Full symmetry, optical activity, and potentials of single-wall and multiwall nanotubes

The full symmetry groups for all single-wall and multiwall carbon nanotubes are found. As for the single-wall tubes, the symmetries form non-Abelian n onsymorphic line groups, enlarging the groups reported in the literature. I n the multiwall case, any type of line and axial point groups can be obtain ed, depending on single-wall constituents and their relative position. The isogonal symmetry is related to the macroscopic tensor properties of the na notubes. The optical activity is studied within this framework, and a detai led classification of the possible nanotube-based optical devices is given. At the microscopic level, full symmetry is used to find general forms of t he characteristic functions of the nanotubes. In particular, the stability of the double-wall configurations and the possibility of chiral currents ar e discussed. Several other consequences are discussed: quantum numbers and related selection rules, phonon spectra, etc. In particular, the bands of t he zigzag and the armchair tubes are generally expected to be fourfold dege nerate. [S0163-1829(99)06427-9].