shot noise in mesoscopic conductors - Low Temperature Laboratory

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6 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 Table 1 (Continued) Subject Section Frequency dependence of noise 5.2, 5.3, 7.1 Resonant tunneling through localized states; Anderson and Kondo models 2.6.3, 7.2 NINIS junctions 4.1 Disordered conductors Noise suppression in metallic di!usive wires 2.6.4, 6.2 Counting statistics Appendix A Multi-terminal generalization and Hanbury Brown}Twiss e!ects 2.6.9, 6.2 Interaction e!ects 2.7, 6.3 Frequency dependence of noise 3.2, 6.4 Disordered contacts and interfaces 2.6.4 Disordered NS and SNS contacts 4.1, 4.3 Crossover to the ballistic regime 2.6.4 Localized regime 2.6.4 Non-degenerate di!usive conductors 6.5 Composite fermions with disorder 7.4 Noise induced by thermal transport Appendix C Chaotic cavities Noise suppression in two-terminal chaotic cavities 2.6.5, 6.6, 6.7 Cavities with di!usive boundary scattering 6.6 Multi-terminal generalization and Hanbury Brown}Twiss e!ects 2.6.5, 6.7 Counting statistics Appendix A Quantum Hall ewect IQHE edge channels 2.6.6, 2.6.10 Hanbury Brown}Twiss e!ects with IQHE edge channels 2.6.7, 2.6.9 FQHE edge channels 7.3 Composite fermions 7.4 Systems with purely capacitive coupling Frequency dependence of noise 3.4, 3.5 1.3. Subjects not addressed in this Review First of all, we emphasize that this is not a general review of mesoscopic physics. In many cases, it is necessary to describe brie#y the systems before addressing their noise properties. Only a few references are provided to the general physical background. These references are not systematic; we cite review articles where this is possible, and give references to the original papers only in cases
such reviews are not readily available. This Review is not intended to be a tool to study mesoscopic physics, though possibly many important ideas are present here. A multitude of sources typically contribute to the noise of electrical conductors. In particular, some of the early experimental e!orts in this "eld su!ered from 1/f-noise which is observed at low frequencies. There is still to our knowledge no established theory of 1/f-noise. The present article focuses on fundamental, unavoidable sources of noise, which are the thermal (Nyquist}Johnson noise) and the shot noise due to the granularity of charge. The reader may "nd an account of other sources of noise in the book by Kogan [3]. We mention also that, though we try to be very accurate in references, this Review cannot be regarded as a historical chronicle of shot noise research. We re-derive a number of results by other methods than were used in the original papers, and even though we make an e!ort to mention all achievements, we do not emphasize historical priorities. 1.4. Fundamental sources of noise Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 7 1.4.1. Thermal noise At non-zero temperature, thermal #uctuations are an unavoidable source of noise. Thermal agitation causes the occupation number of the states of a system to #uctuate. Typically, in electric conductors, we can characterize the occupation of a state by an occupation number n which is either zero or one. The thermodynamic average of the occupation number n is determined by the Fermi distribution function f and we have simply n"f. In an equilibrium state the probability that the state is empty is on the average given by 1!f, and the probability that the state is occupied is on the average given by f. The#uctuations away from this average occupation number are (n!n)"n!2nn#n. Taking into account that for a Fermi system n"n, we"nd immediately that the #uctuations of the occupation number at equilibrium away from its thermal average are given by (n!n)"f (1!f ) . (1) The mean-squared #uctuations vanish in the zero temperature limit. At high temperatures and high enough energies the Fermi distribution function is much smaller than one and thus the factor 1!f in Eq. (1) can be replaced by 1. The #uctuations are determined by the (Maxwell)}Boltzmann distribution. The #uctuations in the occupation number give rise to equilibrium current #uctuations in the external circuit which are via the #uctuation-dissipation theorem related to the conductance of the system. Thus, investigation of equilibrium current #uctuations provides the same information as investigation of the conductance. This is not so with the shot noise of electrical conductors which provides information which cannot be obtained from a conductance measurement. We next brie#y discuss the source of shot noise. 1.4.2. Shot noise Shot noise in an electrical conductor is a consequence of the quantization of the charge. Unlike for thermal noise, to observe shot noise, we have to investigate the non-equilibrium (transport) state of the system.
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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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shot noise in mesoscopic conductors - Low Temperature Laboratory

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