shot noise in mesoscopic conductors - Low Temperature Laboratory

42 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166
Experiments. The simplest experimental system one can imagine which should exhibit the
features of a two-barrier structure is just a one-dimensional channel constrained by two potential
barriers. If the barriers are close to each other, the region between the two barriers can be
considered as a zero-dimensional system and is called a quantum dot. In addition, one usually places
one more electrode (gate), which couples only capacitively to the dot. Roughly speaking, the
voltage applied to the gate shifts all electron levels in the dot with respect to the chemical potential
of the reservoirs, and may tune them to the resonance position. However, typically quantum dots
are so small that Coulomb interaction e!ects (Coulomb blockade) become important, and the
theoretical picture described above is no longer valid. If the space between the barriers is large and
one-dimensional (one channel), interaction e!ects are also important, and a Luttinger liquid state is
formed. For a more extensive discussion of noise in interacting systems, the reader is addressed to
Section 7.
Quantum wells, however, are macroscopic objects, and hence are less sensitive to interactions.
Thus, experiments carried out on quantum wells may probe the non-interacting theory of noise
suppression in a double-barrier system. Sub-Poissonian shot noise suppression in quantum wells
was observed by Li et al. [64] even before a theory of this suppression was available. Li et al. noted
that the suppression is maximal for symmetric barriers, and is insigni"cant for very asymmetric
structures (Fig. 9). This suppression was later observed by van de Roer et al. [65], Ciambrone et al.
[66], Liu et al. [67], and Przadka et al. [68]. Liu et al. compared their experimental data with the
results of numerical simulations attempting to take into account speci"c features of their sample,
and found that theory and experiment are in a reasonable agreement. Yau et al. [69] observed shot
noise suppression in double quantum wells (triple barrier structures). We should note, however,
that in all experimental data available, the Fano factor depends considerably on the applied
voltage in the whole range of voltages. Apparently, this happens because already relatively low
voltages drive the system out of the linear regime. To the best of our knowledge, this issue has not
been addressed systematically, although some results, especially concerning the negative di!erential
resistance range exist. They are summarized in Section 5.
2.6.4. Metallic diwusive wires
1/3-suppression. We consider now transport in multi-channel di!usive wires in the metallic
regime. This means that, on one hand, the length of the wire ¸ is much longer than the meanfree
path l due to disorder. On the other hand, in a quasi-one-dimensional geometry all
electron states are localized in the presence of arbitrarily weak disorder; the localization length
equals ¸ "N l, where N is the number of transverse channels. Thus for a wire to be metallic
we must have ¸;¸ (which of course implies N