我們利用緊束模型來計算雙層手椅狀碳微管的磁電子結構。它的特徵明顯會受到層與層間的交互作用、雙層的對稱結構、通過的磁通量以及基曼效應影響。層與層間的交互作用和不同的對稱結構會在低能附近產生很大的變化，像是能帶、波函數、費米能。而磁場也會使得線性能帶分裂成拋物線能帶、破壞簡併度、打開能隙及改變費米能。磁場和層與層的交互作用會相互競爭而變成金屬或半導體的性質。金屬-半導體轉換會因磁場而產生，但也會受到基曼效應的壓制。這些主要的能帶特徵也會直接反應在磁光吸收譜上。光吸收峰可以用來分辨不同的對稱結構，而起始吸收會和能隙無關。

　　Magnetoelectronic structures of double-walled armchair carbon nanotubes are calculated according to the tight-binding model. Their features are dominated by the intertube interactions, the symmetric configurations, the magnetic flux, and the Zeeman splitting. The drastic changes of the low energy states, such as energy dispersion, wave function, and Fermi level, which also rely on the different symmetries, are caused by the intertube interactions. The magnetic flux could change linear bands into parabolic bands, destroy state degeneracy, open an energy gap, and shift Fermi level. The magnetic flux and the intertube interactions, however, compete with each other in the metallic or semiconducting behavior. The Zeeman splitting would suppress the metal-semiconductor transition while the opposite is true of the magnetic flux. The main characteristics of energy bands are directly reflected in the magneto-optical absorption spectra. The different symmetric configurations can be distinguished by the absorption peaks, and the threshold absorption frequency is not identical with the energy gap.

1 Iijima S. Helical microtubules of graphitic carbon. Nature 1991;354(6348):56-8.
2 Wei J, Jiang B, Zhang X, Zhu H, Wu D. Raman study on double-walled carbon nanotubes. Chem Phys Lett 2003;376:753-7.
3 Li F, Chou SG, Ren W, Gardecki JA, Swan AK, Unlu MS, Goldberg BB, Cheng HM, Dresselhaus MS. Identification of the constituents of double-walled carbon nanotubes using Raman spectra taken with different laser-excitation energies. J Mater Res 2003;18(5):1251-8.
4 Wei J, Ci L, Jiang B, Li Y, Zhang X, Zhu H, Xu C, Wu D. Preparation of highly pure double-walled carbon nanotubes. J Mater Chem 2003;13:1340-4.
5 Flahaut E, Bacsa R, Peigney A, Laurent C. Gram-scale CCVD synthesis of double-walled carbon nanotubes. Chem Comm 2003:1442-3.
6 Chen G, Bandow S, Margine ER, Nisoli C, Kolmogorov AN, Crespi VH, Gupta R, Sumanasekera GU, Iijima S, Eklund PC. Chemically doped double-walled carbon nanotubes: cylindrical molecular capacitors. Phys Rev Lett 2003;90(25):257403(4).
7 For the details of geometric structures see Saito R, Fujita M, Dresselhaus G, Dresselhaus MS. Electronic structure of chiral graphene tubules. Appl Phys Lett 1992;60(18):2204-6. Electronic structure of graphene tubules based on ${C_{60}}$. Phys Rev B 1992;46(3):1804-11.
8 Mintwire JW, Dunlap BI, White CT. Are fullerene tubules metallic? Phys Rev Lett 1992;68(5):631-4.
9 Hamada N, Sawada SI, Oshiyama A. New one-dimensional conductors: graphitic microtubules. Phys Rev Lett 1992;68(10):1579-81.
10 Wildoer JWG, Venema LC, Rinzler AG, Smalley RE, Dekker C. Electronic structure of atomically resolved carbon nanotubes. Nature 1998;391(6662):59-62.
11 Odom TW, Huang JL, Kim P, Lieber CM. Atomic structure and electronic properties of single-walled carbon nanotubes. Nature 1998;391(6662):62-64.
12 Lin MF. Optical spectra of single-wall carbon nanotube bundles. Phys Rev B 2000;62(19):13153-9.
13 Lin MF, Shung KWK. Plasmons and optical properties of carbon nanotubes. Phys Rev B 1994;50(23):17744-7.
14 Shyu FL, Lin MF. Electronic and optical properties of narrow-gap carbon nanotubes. J Phys Soc Jpn 2002;71(8):1820-1823.
15 Shyu FL, Chang CP, Chen RB, Chiu CW, Lin MF. Magnetoelectronic and optical properties of carbon nanotubes. Phys Rev B 2003;67(4):045405(9).
16 Ajiki H, Ando T. Aharonov-Bohm effect in carbon nanotube. Physica B 1994;201:349-52.
17 Kataura H, Kumazawa Y, Minawa Y, Umezu I, Suzuki S, Ohtsuka Y, Achiba Y. Optical properties of single-walled carbon nanotubes. Synth Met 1999;103:2555-8
18 Kazaoui S, Minami N, Yamawaki H, Aoki K, Kataura H, Achiba Y. Pressure dependence of the optical absorption spectra of single-walled carbon nanotube films. Phys Rev B 2000;62(3):1643-6.
19 Bachilo SM, Strano MS, Kittrell C, Hauge RH, Smalley R, Weisman RB. Structure-assigned optical spectra of single-walled carbon nanotubes. Science 2002;298(20):2361-6.
20 Jost O, Gorbunov AA, Pompe W, Pichler T, Friedlein R, Knupfer M, Reibold M, Bauer HD, Dunsch L, Golden MS, Fink J. Diameter grouping in bulk samples of single-walled carbon nanotubes from optical absorption spectroscopy. Appl Phys Lett 1999;75(15):2217-9.
21 Ichida M, Mizuno S, Tani Y, Saito Y, Nakamura A. Exciton effects of optical transitions in single-wall carbon nanotubes. J Phys Soc Jpn 1999;68(10):3131-3.
22 Kwon YK, Tomanek D. Electronic and structural properties of multiwall carbon nanotubes. Phys Rev B 1998;58(24):R16 001-4.
23 Saito R, Dresselhaus G, Dresselhaus MS. Electronic structure of double-layer graphene tubules. J Appl Phys 1993;73(2):494-500.
24 Ajiki H, Ando T. Electronic states of carbon nanotubes. J Phys Soc Jpn 1993;62(4):1255-66.
25 Ajiki H, Ando T. Energy bands of carbon nanotubes in magnetic fields. J Phys Soc Jpn 1996;65(2):505-14.
26 Charlier JC, Michenaud. Energetics of multilayered carbon tubules. Phys Rev Lett 1993;70(12):1858-61.
27 Chiu CW, Chang CP, Shyu FL, Chen RB, Lin MF. Magnetoelectronic excitations in single-walled carbon nanotubes. Phys Rev B 2003;67(16):165421(6).
28 Harrison WA. Electronic Structure and the Properties of Solids, Dover, New York, 1989.
29 Lin MF, Shung KWK. Magnetization of graphene tubules. Phys Rev B 1995;52(11):8423-38.