Environmental Engineering Reference
In-Depth Information
where
g
L/R
(
ω
)isdefinedas
g
L/R
(
ω
)
=
ω
+
i
0
+
−
D
L/R
−
1
.
2
(2.27)
The surface Green's function is self-consistently calculated by
Eq.2.26.Asanothermethodtoobtaintheself-energyduetothelead,
the mode-matching method has been frequently used [18]. Both
methods are originallydeveloped in an electron system.
2.3 Application of Landauer-NEGF Method to Carbon
Nanotube
Asingle-walledcarbonnanotube(SWNT)depictedinFig.2.4,which
is a single graphene layer rolled into a cylindrical shape, has a
new quasi-1D crystalline form. Ever since the discovery of SWNTs
in the early 1990s, it was anticipated that these nanostructures
would have truly remarkable thermal-transport properties as well
as electronic ones, given the strength of the carbon-carbon bond
and the hexagonal network of carbons within a graphene layer.
Nowadays, growing evidence, coming from both experimental and
theoretical studies, indicates that SWNTs do indeed have extremely
high thermal conductivities.
2.3.1
Phonons in Carbon Nanotube
Before discussing the thermal transport in carbon nanotube, we
give a brief review of phonons in SWNTs. In general, the phonon
dispersion relations of a system are obtained by diagonalizing the
Figure 2.4
Schematics of atomic structure of a single-walled carbon
nanotube.
