shot noise in mesoscopic conductors - Low Temperature Laboratory

More documents

Recommendations

Info

150 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 Like every list, the choice re#ects very much our taste, and we do not imply that the predictions not included in this list are of minor importance. -suppression of shot noise in chaotic cavities. Multi-terminal e!ects probing statistics (exchange Hanbury Brown}Twiss (HBT) e!ect; shot noise at tunnel microscope tips; HBT e!ect with FQHE edge states). Frequency-dependent noise beyond Nyquist}Johnson (noise measurements which would reveal the inner energy scales of mesoscopic systems); current #uctuations induced into gates or other nearby mesoscopic conductors. Shot noise of clean NS interfaces; mesoscopic nature of positive cross-correlations in hybrid structures. Shot noise in high magnetic "elds at the half-"lled Landau level. Shot noise in hybrid magnetic structures. The theory, in our opinion, is generally well developed for most of the "eld and adequately covers it. However, a number of problems persist: For instance, there is no clear understanding under which conditions the cross-correlations in multi-terminal hybrid structures may be positive. Recent work [179] suggests that it is only a mesoscopic quantum contribution which is positive, but that to leading order the correlations will be negative as in normal conductors. Considerably more work is required on the frequency dependence of shot noise and on strongly correlated systems. The former (Section 3) o!ers the opportunities to probe the inner energy scales and collective relaxation times of the mesoscopic systems; only a few results are presently available. As for the strongly correlated systems (including possibly unconventional superconductors), this may become (and is already becoming) one of the mainstreams of mesoscopic physics; since even the dc shot noise measurements provide valuable information about the charge and statistics of quasiparticles, we expect a lot of theoretical developments in this direction concerning the shot noise. Some of the unsolved problems in this "eld may be found directly in Section 7, one of the most fascinating being the possibility of probing the quasiparticle statistics in multi-terminal noise measurements with FQHE edge states. One more possible development, which we did not mention in the main body of this Review, concerns shot noise far from equilibrium under conditions when the I}< characteristics are non-linear. The situation with non-linear problems resembles very much the frequency dependent ones: Current conservation and gauge invariance are not automatically guaranteed, and interactions must be taken into account to ensure these properties (for a discussion, see e.g. Ref. [153]). Though in the cases which we cited in the Review the non-linear results seem to be credible, it is still desirable to have a gauge-invariant general theory valid for arbitrary non-linear I}< characteristics. It is also desirable to gain insight and develop estimates of the range of applicability of the usual theories. Recently, Wei et al. [334] derived a gauge invariant expression for shot noise in the weakly non-linear regime, expressing it through functional derivatives of the Lindhard function with respect to local potential "elds. They apply the results to the resonant tunneling diode. Wei et al. [334] also discuss the limit in which the tunneling rates may be assumed to be energy independent. Apparently, the theory of Wei et al. does not treat the e!ect of #uctuations of the potential inside the sample, which may be an important source of noise. Furthermore, Green and Das [335}337] proposed a classical theory of shot noise, based on a direct solution of kinetic equations. They discuss the possibility to detect interaction e!ects in the cross-over region from
thermal to shot noise. It is, however, yet to be shown what results this approach yields in the linear regime and whether it reproduces, for instance, the -suppression of shot noise in metallic di!usive wires. An application of both of these approaches to speci"c systems is highly desirable. What we have mentioned above, concerns the development of a "eld inside mesoscopic physics. We expect, however, that interesting connections will occur across the boundaries of di!erent "elds. An immediate application which can be imagined is the shot noise of photons and phonons. Actually, noise is much better studied in optics than in condensed matter physics (see e.g. the review article [338]), and, as we have just mentioned previously, the theory of shot noise in mesoscopic physics borrowed many ideas from quantum optics. At the same time, mesoscopic physics gained a huge experience in dealing, for instance, with disordered and chaotic systems. Recently a `back-#owa of this experience to quantum optics started. This concerns photonic noise for the transmission through (disordered) waveguides, or due to the radiation of random lasers or cavities of chaotic shape. In particular, the waveguides and cavity may be absorbing or amplifying, which adds new features as compared with condensed matter physics. For references, we cite a recent review by Patra and Beenakker [339]. Possibly, in the future other textbook problems of mesoscopic physics will also "nd their analogies in quantum optics. Phonons are less easy to manipulate with, but, in principle, one can also imagine the same class of problems for them. Generally, shot noise accompanies the propagation of any type of (quasi)-particles; as the last example, we mention plasma waves. 8.2. Summary for a lazy or impatient reader Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 151 Below is a summary of this Review. Though we encourage the reader to work through the whole text (and then she or he does not need this summary), we understand that certain readers are too lazy or too impatient to do this. For such readers we prepare this summary which permits to acquire some information on shot noise in a very short time span. We only include in this summary the statements which in our opinion are the most important. Shot noise occurs in a transport state and is due to #uctuations in the occupation number of states caused by (i) thermal random initial #uctuations; (ii) the random nature of quantummechanical transmission/re#ection (partition noise), which, in turn, is a consequence of the discreteness of the charge of the particles. The actual noise is a combination of both of these microscopic sources and typically these sources cannot be separated. Shot noise provides information about the kinetics of the transport state: In particular, it can be used to obtain information on transmission channels beyond that contained in the conductance. In two-terminal systems, zero-frequency shot noise for non-interacting electrons is suppressed in comparison with the Poisson value S"2eI. One has to take, of course, also into account the di!erences between photon and electron measurements: Apart from the evident Bose versus Fermi and neutral versus charged particles, there are many more. For example, the photon measurement is accompanied by a removal of a photon from the device, while the total electron number is always conserved.
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 149: Boltzmann}Langevin approach (see Se
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?