shot noise in mesoscopic conductors - Low Temperature Laboratory

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144 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 may be shown that for the bulk "lling factor "1/(2m#1), m3Z (Laughlin states), the interaction parameter g takes the same value g"1/(2m#1). The di!erence with the ordinary Luttinger liquid is that the FQHE edge states are chiral: the motion along a certain edge is only possible in one direction. Thus, if we imagine a FQHE strip, the electrons along the upper edge move, say, to the right, and the electrons along the lower edge move to the left. For the transport properties we discuss this plays no role, and expressions (262) and (263) remain valid. In particular, for the FQHE case the quasiparticles with the charge e may be identi"ed with the Laughlin quasiparticles. The distinction between the strong and weak tunneling we described above also gets a clear interpretation (Fig. 37), which is in this form due to Chamon, Freed and Wen [313]. Indeed, consider a FQHE strip with a barrier. If the tunneling is strong (Fig. 37a), the edge states go through the barrier. The backscattering corresponds then to the charge transfer from the upper edge state to the lower one, and this happens via tunneling between the edge states inside the FQHE strip. Thus, in this case, there are Laughlin quasiparticles which tunnel. In principle, the electrons may also be backscattered, but such events have a very low probability (see below). In the opposite regime of weak tunneling, the strip splits into two isolated droplets (Fig. 37b). Now the tunneling through the barrier is again the tunneling between two edge states, but it only may happen outside the FQHE state, where the quasiparticles do not exist. Thus, in this case, one has tunneling of real electrons. 7.3.1. Theory of dc shot noise Shot noise in Luttinger liquids was investigated by Kane and Fisher [314] using the bosonization technique. The conclusion is that for an ideal in"nite one-dimensional system there is no shot noise. Shot noise appears once the barrier is inserted. For the strong tunneling regime the shot noise is S"2ge((ge/2)
Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 145 Fig. 37. The tunneling experiment with the FQHE edge states: (a) strong tunneling; (b) weak tunneling. The shaded areas denote the location of the FQHE droplet(s). For the case of weak tunneling, the shot noise is Poissonian with the charge e, S"2eI: Itis determined by the charge of tunneling electrons. Expressions for noise interpolating between this regime and Eq. (264), as well as a numerical evaluation for g" , are provided by Fendley et al. [316]; Fendley and Saleur [317] and Weiss [318] generalize them to "nite temperatures. For the resonant tunneling process, at resonance, the shot noise is given by [314] S"4ge((ge/2)
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Ya.M. Blanter, M. BuK ttiker / Phys
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8. Concluding remarks, future prosp
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text; they are usually extensions o
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such reviews are not readily availa
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Ya.M. Blanter, M. Bu( ttiker / Phys
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The above considerations are, of co
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and the initial state of our two-pa
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2.3.3. Multi-terminal case We consi
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Note that in the absence of time-de
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equilibrium and shot noise. For low
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and S" e A e< dE ¹(E )[1!¹
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arrier, situated in the region !w/2
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we include weak localization e!ects
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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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