Carbon Nanotubes Band Assignation, Topology, Bloch States and Selection Rules

Details Carbon Nanotubes Band Assignation, Topology, Bloch States and Selection Rules Carbon Nanotubes Band Assignation, Topology, Bloch States and Selection Rules

2001-05-23

arxiv.org/abs/cond-mat/0105451v1

Phys. Rev. B 65 045418 (2002)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

11 pages, 2 figures, 2 tables; pdf available from: http://www.ff.bg.ac.yu/qmf/qsg_e.htm

Scientific paper

10.1103/PhysRevB.65.045418

Various properties of the energy band structures (electronic, phonon, etc.), including systematic band degeneracy, sticking and extremes, following from the full line group symmetry of the single-wall carbon nanotubes are established. The complete set of quantum numbers consists of quasi momenta (angular and linear or helical) and parities with respect to the z-reversal symmetries and, for achiral tubes, the vertical plane. The assignation of the electronic bands is performed, and the generalized Bloch symmetry adapted eigen functions are derived. The most important physical tensors are characterized by the same set of quantum numbers. All this enables application of the presented exhaustive selection rules. The results are discussed by some examples, e.g. allowed interband transitions, conductivity, Raman tensor, etc.

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