Environmental Engineering Reference
In-Depth Information
Figure 2.11
Phonon-transmission histograms
P
(
ζ
) for several frequencies
inthediffusiveregimefor(a)the(5,5)SWNTwith15%
13
Cand
L
=
625nm
and (b) the (8,0) SWNT with 9.4%
14
Cand
L
=
210 nm.
P
(ln
ζ
) for several
frequencies in the localization regime for the same SWNTs as (c) Fig. 2.10a
and (d) Fig. 2.10b. The insets show Var[ln
ζ
] as a function of
<
P
(ln
ζ
)
>
.
transport in disordered quasi-1D systems,
G
/
G
0
=
0.36527. This
suggests that the universal phonon-transmission fluctuation is
closely related to the UCF even though electrons and phonons obey
different quantum statistics. Similar to the UCF, the reason for the
macroscopicallyobservablephonontransmissionfluctuationcanbe
qualitatively understood as follows: The fluctuations of phonon-
transmission channels cannot cancel each other because there are
very few effective transmission channelsdue to isotopescattering.
2.3.3.3 Anderson localization of phonons
In this subsection, we discuss the phonon-transmission histogram
P
(
ζ
) that contains information for every moment of
ζ
(
ω
). Fig-
ure2.11a,bshow
P
(
ζ
)forseveraltypicalfrequenciesinthediffusive