Temperature dependence of the electrical resistivity of metals in the “dirty” limit

It is demonstrated that simultaneous collisions of electrons with impurities and with phonons may result in such large deviations from Matthiessen's rule that, at the “dirty” limit, the temperature-dependent component of resistivity behaves in a qualitatively different fashion than in the “pure” limit. When the Fermi surface of a metal includes segments of large curvature (regions of Bragg reflection in metals describable by the weak-pseudopotential model), for instance, then the well known Bloch law for the temperature dependence of the resistivity is violated in the “dirty” limit. It has been established that Umklapp processes also result in large deviations from Matthiessen's rule, the form of these deviations yielding much information about those processes. It is noted that in the “dirty” limit the electron–phonon component of resistivity may depend on the impurity concentration.

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