shot noise in mesoscopic conductors - Low Temperature Laboratory

52 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166
where f and f are Fermi distribution functions in the reservoirs 1 and 3, respectively. This result is
remarkable since it vanishes for ¹"1 at any temperature: The correlation function (101) is always
`shot-noise-likea.
One more necessary remark is that all the shot noise components in this example are actually
expressed only through absolute values of the scattering matrix elements: phases are not important
for noise in this simple edge channel problem.
Early experiments on noise in quantum Hall systems were oriented to other sources of noise (see
e.g. Refs. [104,105]), and are not discussed here. Shot noise in the quantum Hall regime was studied
by Washburn et al. [106], who measured voltage #uctuations in a six-terminal geometry with
a constriction, which, in principle, allows for direct comparison with the above theory. They
obtained results in two magnetic "elds, corresponding to the "lling factors "1 and "4.
Although their results were dominated by 1/f-noise, Washburn et al. were able to "nd that shot
noise is very much reduced below the Poisson value, and the order of magnitude corresponds to
theoretical results.
2.6.7. Hanbury Brown}Twiss ewects with edge channels
The conductor of Fig. 13 is an electrical analog of the scattering of photons at a half-silvered
mirror (see Fig. 1). Like in the table top experiment of Hanbury Brown and Twiss [7,8], there is the
possibility of two sources which send particles to an object (here the quantum point contact)
permitting scattering into transmitted and re#ected channels which can be detected separately.
Bose statistical e!ects have been exploited by Hanbury Brown and Twiss [7] to measure the
diameter of stars. The electrical geometry of Fig. 13 was implemented by Henny et al. [12], and
the power spectrum of the current correlation between contact 1 (re#ected current) and contact
3 (transmitted current) was measured in a situation where current is incident from contact 4 only.
Contact 2 was closed such that e!ectively only a three-terminal structure resulted. For the edgechannel
situation considered here, in the zero-temperature limit, this does not a!ect the
correlation between transmitted and re#ected current. (At "nite temperature, the presence of the
fourth contact would even be advantageous, as it avoids, as described above, the `contaminationa
due to thermal noise of the correlation function of re#ected and transmitted currents, see Eq. (101)).
The experiment by Henny et al. "nds good agreement with the predictions of Ref. [18], i.e.
Eq. (100). With experimental accuracy the current correlation S is negative and equal in
magnitude to the mean-square current #uctuations S "S in the transmitted and re#ected
beam. The experiment "nds thus complete anti-correlation. This outcome is related to the Fermi
statistics only indirectly: If the incident carrier stream is noiseless, current conservation alone leads
to Eq. (100). As pointed out by Henny et al. [12], the experiment is in essence a demonstration that
in Fermi systems the incident carrier stream is noiseless. The pioneering character of the experiment
by Henny et al. [12] and an experiment by Oliver et al. [107] which we discuss below lies in
the demonstration of the possibility of measuring current}current correlation in electrical conductors
[108]. Henny et al. [12] measured not only the shot noise but used the four-terminal geometry
of Fig. 13 to provide an elegant and interesting demonstration of the #uctuation-dissipation
relation, Eq. (54).
Now it is interesting to ask, what happens if this complete population of the available states is
destroyed (the incident carrier stream is not noiseless any more). This can be achieved [355] by
inserting an additional quantum point contact in the path of the incident carrier beam (see Fig. 14).