Abstract
A review is presented of one-dimensional cutting lines that are utilized
to obtain the physical properties of carbon nanotubes from the
corresponding properties of graphite by the zone-folding scheme.
Quantization effects in general low-dimensional systems are briefly
discussed, followed by a more detailed consideration of one-dimensional
single-wall carbon nanotubes. The geometrical structure of the nanotube
is described, from which quantum confined states are constructed. These
allowed states in the momentum space of graphite are known as cutting
lines. Different representations of the cutting lines in momentum space
are introduced. Electronic and phonon dispersion relations for nanotubes
are derived by using cutting lines and the zone-folding scheme. The
relation between cutting lines and singularities in the electronic
density of states is considered. The selection rules for carbon
nanotubes are shown to be directly connected with the cutting lines.
Different experimental techniques are considered that confirm the
validity of cutting lines and the zone-folding approach.
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