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

Original · EN

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 (v₀,v₁,v₂)∈ Z³ | v₀+v₁+v₂∈ 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.