shot noise in mesoscopic conductors - Low Temperature Laboratory
shot noise in mesoscopic conductors - Low Temperature Laboratory
shot noise in mesoscopic conductors - Low Temperature Laboratory
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44 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166<br />
Fig. 10. Distribution function of transmission coe$cients (87) for ¸/l"10.<br />
the distribution function of transmission coe$cients:<br />
P(¹)" l 1<br />
2¸ ¹1!¹ , ¹ (¹(1, ¹ "4 exp(!2¸/l) , (87)<br />
<br />
and P(¹)"0 otherwise. As discussed, it has a bimodal form: almost open and almost close<br />
channels are preferred. The dependence P(¹) is illustrated <strong>in</strong> Fig. 10.<br />
The distribution function P(¹) must be used now to average expressions (40) and (57) over<br />
impurity con"gurations. Direct calculation con"rms Eq. (86), and, thus, the distribution function<br />
(87) yields the Drude-Sommerfeld formula (85) for the average conductance. Furthermore, we<br />
obta<strong>in</strong><br />
¹(1!¹)" l<br />
3¸ ,<br />
which implies that the zero-temperature <strong>shot</strong> <strong>noise</strong> power is<br />
S" e< N l<br />
<br />
3 ¸ "1<br />
3 S . (88)<br />
<br />
The <strong>shot</strong> <strong>noise</strong> suppression factor for metallic di!usive wires is equal to F"1/3. The remarkable<br />
feature is that this result is universal: As long as the geometry of the wire is quasi-one-dimensional<br />
and l;¸;¸ (metallic di!usive regime), the Fano factor does not depend on the degree of<br />
<br />
disorder, the number of transverse channels, and any other <strong>in</strong>dividual features of the sample. This<br />
result was "rst obta<strong>in</strong>ed by Beenakker and one of the authors [74] us<strong>in</strong>g the approach described<br />
above. Independently, Nagaev [75] derived the same suppression factor by us<strong>in</strong>g a classical<br />
<br />
theory based on a Boltzmann equation with Langev<strong>in</strong> sources. This theory and subsequent<br />
developments are described <strong>in</strong> Section 6.<br />
It seems that the question whether the Fano factor depends on the type of disorder has never been addressed. In all<br />
cases disorder is assumed to be Gaussian white <strong>noise</strong>, i.e. ;(r);(r)J(r!r).