shot noise in mesoscopic conductors - Low Temperature Laboratory

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58 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 That of course is a consequence of the assumption that the cavity can be described by using Dyson's circular ensemble. For open cavities, one "nds " "!3 "!3 " N /(16N !1) , (110) where we assumed that all leads are identical and support N transverse channels. This implies S "S , S "4S /3, or S"!2S /3. Thus, exchange e!ects suppress noise in open chaotic cavities. The situation changes if the cavity is separated from the leads by tunnel barriers. Assuming that the transmission coe$cients of all barriers in all transverse channels are identical and equal ¹, N ¹
Edge channels in the quantum Hall ewect regime. Interesting tests of exchange (interference) e!ects can also be obtained in high magnetic "elds using edge channels. In fact, this leads to a simple example where the phase dependence of the exchange e!ect is indeed essential [9]. Imagine that the system is placed into a strong magnetic "eld, and the transport is only due to edge channels. We assume that there is only one edge state #owing from 1 through 2 and 3 to 4 and back to 1 (Fig. 17). Furthermore, for simplicity we assume that all the leads are identical, and the transmission probability to enter from the lead to the edge state is ¹. A direct calculation gives [9] ¹(1!¹) " " [1#(1!¹)!2(1!¹) cos ] , ¹(1!¹) exp(i) "H" [1#(1!¹)!2(1!¹) cos ] , where is the phase accumulated along the whole trajectory, and the phase dependence in the denominator appears due to the possibility of multiple traversals of the full circle. We have S " 2e< ¹(1!¹) (1!cos ) . (111) [1#(1!¹)!2(1!¹) cos ] Here the term with 1 represents the `classicala contributions S #S , while that with cos accounts for the exchange e!ect S. We see that, depending on , exchange e!ects may either suppress (down to zero, for "0) or enhance (up to 2(S #S ), for ") the total noise. This is an example illustrating the maximal phase sensitivity which the exchange e!ect can exhibit. This simple example gives also some insight on how exchange e!ects survive ensemble averaging. Since the phase occurs not only in the numerator but also in the denominator, the average of Eq. (111) over an ensemble of cavities with the phase uniformly distributed in the interval from 0to2 is non-zero and given by S " 2e< Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 59 ¹(1!¹) [1!(1!¹)][1#(1!¹)] . (112) The ensemble-averaged exchange contribution vanishes both in the limit ¹"0 and in the limit ¹"1. Note that if another order of contacts is chosen, 1P3P2P4, the whole situation changes: the exchange term is now phase insensitive and has a de"nite sign (negative, i.e. exchange suppresses noise) [9]. This is because the trajectories responsible for exchange terms do not form closed loops in this case. Experiments. The phase-sensitive Hanbury Brown}Twiss e!ect discussed above has not so far been probed in experiments. However, a related experiment was carried out by Liu et al. [117,118], who measured the mean-squared #uctuations S of the current in the lead 3, of a four-probe structure, applying voltages in the same three-fold ways that we have discussed.
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Ya.M. Blanter, M. BuK ttiker / Phys
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8. Concluding remarks, future prosp
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text; they are usually extensions o
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Ya.M. Blanter, M. Bu( ttiker / Phys
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The noise power (201) is strongly v
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Fig. 32. Experimental results of Ku
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where Ya.M. Blanter, M. Bu( ttiker
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where the quantity is expressed th
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6.3. Interaction ewects Ya.M. Blant
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one "rst goes from the non-interact
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non-thermalized electrons, the high
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Fig. 34. Geometry of the chaotic ca
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which describes strictly ballistic
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approximately e/C. Between the peak
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Boltzmann}Langevin approach (see Se
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thermal to shot noise. It is, howev
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Note added in proof Ya.M. Blanter,
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and Lee et al. [340] obtain in this
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shot noise in mesoscopic conductors - Low Temperature Laboratory

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