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本文考虑自旋轨道耦合作用的情况下,采用紧束缚近似螺旋对称模型计算了单壁碳纳米管的电子能带结构.研究发现:对于Armchair型单壁碳纳米管,自旋轨道耦合作用和弯曲效应共同导致了费米面Dirac点附近电子能带结构的能隙;对于Zigzag型和手性单壁碳纳米管,自旋轨道耦合作用使得电子最高占据态和最低未占据态产生能级劈裂,能级劈裂的大小不但与碳纳米管的直径和手性角密切相关,而且相对于费米面是不对称的;根据指数(n,m)可以将Zigzag型和手性单壁碳纳米管分为金属性碳纳米管(ν=0)
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关键词:
- 单壁碳纳米管 /
- 自旋轨道耦合 /
- 紧束缚近似螺旋对称模型
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
[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 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 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 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 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 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 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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