M Damnjanović et al 2003 J. Phys. A: Math. Gen. 36 5707 doi:10.1088/0305-4470/36/21/302
M Damnjanović1, I Milosević1, T Vuković1 and J Maultzsch2
Show affiliationsNanotubes as well as polymers and quasi-1D subsystems of 3D crystals have line group symmetry. This allows two types of quantum numbers: roto-translational and helical. The roto-translational quantum numbers are linear and total angular (not conserved) momenta, while the helical quantum numbers are helical and complementary angular momenta. Their mutual relations determine some topological properties of energy bands, such as systematic band sticking or van Hove singularities related to parities. The importance of these conclusions is illustrated by the optical absorption in carbon nanotubes: parity may prevent absorption peaks at van Hove singularities.
61.46.-w Structure of nanoscale materials
02.20.Bb General structures of groups
61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling
82D25 Crystals (For crystallographic group theory, see 20H15)
Issue 21 (30 May 2003)
Received 20 January 2003, in final form 7 April 2003
Published 13 May 2003
M Damnjanović et al 2003 J. Phys. A: Math. Gen. 36 5707
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