An exhaustive classification scheme for single-wall carbon nanotubes

The Fermi-level subband indices of single-wall carbon nanotubes (SWCNTs) are investigated by exploring the positions of graphene degenerate points relative to nanotubes subbands. By these algebraic methods, SWCNTs are naturally classified into eight types: two types for both metal-1 and -2; and four types for semiconductor. Using the general arguments of number theory, this classification scheme is, for the first time, shown to be exhaustive. The subbands indices are also given explicitly by formulae and algorithms readily applicable to computations.