shot noise in mesoscopic conductors - Low Temperature Laboratory

a manifestation of interference e!ects in multi-particle wave functions (Slater determinants of
single-particle wave functions) which result from the indistinguishability of carriers. In contrast, the
e!ects we have already seen in weak "elds, which contribute to the conductance as well as to the
shot noise are a consequence of second order or direct interference.
The two-terminal geometry of Fig. 20a is not appropriate for the observation of the exchange
interference e!ects, since shot noise vanishes without scattering between edge channels. If scattering
is introduced, shot noise becomes "nite, but at the same time the conductance becomes sensitive
to the #ux, due to direct interference. One can try to separate AB e!ects in the shot noise due to
direct and exchange interference, but this is awkward.
A possible way out was proposed in Ref. [112], which suggested four-terminal geometries with
two weak coupling contacts. We follow here a subsequent, clearer discussion given in Ref. [111].
The geometry is shown in Fig. 20b. This is a quantum dot in a strong magnetic "eld coupled via
two quantum point contacts to reservoirs. The ring geometry is actually not needed in the
experiment and serves only for conceptual clarity. Current #ows between contacts 1 and 2, and
the contacts 3 and 4 are inserted locally at the quantum point contact between the edge states in the
leads. The magnetic "eld is such that the two-probe conductance is quantized, but weak enough
such that at the quantum point contact the left- and right-going wave functions of the two edge
channels overlap. As is well known, the fact that the wave functions in the quantum point contact
overlap, does not destroy the quantization, as long as the potential of the quantum point contact is
smooth. We take the scattering matrix relating the amplitudes of carriers in the contact 3 (or 4) with
those in the edge channels nearby to be of the same form (113) as for the `beam splittera discussed
above. Here it is now essential to assume that coupling is weak thus we take ;1. In the
experiment proposed in Refs. [112,111] the same voltage < is applied simultaneously to the
contacts 1 and 2. Then we have
S "S "(2e