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16 Impurity Scattering and Conductivity
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Published:September 2004
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Abstract
We now return to the problem of calculating the resistance of a metallic conductor due to scattering against impurities. The basic physics of impurity scattering was discussed in Chapter 12, where we saw how the single-particle Green’s function acquired a finite lifetime after averaging over the positions of the impurities. In Chapter 15 the conductivity was calculated within the Boltzmann equation approach. We now rederive the Boltzmann equation result starting from a microscopic quantum approach. The advantage of this microscopic approach, besides giving a first principle justification of the Boltzmann equation, is that it can be extended to include correlation and coherence effects that cannot be described in the semi-classical Boltzmann approach. In order to get familiar with the techniques, we therefore start by deriving the semi classical result. Then we go on to include the quantum mechanical effect known as weak localization, which is due to interference between time reversed paths. Weak localization involves coherent scattering on many impurities, and it can therefore not be explained semi-classically.
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