14.3 Carbon Nanotubes
411
Fig. 14.18 a Brillouin
zone of the graphene lattice
(bold line) and allowed
k-values for a (6, 6)
armchair nanotube. b Band
structure of a (6, 6) carbon
nanotube. Adapted from
[1371]. c Brillouin zone of
the graphene lattice (bold
line) and allowed k-values
for a (6, 0) zig-zag carbon
nanotube. In the lower part
the real space structure is
visualized. (d) Band
structure of graphene (left)
and a (6, 6) nanotube
(right). Adapted
from [1372]
Fig. 14.19 a, b Brillouin
zone of the graphene lattice
(bold line) and allowed
k-values for a (a) (6, 0) and
a (b) (8, 0) zig-zag
nanotube. c Band structures
of a (12,0) metallic and
(13, 0) semiconducting
armchair carbon nanotube.
Adapted from [1371]
14.3.3 Optical Properties
Optical transitions occur with high probability between the van-Hove singularities of the DOS. The
theoretical absorption spectrum of a (10, 0) nanotube is shown in Fig. 14.21.
In an ensemble of nanotubes various types and sizes occur. The transition energies of all possible
nanotubes sorted by diameter are assembled in the Kataura plot (Fig. 14.22a). Experimental data are
shwon in Fig. 14.22b. The two branches of semiconducting nanotubes ν = ±1 yield different transition
energies. The overall dependence of the transition energy follows a 1/d-law.