pdf, 9 MiB - Infoscience - EPFL
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4.5. VARIATIONAL MONTE-CARLO APPLIED TO THE CARBON NANOTUBES97<br />
a)<br />
b) c)<br />
( 2,1)<br />
( 2,2)<br />
(3,0)<br />
Figure 4.9: Reciprocal space of a) the (2,1) tube , b) the armchair (2,2) tube,<br />
and c) the zig-zag (3,0) tube. The armchair and zig-zag tubes have a metallic<br />
dispersion.<br />
4.5 Variational Monte-Carlo applied to the Carbon<br />
nanotubes<br />
The study of carbon nanotubes is also an interesting event, since their discovery<br />
by Iijima in 1991 [116], has become a full research field with significant contributions<br />
from all areas of research in solid-state. Single-walled carbon nanotube<br />
(SWCNT) are constituted by a single graphene plane wrapped into a cylinder.<br />
The Fermi surface of graphene is very particular: it is reduced to six discrete<br />
points at the corners of the 2D lattice Brillouin zone [117] as shown in Fig.4.1.<br />
As a result, depending on their diameter and their chirality which determine<br />
the boundary conditions of the electronic wave functions around the tube, the<br />
nanotube can be either semiconducting or metallic, depending on the lines of k<br />
points in the Brillouin Zone crosses the 6 points of the Fermi surface (see Fig.<br />
4.9). It has been shown that only the zero-chirality armchair nanotubes have zero<br />
electronic band gap, the others having a small charge gap and being therefore<br />
semi-conductors or insulators depending on their radius and chirality. Let us note<br />
that the special zig-zag geometry has also a zero charge gap in the free electronic<br />
band theory.<br />
While superconductivity is well established in graphene, this phenomenon was<br />
only recently investigated for the nanotubes : intrinsic superconductivity was<br />
experimentally observed in ropes of nanotubes [118]. Data show the existence of<br />
intrinsic superconductivity in ropes of carbon nanotubes in which the number of<br />
tubes varies between 30 and 400. The question of the existence of superconducting<br />
correlations in the limit of the individual tube cannot however be answered yet.<br />
Whereas graphene is doped with alkali-dopants, there are no chemical dopants<br />
in the ropes of carbon nanotubes. As shown in previous works there is some