在本篇論文中我們使用緊束模型（tight–binding model）的方法來求得單層碳微管的磁性能帶結構。其能帶結構會受到碳微管的幾何結構( 和 )、曲度效應、混成效應、spin-B interaction各方面因素的影響，其特徵結果會直接反應在磁化係數（Magnetization）和微分磁化率（Differential Susceptibility）的表現上。在能隙發生金屬與半導體轉換的地方，磁化係數會有cusps的產生，微分磁化率會有對數發散的產生。在小磁場的範圍，曲度效應和 電子會使磁化係數和微分磁化率變小，但不會改變磁性。當磁通量等於零時，曲度效應和 電子對磁化係數沒有影響（M=0），但是對微分磁化率有很大的影響。

We use the tight-binding model to calculate the magneto band structures of single-walled carbon nanotubes. They strongly depend on the geometric structures,the curvature effects, the mixture effects, and the spin-B interaction. Their features are directly reflected in the magnetization and the differential susceptibility. Within the presence of the metal-semiconductor transition, the magnetization exhibits the discontinuous cusp structures and the differential susceptibility occurs logarithmic divergencies. At the small flux, the curvature effect and the -electron would decrease the magnetization and the differential susceptibility, but would not change the magnetism. When the flux equals to zero, the curvature effect and the -electron would not affect the magnetization ( M=0 ), but have effect on the differential susceptibility.

[1] S. Iijima, Nature 354, 56(1991).
[2] M. Fujita, K. Wakabayashi, K. Nakada, and K, Kusakabe, J. Phys. Soc. Jpn. 65, 1920(1996).
[3] For the details of curvature effects see F. L. Shyu and M. F. Lin,
J. phys. Soc. Jpn. 71, 1820 (2002)
[4] C.W. Chiu, C.P. Chang, F.L. Shyu, R.B. Chen, and M.F. Lin,
Phys. Rev. B 67, 165421(2003)
[5] F.L. Shyu, C.P. Chang, R.B. Chen, C.W. Chiu, and M.F. Lin,
Phys. Rev. B 67, 045405(2003)
[6] H. Ajiki, and T. Ando, J. Phys. Soc. Jpn. 62, 1255(1992)
[7] H. Ajiki, and T. Ando, J. Phys. Soc. Jpn. 65, 505(1996)
[8] H. Ajiki, and T. Ando, J. Phys. Soc. Jpn. 64, 4382(1995)
[9] Jian Ping Lu, Phys. Rev. L 74, 1123(1995)
[10] M. F. Lin, and Kenneth W-K. Shung, Phys. Rev. B 48, 5567(1993)
[11] R. Saito, G. Dresselhaus, and M.S. Dresselhaus, Phys. Rev. B 50, 14698(1994)
[12] M. F. Lin, and Kenneth W-K. Shung, Phys. Rev. B 52, 8423(1995)
[13] H. Ajiki, and T. Ando, J. Phys. Soc. Jpn. 62, 2470(1993)
[14] F. Tsui, L. Jin, and O. Zhou, Appl. Phys. Lett. 76, 1452(2000).
[15] Shunji Bandow, J. Appl. Phys. 80,1020(1996)
[16] Feng Chen, Yuyi Xue, Viktor G. Hadjiev, and C. W. Chu, Appl. Phys. Lett. 83, 4601(2003).
[17] J. Heremans, C. H. Olk, and D.T. Morelli, Phys. Rev. B 49, 15122(1994)
[18] P. R. Wallace, Phys. Rev. 71, 622(1947)
[19] M. F. Lin, J. Phys. Soc. Jpn. 67, 1094(1998)