shot noise in mesoscopic conductors - Low Temperature Laboratory

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