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84926531980
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Present address: Dansk Institut for Fundamental Metrologi, Anker Engelundsvej 1, DK 2800 Lyngby, Denmark.
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84926552254
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Present address: Institut för Tillämpad Fysik, Chalmers Tekniska Högskola och Göteborgs Universitet, S 41296 Göteborg, Sweden.
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84926550786
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makeatother
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For a system where the two subsystems scatter from the same impurities, diagrams that connect the two conductivity bubbles must be included and the transconductivity cannot be written as a product of the impurity averaged conductivities of the two subsystems. See also Ref. onlineciteimp imp.
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It is easy to verify ( ref1storder) independently by the following simple argument, which takes into account the external field experienced by layer 2 due to charge perturbations in layer 1: FL (Omitted equation) where we used continuity equation to relate ρ1 and boldmathj1. The charge of the carriers was taken to be -e, although a generalization to mixed carrier systems is straightforward. The term in the square brackets is the transconductivity tensor, which agrees with Eq. ( ref1storder).
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This factorization is not possible if one must consider scattering processes where the electrons in the two quantum wells scatter against the same impurities. The main source for impurity scattering is due to the ionized impurities in the outside barriers and hence the electrons in a given well feel mainly their ``own'' impurities. The ratio of the strength of the screened charged impurity potential Vimp,i(q) in identical wells separated by a distance d, with well 1 closer to the impurity than well 2, is (within the Thomas Fermi screening approximation) Vmathrmimp,2(q)/Vmathrmimp,1(q) = q exp(-qd)/ [q mathrmTF(1-e-2qd) + q], independent of the distance of the impurities to the wells. For experimental parameters in Ref. onlinecitegram_all, this ratio is lesssim 0.05. Further, the barrier separating the two quantum wells is undoped (and consequently has a low impurity concentration) and hence we feel that these correlated impurity processes can safely be neglected.
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One should note that Fig. reffig:vertex does not include all possible diagrams. Examples of such higher order diagrams are analyzed in Sec. refsec:WL.
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See, for example, Ref. onlinecitemahan, Sec. 7.1.c.
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