English

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

Mathematical Physics 2007-05-23 v2 Materials Science Group Theory math.MP

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.

Keywords

Cite

@article{arxiv.math-ph/0602014,
  title  = {On the linear representations of the symmetry groups of single-wall carbon nanotubes},
  author = {Nicolae Cotfas},
  journal= {arXiv preprint arXiv:math-ph/0602014},
  year   = {2007}
}

Comments

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