Electronic structure of helically coiled carbon nanotubes: Relation between the phason lines and energy band features

Recently carbon nanotubes with coiled structures (carbon helix) were found and have attracted much attention. The electronic structures of two families of such helices, whose structures are proposed by two of the present authors (Ihara and Itoh), are calculated using a tight-binding method based on development maps. It is shown that the various band structures are classified by parameters characterizing the geometry of helices based on the concept of ''phason line.'' Semimetallic character, which could not be manifested in straight tubes, is found in only one of those families.