A natural helical crystal lattice model for carbon nanotubes

We propose a novel helical crystal lattice model for chiral and achiral carbon nanotubes (CNTs) where the unit cell and the helical crystal vector are defined in a unique and systematic manner for arbitrary CNTs. The small unit cell of this helical crystal lattice leads to a natural and convenient description of the electronic structure of chiral CNTs. Also, using this model, the degenerate frontier Bloch wave functions at the Γ point can be conveniently chosen by their symmetry properties. In particular, the contour of the Bloch wave functions at the Fermi level can be easily predicted for all metallic CNTs.