shot noise in mesoscopic conductors - Low Temperature Laboratory

More documents

Recommendations

Info

34 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 Fig. 6. Geometry of the quantum point contact in the hard-wall model (a) and the e!ective potential for one-dimensional motion (b). Fig. 7. Conductance (upper plot) and shot noise (lower plot) as functions of the gate voltage, as measured by Reznikov et al. [42]. Di!erent curves correspond to "ve di!erent bias voltages. Copyright 1995 by the American Physical Society. (Fig. 6a). If the distance between the walls d(x) (width of the contact) is changing slowly in comparison with the wavelength, transverse and longitudinal motion can be approximately separated. The problem is then e!ectively reduced to one-dimensional motion in the adiabatic potential ;(x)"n/2md(x), which depends on the width pro"le and the transverse channel number n. Changing the gate voltage leads to the modi"cation of the potential pro"le. Theoretically it is easier to "x the geometry of the sample, i.e. the form of the potential, and vary the Fermi energy in the channel E (Fig. 6b). The external potential is smooth, and therefore may be treated semi-classically. This means that the channels with n(k d / (here k ,(2mE ), and d is the minimal width of the contact) are open and transparent, ¹ "1, while the others are closed, ¹ "0. The conductance (40) is proportional to the number of open channels and therefore exhibits plateaus as a function of the gate voltage. At the plateaus, shot noise is equal to zero, since all the channels are either open or closed. The semi-classical description fails when the Fermi energy lies close to the top of the potential in one of the transverse channels. Then the transmission coe$cient for this channel increases from zero to one due to quantum tunneling through the barrier and quantum re#ection at the barrier. The transition from one plateau to the next is associated with a spike in the shot noise as we will now discuss. A more realistic description of the quantum point contact takes into account that the potential in the transverse direction y is smooth [34]. The constriction can then be thought of as a bottleneck with an electrostatic potential of the form of a saddle. Quite generally, the potential can be expanded in the directions away from the center of the constriction,
Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 35 The transmission probability ¹ (E) exhibits a crossover from zero to one as the energy E passes the value < # (n#1/2). The resulting zero temperature shot noise as a function of < , using Eq. (57), is illustrated in Fig. 5 for the case "4 (curve 2). The conductance of this quantum point contact is shown in Fig. 5 as curve 1. As expected, the shot noise dependence is a set of identical spikes between the plateaus. The height of each spike is e
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 17 and 18: and the initial state of our two-pa
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 29 and 30: equilibrium and shot noise. For low
Page 33: Ya.M. Blanter, M. Bu( ttiker / Phys
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 and 78: introducing the transmission coe$ci
Page 79 and 80: investigated experimentally. A self
Page 85 and 86:
and the non-equilibrium resistance
Page 87 and 88:
the sample. These electrons are des
Page 89 and 90:
Ya.M. Blanter, M. Bu( ttiker / Phys
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:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
We note here, however, that there i
Page 109 and 110:
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 121 and 122:
Page 123 and 124:
one "rst goes from the non-interact
Page 125 and 126:
non-thermalized electrons, the high
Page 127 and 128:
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?