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

Nicolae Cotfas
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Abstract

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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Nicolae Cotfas. 2006-02-08. On the linear representations of the symmetry groups of single-wall carbon nanotubes. https://doi.org/10.1088/0305-4470/39/31/007

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