shot noise in mesoscopic conductors - Low Temperature Laboratory

More documents

Recommendations

Info

78 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 Fig. 24. (a) Theoretical results (134) for various amplitudes of the ac voltage; dotted line shows the dc results. (b) Experimental results of Schoelkopf et al. [154] for the same parameters. (c) Experimental results plotted as RS/R
investigated experimentally. A self-consistent spectrum for photon-assisted noise spectra can probably be developed along the lines of Ref. [153]. 3.4. Noise of a capacitor Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 79 Now we turn to the problems where the energy dependence of the scattering matrices is essential. Rather than trying to give the general solution (which is only available for the case when the potential inside the system is spatially uniform [156,157]), we provide a number of examples which could serve as a basis for further investigations of "nite frequency noise. The simple case of shot noise in a ballistic wire was studied by Kuhn et al. [158,159]. They found signatures of the inverse #ight time v /¸. However, the interactions are taken into account only implicitly via what the authors call `quantum generalization of the Ramo}Shockley theorema. We do not know in which situations this approach is correct, and it certainly cannot be correct universally. Thus, even this simple case cannot be considered as solved and needs further consideration. We start from the simplest system } a mesoscopic capacitor (Fig. 25a), which is connected via two leads to equilibrium reservoirs. Instead of the full Poisson equation interactions are described with the help of a geometrical capacitance C. There is no transmission from the left to the right plate, and therefore there is no dc current from one reservoir to the other. Moreover, this system does not exhibit any noise even at "nite frequency if the scattering matrix is energy independent. Indeed, if only the matrices s and s are non-zero, we obtain from Eq. (51) e S()" 2 dE Tr [1!s (E)s (E#)] [1!s (E#)s (E)]f (E)(1!f (E#)) . (135) Here we used the superscript (0) to indicate that the #uctuations of the particle current, and not the total current, are discussed. If the scattering matrices are energy independent, Eq. (135) is identically zero due to unitarity. Another way to make the same point is to note that since S "0, the only way to conserve current would be S "0. Before proceeding to solve this problem, we remark that Eq. (135) describes an equilibrium #uctuation spectrum and via the #uctuation dissipation theorem S ()" 2g () coth (/2k ¹) is related to the real part of a conductance g () given by g ()" e dE Tr[1!s (E)s (E#)] f (E)!f (E#) . (136) Fig. 25. A mesoscopic capacitor (a); a mesoscopic conductor vis-à-vis a gate (b).
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: Ya.M. Blanter, M. Bu( ttiker / Phys
Page 29 and 30: equilibrium and shot noise. For low
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 47 and 48: we include weak localization e!ects
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 69 and 70: Physically, this corresponds to ele
Page 73 and 74: Our starting point is Eq. (51), whi
Page 77: introducing the transmission coe$ci
Page 85 and 86: and the non-equilibrium resistance
Page 87 and 88: the sample. These electrons are des
Page 93 and 94: with D ,¹ (2!¹ ). Performing t
Page 97 and 98: For completeness, we mention that i
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 131 and 132:
Page 133 and 134:
which describes strictly ballistic
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
approximately e/C. Between the peak
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Boltzmann}Langevin approach (see Se
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
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
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?