shot noise in mesoscopic conductors - Low Temperature Laboratory

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112 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 Fig. 31. Voltage dependence of the Fano factor (202) for the same set of parameters as Fig. 30 (solid line); Fano factor (78) for a charge neutral quantum well (dashed line). Poissonian. Jahan and Anwar [236], who also found super-Poissonian noise enhancement, included self-consistent e!ect at the level of the stationary transmission probabilities, but also did not take partition noise into account. As we already mentioned, an explanation of the super- Poissonian noise in terms of the potential #uctuations was given by Iannaccone et al. [240], and the analytical theory of this enhancement, identifying the relevant energy scales, was proposed in Refs. [241,226]. Experimentally, enhancement of noise in quantum wells, as the voltage approaches the range of negative di!erential resistance, was observed already in the early experiments by Li et al. [64] and by Brown [231]. The super-Poissonian shot noise in the negative di!erential resistance range was observed by Iannaccone et al. [240]. Kuznetsov et al. [232] have presented a detailed investigation of the noise oscillations from sub-Poissonian to super-Poissonian values of a resonant quantum well in the presence of a parallel magnetic "eld. The magnetic "eld leads to multiple voltage ranges of negative di!erential resistance and permits a clear demonstration of the e!ect. Their results are shown in Fig. 32. To conclude this section, we discuss the following issue. To obtain the super-Poissonian noise enhancement, we needed multi-stable behavior of the I}< curve; in turn, the multi-stability in quantum wells is induced by charging e!ects. It is easy to see, however, that the charging (or, generally, interaction) e!ects are not required to cause the multi-stability. Thus, if instead of a voltage-controlled experiment, we discuss a current-controlled experiment, the I}< characteristics for the uncharged quantum well (Fig. 30) are multi-stable for any external current. For the case of an arbitrary load line there typically exists a "nite range of external parameters where multi-stable behavior is developed. Furthermore, the quantum wells are not the only systems with multi-stability; as one well-known example we mention Esaki diodes, where the multi-stability is caused by the structure of the energy bands [243].
Fig. 32. Experimental results of Kuznetsov et al. [232] which show noise in resonant quantum wells in parallel magnetic "eld. A dotted line represents the Poisson value. It is clearly seen that for certain values of applied bias voltage the noise is super-Poissonian. Copyright 1998 by the American Physical Society. Usually, such bistable systems are discussed from the point of view of telegraph noise, which is due to spontaneous random transitions between the two states. This is a consideration complementary to the one we developed above. Indeed, in the linear approximation the system does not know that it is multi-stable. The shot noise grows inde"nitely at the instability threshold only because the state around which we have linearized the system becomes unstable rather than metastable. This is a general feature of linear #uctuation theory. Clearly, the divergence of shot noise in the linear approximation must be a general feature of all the systems with multi-stable behavior. Interactions are not the necessary ingredient for this shot noise enhancement. On the other hand, as we have discussed, the transitions between di!erent states, neglected in the linear approximation, will certainly soften the singularity and drive noise to a "nite value at the instability threshold. To describe in this way the interplay between shot noise and random telegraph noise remains an open problem. 6. Boltzmann}Langevin approach to noise: disordered systems 6.1. Fluctuations and the Boltzmann equation Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 113 In this section we describe the generalization of the Langevin method to disordered systems. As is well known, the evolution of the (average) distribution function fM (r, p, t) is generally described by the Boltzmann equation, (R #*#eER p) fM (r, p, t)"I[ fM ]#I [ fM ] . (203) Here E is the local electric "eld, I [ fM ] is the inelastic collision integral, due to the electron}electron and electron}phonon scattering (we do not have to specify this integral explicitly at this stage), and
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8. Concluding remarks, future prosp
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text; they are usually extensions o
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such reviews are not readily availa
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The above considerations are, of co
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and the initial state of our two-pa
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2.3.3. Multi-terminal case We consi
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Note that in the absence of time-de
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equilibrium and shot noise. For low
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and S" e A e< dE ¹(E )[1!¹
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arrier, situated in the region !w/2
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we include weak localization e!ects
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Edge channels in the quantum Hall e
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