Umklapp scattering and electron pairing cutoff in BCS superconductors
X. H. Zheng, D. G. Walmsley
Abstract
In a superconductor electrons form pairs for which the end states of normal and umklapp scattering may overlap. This cuts electron pairing off at a phonon frequency, ωc, low compared with the Debye frequency, ωD. Using this insight, correct values of 2Δ/kBTc (average error 8.9%) for 12 superconductive metals, including Hg and Pb, are achieved from simple BCS formalism with an average ωc/ωD of 0.148: Landau's idea of a Fermi liquid may cover strong-coupling superconductors. The cancellation between normal and umklapp scattering may be more important than a strong electron-phonon interaction in reaching a high critical temperature Tc.
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