Impurity effects in twisted carbon nanotubes

We consider electronic spectra of twisted carbon nanotubes and their perturbation by impurity atoms absorbed at different positions on nanotube surface within the framework of Anderson hybrid model. A special attention is given to the cases when 1D Weyl (massless Dirac) modes are present in the nanotube spectrum and their hybridization with localized impurity states produces, with growing impurity concentration c, onset of a mobility gap near the impurity level and then opening, at yet higher c, of some narrow range of delocalized states within this mobility gap. Such behaviors are compared with similar effects in the previously studied 2D graphene, carbon nanoribbons, and non-twisted carbon nanotubes. Some possible practical applications are discussed.