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Volumn 60, Issue 4, 1999, Pages 2728-2739

Full symmetry, optical activity, and potentials of single-wall and multiwall nanotubes

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[No Author keywords available]

Indexed keywords


EID: 0000798498     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.60.2728     Document Type: Article
Times cited : (294)

References (34)
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    • I. Milošević, A. Damjanović, and M. Damnjanović, in Quantum Mechanical Simulation Methods for Studying Biological Systems, edited by D. Bicout and M. Field (Springer-Verlag, Berlin, 1996), Chap. XIV.
    • I. Milošević, A. Damjanović, and M. Damnjanović, in Quantum Mechanical Simulation Methods for Studying Biological Systems, edited by D. Bicout and M. Field (Springer-Verlag, Berlin, 1996), Chap. XIV.
  • 13
    • 85037911208 scopus 로고    scopus 로고
    • The following standard notation is used: (Formula presented) is the vertical mirror plane, I is the (Formula presented) identity matrix, while a denotes the translational period. Also, (Formula presented) is the rotation for (Formula presented) around the z axis, where (Formula presented) and (Formula presented) are coprime integers. Instead of this helical group (Formula presented), generated by (Formula presented), the groups generated by (Formula presented), with (Formula presented) (Formula presented), give the same full symmetry group (Ref. 6). Among these (Formula presented)’s there is at least one that is coprime with q; with this (Formula presented) it is obvious that the set (Formula presented) contains the rotations for all the multiples of (Formula presented) (followed by some translations).
    • The following standard notation is used: (Formula presented) is the vertical mirror plane, I is the (Formula presented) identity matrix, while a denotes the translational period. Also, (Formula presented) is the rotation for (Formula presented) around the z axis, where (Formula presented) and (Formula presented) are coprime integers. Instead of this helical group (Formula presented), generated by (Formula presented), the groups generated by (Formula presented), with (Formula presented) (Formula presented), give the same full symmetry group (Ref. 6). Among these (Formula presented)’s there is at least one that is coprime with q; with this (Formula presented) it is obvious that the set (Formula presented) contains the rotations for all the multiples of (Formula presented) (followed by some translations).
  • 14
    • 85037908974 scopus 로고    scopus 로고
    • T. Vuković, Ph.D. thesis, University of Beograd, 1999.
    • T. Vuković, Ph.D. thesis, University of Beograd, 1999.
  • 15
    • 0000772160 scopus 로고
    • W. A. de Heer, et al., Science 268, 845 (1995).
    • (1995) Science , vol.268 , pp. 845
    • de Heer, W.A.1
  • 19
    • 0001143022 scopus 로고    scopus 로고
    • The third-rank tensor (Formula presented) used in that paper is related to the tensor A by (Formula presented) (Formula presented) is the frequency of the incoming light, c the light speed in vacuum, and (Formula presented) the Levi-Civita tensor.
    • S. Tasaki, K. Maekawa, and T. Yamabe, Phys. Rev. B 57, 9301 (1998). The third-rank tensor (Formula presented) used in that paper is related to the tensor A by (Formula presented) (Formula presented) is the frequency of the incoming light, c the light speed in vacuum, and (Formula presented) the Levi-Civita tensor.
    • (1998) Phys. Rev. B , vol.57 , pp. 9301
    • Tasaki, S.1    Maekawa, K.2    Yamabe, T.3
  • 33
    • 85037913199 scopus 로고    scopus 로고
    • Since the whole zigzag and armchair nanotubes are produced by the action of the subgroup (Formula presented) on an arbitrary atom, each atom is invariant under one (nontrivial) transformation of the full symmetry group (the stabilizers of the atoms are nontrivial). For example, the starting atom is invariant under the point group (Formula presented) in the zigzag tube, and under (Formula presented) in the armchair tube.
    • Since the whole zigzag and armchair nanotubes are produced by the action of the subgroup (Formula presented) on an arbitrary atom, each atom is invariant under one (nontrivial) transformation of the full symmetry group (the stabilizers of the atoms are nontrivial). For example, the starting atom is invariant under the point group (Formula presented) in the zigzag tube, and under (Formula presented) in the armchair tube.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.