Electronic structure of graphene tubules based on ${\mathrm{C}}_{60}$

The electronic structures of some possible carbon fibers nucleated from the hemisphere of a ${\mathrm{C}}_{60}$ molecule are presented. A one-dimensional electronic band-structure model of such carbon fibers, having not only rotational symmetry but also screw axes, is derived by folding the two-dimensional energy bands of graphite. A simple tight-binding model shows that some fibers are metallic and are stable against perturbations of the one-dimensional energy bands and the mixing of σ and π bands due to the curvature of the circumference of the fiber.