Page 43 - Carbon Nanotubes

34 M. S. DRESSELHAUS al.
et
that the hexagonal PG/mcc (D&) space group has the other mechanism for doping the tubules. Doping of
lowest energy, leading to a gain in cohesive energy of the nanotubes by insertion of an intercalate species
2.4 meV/C atom. The orientational alignment between between the layers of the tubules seems unfavorable
tubules leads to an even greater gain in cohesive en- because the interlayer spacing is too small to accom-
ergy (3.4 eV/C atom), The optimal alignment between modate an intercalate layer without fracturing the
tubules relates closely to the ABAB stacking of graph- shells within the nanotube.
ite, with an inter-tubule separation of 3.14 A at clos- No superconductivity has yet been found in carbon
est approach, showing that the curvature of the nanotubes or nanotube arrays. Despite the prediction
tubules lowers the minimum interplanar distance (as that 1D electronic systems cannot support supercon-
is also found for fullerenes where the corresponding ductivity[33,34], it is not clear that such theories are
distance is 2.8 A). The importance of the inter-tubule applicable to carbon nanotubes, which are tubular
interaction can be seen in the reduction in the inter- with a hollow core and have several unit cells around
tubule closest approach distance to 3.14 A for the the circumference. Doping of nanotube bundles by the
P6/mcc (D,",) structure, from 3.36 A and 3.35 A, re- insertion of alkali metal dopants between the tubules
spectively, for the tetragonal P42/mmc (D&) and could lead to superconductivity. The doping of indi-
P6/mmm (D&) space groups. A plot of the electron vidual tubules may provide another possible approach
dispersion relations for the most stable case is given to superconductivity for carbon nanotube systems.
in Fig. 6[16,17,30], showing the metallic nature of this
tubule array by the degeneracy point between the H
and K points in the Brillouin zone between the valence 5. DISCUSSION
and conduction bands. It is expected that further cal- This journal issue features the many unusual prop-
culations will consider the interactions between nested erties of carbon nanotubes. Most of these unusual
nanotubes having different symmetries, which on properties are a direct consequence of their 1D quan-
physical grounds should interact more weakly, because tum behavior and symmetry properties, including their
of a lack of correlation between near neighbors. unique conduction properties[l 11 and their unique vi-
Modifications of the conduction properties of brational spectra[8].
semiconducting carbon nanotubes by B (p-type) and Regarding electrical conduction, carbon nanotubes
N (n-type) substitutional doping has also been dis- show the unique property that the conductivity can be
cussed[3 11 and, in addition, electronic modifications either metallic or semiconducting, depending on the
by filling the capillaries of the tubes have also been tubule diameter dt and chiral angle 0. For carbon
proposed[32]. Exohedral doping of the space between nanotubes, metallic conduction can be achieved with-
nanotubes in a tubule bundle could provide yet an- out the introduction of doping or defects. Among the
tubules that are semiconducting, their band gaps ap-
pear to be proportional to l/d[, independent of the
tubule chirality. Regarding lattice vibrations, the num-
ber of vibrational normal modes increases with in-
creasing diameter, as expected. Nevertheless, following
from the 1D symmetry properties of the nanotubes,
the number of infrared-active and Raman-active modes
remains independent of tubule diameter, though the
vibrational frequencies for these optically active modes
are sensitive to tubule diameter and chirality[8]. Be-
cause of the restrictions on momentum transfer be-
tween electrons and phonons in the electron-phonon
interaction for carbon nanotubes, it has been predicted
that the interaction between electrons and longitudi-
nal phonons gives rise only to intraband scattering and
not interband scattering. Correspondingly, the inter-
action between electrons and transverse phonons gives
rise only to interband electron scattering and not to
intraband scattering[35].
These properties are illustrative of the unique be-
havior of 1D systems on a rolled surface and result
from the group symmetry outlined in this paper. Ob-
servation of ID quantum effects in carbon nanotubes
KT AH KM LHrMAL
requires study of tubules of sufficiently small diameter
Fig. 6. Self-consistent band structure (48 valence and 5 con- to exhibit measurable quantum effects and, ideally,
duction bands) for the hexagonal I1 arrangement of nano- the measurements should be made on single nano-
tubes, calculated along different high-symmetry directions in
the Brillouin zone. The Fermi Ievel is positioned at the de- tubes, characterized for their diameter and chirality.
generacy point appearing between K-H, indicating metallic Interesting effects can be observed in carbon nano-
behavior for this tubule array[l7]. tubes for diameters in the range 1-20 nm, depending