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theoretical picture described above is no longer valid.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