shot noise in mesoscopic conductors - Low Temperature Laboratory

More documents

Recommendations

Info

148 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 the strong tunneling (weak backscattering) regime the e!ective charge of the carriers is e/3. As the tunneling becomes weak, the e!ective charge crosses over to e, as expected for the strong backscattering regime. They also carefully checked the crossover between the shot noise and the equilibrium noise, and found an excellent agreement with the theory. Though the results of Refs. [328,329] basically coincide, we must point out an important di!erence which is presently not understood. The transmission in the experiment by de-Picciotto et al. [329] is not entirely perfect: they estimate that for the sets of data they plot the transmission coe$cients are ¹"0.82 and 0.73. Taking this into account, they phenomenologically insert the factor ¹ in the expression for the shot noise and "t the data to the curve S"(2e/3)¹I . In this way, they obtain a good agreement between the theory and experiment. On the other hand, Saminadayar et al. [328] "t their data to the curve S"(2e/3)I (without the factor ¹). An attempt to replot the data taking the factor ¹ into account leads to an overestimate of the electron charge. The theory we described above predicts a more complicated dependence than just the factor ¹; therefore it may be important to clarify this detail in order to improve our understanding of the theory of FQHE edge states. Reznikov et al. [330] performed similar measurements in the magnetic "eld corresponding to the "lling factor " . Changing the gate voltage (and thus varying the shape of the quantum point contact) they have observed two plateaus of the conductance, with the heights ( )(e/2) and (2/5)(e/2), respectively. The noise measurements showed that the e!ective charges at these plateaus are e/3 and e/5, respectively. These results are in agreement with the subsequent theory of Imura and Nomura [326], and also with the predictions of the composite fermion model (see below): They assumed that there are two transmission channels which in turn open with the gate voltage. This experiment is important since it clearly shows that what is measured in the FQHE shot noise experiments is not merely a "lling factor (like one could suspect for " ), but really the quasiparticle charge. 7.4. Composite fermions An alternative description of the FQHE systems is achieved in terms of the composite fermions. Starting from the FQHE state with the "lling factor "p/(2np$1), n, p3Z, one can perform a gauge transformation and attach 2n #ux quanta to each electron. The resulting objects (an electron with the #ux attached) still obey the Fermi statistics and hence are called composite fermions (CF). The initial FQHE state for electrons corresponds in the mean "eld approximation to the "lling factor "p for CF, i.e. the composite fermions are in the integer quantum Hall regime with the p Landau levels "lled. In particular, the half- "lled Landau level corresponds to the CF in zero magnetic "eld. Composite fermions interact electrostatically via their charges, and also via the gauge "elds, which are a measure of the di!erence between the actual #ux quanta attached and the #ux treated in the mean "eld approximation. It is important that, at least in the mean "eld approximation, the composite Fermions do not form a strongly interacting system, and therefore may be regarded as independent particles. One can then proceed by establishing an analogy with the transport of independent or weakly interacting electrons. Von Oppen [331] considers the shot noise of composite fermions at the half-"lled Landau levels, assuming that the sample is disordered. He develops a classical theory based on the
Boltzmann}Langevin approach (see Section 6), incorporating interactions between them. Though the #uctuations of both electric and magnetic "elds now become important, in the end he obtains the same result as for normal di!usive wires: In the regime of negligible interactions between the CFs, the Fano factor equals and is universal. Likewise, in the regime when the CF distribution function is in local equilibrium (analog of the hot electron regime), the suppression factor is 3/4. Kirczenow [332] considers current #uctuations in the FQHE states, appealing to statistical particle counting arguments. However, he does not take into account any kind of scattering, and only treats equilibrium (Nyquist) noise for which the result is known already. Shot noise in the FQHE strip ("2/(2p#1)) with a tunnel barrier was discussed by de Picciotto [333], who assumed that the composite Fermions are transmitted through the quantum point contact similarly to the non-interacting electrons. Namely, there are p channels corresponding to the p CF Landau levels. Each channel is characterized by an individual transmission coe$cient. As the gate voltage is changed the channels open (the corresponding transmission coe$cient crosses over from 0 to 1), and the conductance exhibits plateaus with the height (e/2)l/(2l#1), 1(l(p). The shot noise at the plateau l is then given as the Poisson backscattered current with the e!ective charge e/(2l#1). Though this paper is phenomenological and requires further support from microscopic theory, we note that all the features predicted in Ref. [333] are not only in agreement with the Luttinger liquid approach by Imura and Nomura [326], but also were observed experimentally [330] for " (see above). In this case there are two channels corresponding to p"1 and 2, which implies conductance plateaus with heights ( )(e/2) and (for higher gate voltage) ( )(e/2); the corresponding charges measured in the shot noise experiment are e/3 and e/5, respectively. 8. Concluding remarks, future prospects, and unsolved problems 8.1. General considerations Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 149 In this section, we try to outline the directions along which the "eld of shot noise in mesoscopic systems has been developing, to point out the unsolved problems which are, in our opinion, important, and to guess how the "eld will further develop. A formal summary can be found at the end of the section. Prior to the development of the theory and the experiments on shot noise in mesoscopic physics, there already existed a considerable amount of knowledge in condensed matter physics, electrical engineering, and especially optics. Both theory and experiments are available in these "elds, and the results are well established. Similarly in mesoscopic physics, there exists a fruitful interaction between theory and experiment. However, presently there are many theoretical predictions concerning shot noise, not only extensions of the existing theories, but which really address new sub-"elds, which are not yet tested experimentally. Below we give a short list of these predictions. To this end, he has to assume implicitly the existence of two CF reservoirs, described by equilibrium Fermi distribution functions.
Page 1 and 2:
Ya.M. Blanter, M. BuK ttiker / Phys
Page 3 and 4:
8. Concluding remarks, future prosp
Page 5 and 6:
text; they are usually extensions o
Page 7 and 8:
such reviews are not readily availa
Page 9 and 10:
Ya.M. Blanter, M. Bu( ttiker / Phys
Page 11 and 12:
The above considerations are, of co
Page 13 and 14:
Page 15 and 16:
Page 17 and 18:
and the initial state of our two-pa
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
2.3.3. Multi-terminal case We consi
Page 25 and 26:
Note that in the absence of time-de
Page 27 and 28:
Page 29 and 30:
equilibrium and shot noise. For low
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
and S" e A e< dE ¹(E )[1!¹
Page 41 and 42:
arrier, situated in the region !w/2
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
we include weak localization e!ects
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
Edge channels in the quantum Hall e
Page 61 and 62:
Fig. 19. (a) Geometry of a ring thr
Page 63 and 64:
a manifestation of interference e!e
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Physically, this corresponds to ele
Page 71 and 72:
Page 73 and 74:
Our starting point is Eq. (51), whi
Page 75 and 76:
Page 77 and 78:
introducing the transmission coe$ci
Page 79 and 80:
investigated experimentally. A self
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
and the non-equilibrium resistance
Page 87 and 88:
the sample. These electrons are des
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
with D ,¹ (2!¹ ). Performing t
Page 95 and 96:
Page 97 and 98: For completeness, we mention that i
Page 99 and 100: Ya.M. Blanter, M. Bu( ttiker / Phys
Page 107 and 108: We note here, however, that there i
Page 111 and 112: The noise power (201) is strongly v
Page 113 and 114: Fig. 32. Experimental results of Ku
Page 115 and 116: where Ya.M. Blanter, M. Bu( ttiker
Page 117 and 118: where the quantity is expressed th
Page 119 and 120: 6.3. Interaction ewects Ya.M. Blant
Page 123 and 124: one "rst goes from the non-interact
Page 125 and 126: non-thermalized electrons, the high
Page 129 and 130: Fig. 34. Geometry of the chaotic ca
Page 133 and 134: which describes strictly ballistic
Page 141 and 142: approximately e/C. Between the peak
Page 147: Ya.M. Blanter, M. Bu( ttiker / Phys
Page 151 and 152: thermal to shot noise. It is, howev
Page 153 and 154: Note added in proof Ya.M. Blanter,
Page 155 and 156: and Lee et al. [340] obtain in this
show all

shot noise in mesoscopic conductors - Low Temperature Laboratory

Create successful ePaper yourself

Delete template?

Save as template?