shot noise in mesoscopic conductors - Low Temperature Laboratory

Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 121
Fig. 33. Shot noise observed at the same sample for three di!erent temperatures by Steinbach et al. [80]. Dashed and
solid lines indicate the -suppression and the hot electron result F"3/4. The temperature is the lowest for the lowest
curve. Copyright 1996 by the American Physical Society.
At this point, we summarize the information we obtained from the scattering and Boltzmann}
Langevin approaches about the e!ects of the electron}electron interactions on noise. There are two
characteristic times, one responsible for dephasing processes, , and another one due to inelastic
(
scattering (electron heating), . We expect ; . Dephasing does not have an e!ect on noise,
(
and thus for short enough samples, D/¸<
, the Fano factor is (irrespectively of the relation
between D/¸ and ). For long wires, D/¸;,
the Fano factor equals 3/4 due to electron
(
heating. For even longer wires the electron}phonon interactions become important (see below),
and shot noise is suppressed down to zero.
The microscopic theory, however, predicts three characteristic times responsible for electron}electron
scattering in disordered systems (for a nice qualitative explanation, see Ref. [251]).
One is the dephasing time , another one is the energy relaxation time, , and the third one, for
(
which we keep the notation , has the meaning of the average time between electron}electron
collisions. While the dephasing time is quantum-mechanical and cannot be accounted for in the
classical theory, the information about and is contained in the collision integral (227). For
three-dimensional disordered systems, all the three times coincide: The presence of dephasing
always means the presence of inelastic scattering and electron heating. The situation is, however,
di!erent in two- and one-dimensional systems, where the three times di!er parametrically, with the
relation [251,247] ; ; . This is in apparent contrast with the intuitive predictions of the
(
scattering approach, and opens a number of questions. First, it is not clear whether or is
responsible for the }3/4 crossover in the classical theory. Then, the role of dephasing, which is
not taken into account in the Boltzmann}Langevin approach, may need to be revisited. These
questions may only be answered on the basis of a microscopic theory.
We must point out here that interactions, besides altering the amplitude of shot noise, also create
an additional source of noise in di!usive conductors, since the moving electrons produce #uctuating
electromagnetic "eld, as discovered by von Oppen and Stern [252]. Referring the reader to
Ref. [252] for details, we mention that this noise is proportional to < for low voltages, and to
for D/¸;;k ¹. As a function of frequency, this noise saturates for low frequen-
cies, and vanishes for