The electronic structure of nonpolyhex carbon nanotubes

Generalizing the folding method to any periodic two-dimensional planar carbon structures we have calculated the corresponding electronic structures in the framework of the one orbital one site tight-binding (Bloch-Hückel) method by solving the eigenvalue problems in a numerical way. We discussed the metallic or the nonmetallic behavior of the nanotubes by applying the folding vectors of parameters (m, n). We extended the topological coordinate method to two-dimensional periodic planar structures as well. Nearly regular hexagonal, pentagonal, and heptagonal polygons were obtained. The curvatures of the final relaxed structures can be read from the sizes of the polygons. Thus relying only on the topological information we could describe the shape of the tubular structures and their conductivity behaviors.