Optical and vibrational properties of toroidal carbon nanotubes.

Toroidal carbon nanotubes (TCNTs), which have been evaluated for their potential applications in terahertz communication systems, provide a challenge of some magnitude from a purely scientific perspective. A design approach to TCNTs, as well as a classification scheme, is presented based on the definition of the six hollow sections that comprise the TCNT, slicing each of them to produce a (possibly creased) planar entity, and projecting that entity onto a graphene lattice. As a consequence of this folding approach, it is necessary to introduce five- and seven-membered rings as defect sites to allow the fusing together of the six segments into final symmetric TCNTs.