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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48 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166<br />
Eq. (92) describes a crossover from F" (the metallic regime) to F"1 (classical po<strong>in</strong>t contact<br />
between metallic di!usive banks) and actually follows [92] from Eq. (91).<br />
Disordered <strong>in</strong>terfaces. Schep and Bauer [93] considered transport through disordered <strong>in</strong>terfaces,<br />
modeled as a con"guration of short-ranged scatterers randomly distributed <strong>in</strong> the plane perpendicular<br />
to the direction of transport. In the limit g;N , with g and N be<strong>in</strong>g the dimensionless<br />
conductance and the number of transverse channels, respectively, they found the follow<strong>in</strong>g<br />
distribution function of transmission coe$cients:<br />
P(¹)" g<br />
N <br />
1<br />
¹1!¹ , 1# N <br />
2g <br />
(¹(1 , (93)<br />
and zero otherwise. Eq. (93) accidentally has the same form as the distribution function of<br />
transmission coe$cients for the symmetric opaque double-barrier structure. The <strong>noise</strong> suppression<br />
factor for this system equals , e.g. the suppression is weaker than for metallic di!usive wires.<br />
2.6.5. Chaotic cavities<br />
1/4-suppression. Chaotic cavities are quantum systems which <strong>in</strong> the classical limit would exhibit<br />
chaotic electron motion. We consider ballistic chaotic systems without any disorder <strong>in</strong>side the<br />
cavity; the chaotic nature of classical motion is a consequence of the shape of the cavity or due to<br />
surface disorder. The results presented below are averages over ensembles of cavities. The ensemble<br />
can consist of a collection of cavities with slightly di!erent shape or a variation <strong>in</strong> the surface<br />
disorder, or it can consist of cavities <strong>in</strong>vestigated at slightly di!erent energies. Experimentally,<br />
chaotic cavities are usually realized as quantum dots, formed <strong>in</strong> the 2D electron gas by back-gates.<br />
They may be open or almost closed; we discuss "rst the case of open chaotic quantum dots, shown<br />
<strong>in</strong> Fig. 12a. We neglect charg<strong>in</strong>g e!ects. One more standard assumption, which we use here, is<br />
that there is no direct transmission: electrons <strong>in</strong>cident from one lead cannot enter another lead<br />
without be<strong>in</strong>g re#ected from the surface of the cavity (like Fig. 12a).<br />
The description of transport properties of open chaotic cavities based on the random matrix<br />
theory was proposed <strong>in</strong>dependently by Baranger and Mello [96] and Jalabert et al. [97]. They<br />
assumed that the scatter<strong>in</strong>g matrix of the chaotic cavity is a member of Dyson's circular ensemble<br />
of random matrices, uniformly distributed over the unitary group. For the cavity where both left<br />
and right leads support the same number of transverse channels N