A new type of superlattice based on carbon nanotubes

We show that electron motion in a (n,1) carbon nanotube corresponds to a de Broglie wave propagating along a helical line on the nanotube wall. This helical motion leads to periodicity of the electron potential energy in the presence of an electric field normal to the nanotube axis. The period of this potential, which is proportional to the nanotube radius, is always greater than the interatomic distance in the nanotube. Therefore the behavior of an electron in such a nanotube subject to a transverse electric field is similar to that in a semiconductor superlattice.