Physics of carbon nanotubes

The fundamental relations governing the geometry of carbon nanotubes are reviewed, and explicit examples are presented. A framework is given for the symmetry properties of carbon nanotubes for both symmorphic and non-symmorphic tubules which have screw-axis symmetry. The implications of symmetry on the vibrational and electronic structure of 1D carbon nanotube systems are considered. The corresponding properties of double-wall nanotubes and arrays of nanotubes are also discussed.