shot noise in mesoscopic conductors - Low Temperature Laboratory

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4 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 1. Introduction 1.1. Purpose of this Review During the past two decades mesoscopic physics has developed into a fascinating sub"eld of condensed matter physics. In this article, we review a special topic of this "eld: We are concerned with the dynamical noise properties of mesoscopic conductors. After a modest start, a little more than a decade ago, both theories and experiments have matured. There is now already a substantial theoretical literature and there are a number of interesting experiments with which theoretical predictions can be compared. Some experiments ask for additional theoretical work. The "eld has thus reached a stage in which a review might be useful as a "rst orientation for researchers who wish to enter the "eld. Also researchers which are already active in the "eld might appreciate a review to help them keep an overview over the rapid development which has occurred. Any review, of course, re#ects the authors' preferences and prejudices and in any case cannot replace the study of the original literature. Presently, there are no reviews covering the actual state of development of the "eld. The only article which provides a considerable list of references, and gives a description of many essential features of shot noise in mesoscopic systems, has been written in 1996 by de Jong and Beenakker [1]. It is useful as a "rst introduction to the subject, but since then the "eld has developed considerably, and a broader review is clearly desirable. An additional brief review has been written by Martin [2]. The subject has been touched in books with broader scopes by Kogan [3] (Chapter 5) and Imry [4] (Chapter 8). These reviews, and in particular, the work of de Jong and Beenakker [1], provided a considerable help in starting this project. 1.2. Scope of the Review Our intention is to present a review on shot noise in mesoscopic conductors. Ane!ort is made to collect a complete list of references, and if not comprehensively re-derive, then at least to mention results relevant to the "eld. We do not cite conference proceedings and brief commentaries, unless we feel that they contain new results or bring some understanding which cannot be found elsewhere. Certainly, it is very possible that some papers, for various reasons, have not come to our attention. We apologize to the authors whose papers we might have overlooked. Trying to classify the already large literature, we chose to divide the Review into sections according to the methods by which the results are derived and not according to the systems we describe. Many results can be obtained in the framework of the scattering approach and/or by classical methods. We deliberately avoid an explanation of the Green's function method, the master equation approach, and the bosonization technique. An attempt to explain how any one of these approaches work would probably double the size of this Review, which is already long enough. Consequently, we make an e!ort to re-derive the results existing in the literature by either the scattering or one of the classical (but not the master equation) approaches, and to present a unifying description. Certainly, for some systems these simple methods just do not work. In particular, this concerns Section 7, which describes shot noise in strongly correlated systems. Results obtained with more sophisticated methods are discussed only brie#y and without an attempt to re-derive them. We incorporate a number of original results in the
text; they are usually extensions of results available in the literature, and are not specially marked as original. A good review article should resemble a textbook useful to learn the subject but should also be a handbook for an expert. From this perspective this Review is more a textbook than a handbook. We encourage the reader who wants to enter the "eld to read the Review from the beginning to the end. On the other hand, we also try to help the experts, who only take this Review to look for the results concerning some particular phenomenon. It is for this reason that we have included Table 1 with references to the di!erent subsections in which the subject is discussed. The Review is concluded with a brief summary. Table 1 The results reviewed in this article arranged by subject Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 5 Subject Section Ballistic conductors Electron}phonon interactions 6.3 Electron}electron interactions in non-degenerate ballistic conductors 6.5 Hanbury Brown}Twiss e!ects 2.6.8, 2.6.9, 4.1, Appendix B Aharonov}Bohm e!ect 2.6.10 Tunnel barriers Normal barriers 2.6.1 Barriers in di!usive conductors 2.6.4 Coulomb blockade regime 7.1 Frequency dependence of noise 3.2, 3.3 Barriers of oscillating random height 3.3 NS interfaces 4.1 Josephson junctions 4.2 Barriers in Luttinger liquids 7.3 Counting statistics for normal and NS barriers Appendix A Quantum point contacts Normal quantum point contacts 2.6.2 SNS contacts 4.3 Double-barrier structures Resonant tunneling; linear regime 2.6.3 Double-barrier suppression 2.6.3, 5.2 Counting statistics Appendix A Double wells and crossover to the di!usive regime 2.6.3, 5.2 Quantum wells in the non-linear regime: super-Poissonian shot noise enhancement 5.3 Interaction e!ects in quantum wells 2.7, 5.2, 5.3 Coulomb blockade in quantum dots (normal, superconducting, or ferromagnetic electrodes) 7.1
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Edge channels in the quantum Hall e
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Fig. 19. (a) Geometry of a ring thr
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a manifestation of interference e!e
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Physically, this corresponds to ele
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Our starting point is Eq. (51), whi
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introducing the transmission coe$ci
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investigated experimentally. A self
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and the non-equilibrium resistance
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the sample. These electrons are des
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with D ,¹ (2!¹ ). Performing t
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For completeness, we mention that i
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We note here, however, that there i
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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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