H 2002 Phys. Rev. Lett. 88 126801
[14] Jarillo-Herrero P, Kong J, van der Zant H S J, Dekker C, Kouwenhoven L P, Franceschi S D 2005 Nature (London) 434 484
[15] Jarillo-Herrero P, Kong J, van der Zant H S J, Dekker C, Kouwenhoven L P, Franceschi S D 2005 Phys. Rev. Lett. 94 186806
[16] Chico L, Lopez-Sancho M P, Munoz M C 2004 Phys. Rev. Lett. 93 176402
[17] Chico L, Lopez-Sancho M P, Munoz M C 2009 Phys. Rev. B 79 235423
[18] Huertas-Hernando D, Guinea F, Brataas A 2006 Phys. Rev. B 74 155426
[19] Zhou J, Liang Q F, Dong J M 2009 Phys. Rev. B 79 195427
[20] Tsukagoshi, Alphenaar B W, Ago H 1999 Nature (London) 401 572
[21] Kuemmeth F, Ilani S, Ralph D, McEuen P 2008 Nature (London) 452 448
[22] Izumida W, Sato K, Saito R 2009 J. Phys. Soc. Jpn. 78 070407
[23] Kato T, Onari S, Inoue J 2010 Physica E 42 729
[24] Porezag D, Frauenheim Th, Khler Th 1995 Phys. Rev. B 59 12678
[25] Yao Y G, Ye F, Qi X L, Zhang S C, Fang Z 2007 Phys. Rev. B 75 041401 (R)
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[1] Iijima S 1991 Nature (London) 354 56
[2] Mintmire J M, Dunlap B I, White C T 1992 Phys. Rev. Lett. 68 631
[3] Hamada N, Sawada S, Oshiyama A 1992 Phys. Rev. Lett. 68 1579
[4] Ouyang M, Huang J, Cheung C L, Lieber C M 2001 Science 292 7302
[5] Zhang Z H, Peng J C, Chen X H 2001 Acta Phys. Sin. 50 1150 (in Chinese) [张振华、彭景翠、陈小华 2001 物理学报 50 1150]
[6] Ou Y Y, Peng J C, Wang H, Yi S P 2008 Acta Phys. Sin. 57 615 (in Chinese) [欧阳玉、彭景翠、王 慧、易双萍 2008 物理学报 57 615]
[7] Mei L W, Zhang Z H, Ding K H 2009 Acta Phys. Sin. 58 1971 (in Chinese) [梅龙伟、张振华、丁开和 2009 物理学报 58 1971]
[8] Satio R, Fujita M, Dresselhaus G, Dresselhaus M S 1992 Appl. Phys. Lett. 60 2204
[9] Satio R, Fujita M, Dresselhaus G, Dresselhaus M S 1992 Phys. Rev. B 46 1804
[10] Popov V N 2004 New J. Phys. 6 17
[11] Popov V N, Henrard 2004 Phys. Rev. B 70 115407
[12] Ando T 2000 J. Phys. Soc. Jpn. 69 1757
[13] Liang W, Bocktath M, Park H 2002 Phys. Rev. Lett. 88 126801
[14] Jarillo-Herrero P, Kong J, van der Zant H S J, Dekker C, Kouwenhoven L P, Franceschi S D 2005 Nature (London) 434 484
[15] Jarillo-Herrero P, Kong J, van der Zant H S J, Dekker C, Kouwenhoven L P, Franceschi S D 2005 Phys. Rev. Lett. 94 186806
[16] Chico L, Lopez-Sancho M P, Munoz M C 2004 Phys. Rev. Lett. 93 176402
[17] Chico L, Lopez-Sancho M P, Munoz M C 2009 Phys. Rev. B 79 235423
[18] Huertas-Hernando D, Guinea F, Brataas A 2006 Phys. Rev. B 74 155426
[19] Zhou J, Liang Q F, Dong J M 2009 Phys. Rev. B 79 195427
[20] Tsukagoshi, Alphenaar B W, Ago H 1999 Nature (London) 401 572
[21] Kuemmeth F, Ilani S, Ralph D, McEuen P 2008 Nature (London) 452 448
[22] Izumida W, Sato K, Saito R 2009 J. Phys. Soc. Jpn. 78 070407
[23] Kato T, Onari S, Inoue J 2010 Physica E 42 729
[24] Porezag D, Frauenheim Th, Khler Th 1995 Phys. Rev. B 59 12678
[25] Yao Y G, Ye F, Qi X L, Zhang S C, Fang Z 2007 Phys. Rev. B 75 041401 (R)
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