shot noise in mesoscopic conductors - Low Temperature Laboratory

The above considerations are, of course, rather simplistic and should not be considered as
a quantitative theory. Since statistical e!ects play a role, one would like to see a derivation which
relates the noise to the symmetry of the wave functions. Since we deal with many indistinguishable
particles, exchange e!ects can come into play. The following sections will treat these questions
in detail.
1.5. Composition of the Review
Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 11
The review starts with a discussion of the scattering approach (Section 2). This is a fully
quantum-mechanical theory which applies to phase-coherent transport. It is useful to take
this approach as a starting point because of its conceptual clarity. The discussion proceeds
with a number of speci"c examples, like quantum point contacts, resonant double barriers,
metallic di!usive wires, chaotic cavities, and quantum Hall conductors. We are interested not
only in current #uctuations at one contact of a mesoscopic sample but also in the correlations
of currents at di!erent contacts. Predictions and experiments on such correlations are
particularly interesting since current correlations are sensitive to the statistical properties
of the system. Comparison of such experiments with optical analogs is particularly
instructive.
Section 3 describes the frequency dependence of noise via the scattering approach. The main
complication is that generally one has to include electron}electron interactions to obtain #uctuation
spectra which are current conserving. For this reason, not many results are currently
available on frequency-dependent noise, though the possibility to probe in this way the inner
energy scales and collective response times of the system looks very promising.
We proceed in Section 4 with the description of superconducting and hybrid structures, to which
a generalized scattering approach can be applied. New noise features appear from the fact that the
Cooper pairs in superconductors have the charge 2e.
Then in Sections 5 and 6 we review recent discussions which apply more traditional classical
approaches to the #uctuations of currents in mesoscopic conductors. Speci"cally, for a number of
systems, as far as one is concerned only with ensemble-averaged quantities, the Langevin and
Boltzmann}Langevin approaches provide a useful discussion, especially since it is known how to
include inelastic scattering and e!ects of interactions.
Section 7 is devoted to shot noise in strongly correlated systems. This section di!ers in many
respects from the rest of the Review, mainly because strongly correlated systems are mostly
too complicated to be described by the scattering or Langevin approaches. We resort to a brief
description and commentary of the results, rather than to a comprehensive demonstration how
they are derived.
We conclude the Review (Section 8) with an outlook. We give our opinion concerning possible
future directions along which the research on shot noise will develop. In the concluding section, we
provide a very concise summary of the state of the "eld and we list some (possibly) important
unsolved problems.
Some topics are treated in a number of Appendices mostly to provide a better organization of the
paper. The Appendices report important results on topics which are relatively well rounded, are
relevant for the connections between di!erent sub-"elds, and might very well become the subject of
much further research.