Electronic structure of porous nanotube

The electronic structures of porous carbon nanotubes, nanotubes perforated periodically on the cylindrical surface, are studied on the basis of the tight-binding model within the Hückel approximation. The electronic structures depend not only on the pitch and the helicity but also on the shape of the pore. The band gap varies depending on the perforation. When the armchair pore, which is a pore consisting mainly of armchair edges, is introduced into an armchair tube, the band gap is still equal to zero. On the other hand, the zigzag pore, which is a pore consisting of zigzag edges, causes a finite band gap. For a zigzag tube, regardless of the shape of the pore, it is semiconductive and its band gap is smaller than the same tube without a pore expected to be semiconductive. The density of states near Fermi level can be increased by perforation. Introducing a larger pore into the armchair tube leads to localized states near Fermi level. This is similar to the edge state in the graphene ribbon. Depending on the pitch and the helicity, the various band structures appear in porous nanotube with two atoms taken away from the unit cell. Completely flat band also appear in some cases. In those systems flat band ferromagnetism could be expected. Perforation enables us to control the electronic structure of nanotube.