Saturation of strong electron–electron umklapp scattering at high temperature
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According to the empirical Lindemann criterion, the displacement fluctuations are much smaller than the lattice constant even at the melting temperature, i.e. 〈u2〉<0.01a2 (this is simply an indication of the fact that liquid–solid phase transition is a strong first order transition). Phonons play the role of static disorder, and one can evaluate the electron transport properties limited by such atoms displacements both in the strong (tight binding) and in the weak coupling limits. It shows that the metal insulator transition point is unreachable in both cases, namely all the metallic results for three dimensional systems still hold. We believe that the results of Refs. [21] and [22] are artifacts of (a) using unphysical limit of infinitely large electron–phonon interaction constant, i.e. 〈u2〉>a2, and (b) disregarding the localization physics even in this unphysical regime.
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