  Electron motion in a (n,1) carbon nanotube is shown to correspond 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 is proportional to the nanotube radius and is greater than the
interatomic distance in the nanotube. As a result, the behavior of an electron
in a (n,1) nanotube subject to a transverse electric field is similar to that
in a semiconductor superlattice. In particular, Bragg scattering of electrons
from the long-range periodic potential results in the opening of gaps in the
energy spectrum of the nanotube. Modification of the bandstructure is shown to
be significant for experimentally attainable electric fields, which raises the
possibility of applying this effect to novel nanoelectronic devices.
