On the linear representations of the symmetry groups of single-wall carbon nanotubes

Details On the linear representations of the symmetry groups of single-wall carbon nanotubes On the linear representations of the symmetry groups of single-wall carbon nanotubes

2006-02-04

arxiv.org/abs/math-ph/0602014v2

J. Phys. A: Math. Gen. 39 (2006) 9755-9765

Physics

Mathematical Physics

Major change of content. More details will be available at http://fpcm5.fizica.unibuc.ro/~ncotfas

Scientific paper

10.1088/0305-4470/39/31/007

The positions of atoms forming a carbon nanotube are usually described by using a system of generators of the symmetry group. Each atomic position corresponds to an element of the set Z x {0,1,...,n} x {0,1}, where n depends on the considered nanotube. We obtain an alternate rather different description by starting from a three-axes description of the honeycomb lattice. In our mathematical model, which is a factor space defined by an equivalence relation in the set {(v_0,v_1,v_2)\in Z^3 | v_0+v_1+v_2\in {0,1}}, the neighbours of an atomic position can be described in a simpler way, and the mathematical objects with geometric or physical significance have a simpler and more symmetric form. We present some results concerning the linear representations of single-wall carbon nanotubes in order to illustrate the proposed approach.

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