Environmental Engineering Reference
In-Depth Information
Figure 3.2
The weighting factor in the Landauer formula for thermal
conductance (Eq. 3.9).
thequantumofelectricalconductance
g
0
=
e
2
/
h
,
σ
0
isnotaconstant
but linearly proportional to the temperature. A ballistic transport
channelofelectroncontributesaquantumofelectricalconductance
accompanied by a quantum of thermal conductance. It is easy to
prove that
g
0
and
σ
0
satisfy the Wiedemann-Franz Law:
σ
0
2
k
B
T
3
e
2
g
0
=
π
=
L
0
T
.
(3.11)
The quantum of thermal conductance is universal, independent
of the characteristic of material. Moreover, it is also independent
of particle statistics (i.e., universal for fermions, bosons, and
anyons) [6]. The quantum of thermal conductance is first predicted
theoretically [5]. However, its experimental evidence is extremely
di
cult, mainly because
1. Very low temperature is required for the observation of quan-
tized thermal conductance. At normal temperatures thermal
conductance will not be quantized, since a lot of phonon modes
are simultaneously excited and all of them contribute to thermal
conductance. It is necessary to decrease the temperature till
