Inequalities, instabilities, and renormalization in metals and other fermi liquids

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Abstract

This paper discusses various aspects of microscopic Fermi-liquid theory, with particular emphasis on its application to metals. It is shown that under certain conditions we have the inequalities m* 1+ 1 3F1≥m, m* 1+ 1 12Z1≥m. The appropriate formulation of the theory is presented for the case that the fermions interact with an arbitrary background (e.g. 3He4He mixtures). A microscopic proof of the stability conditions is given. The effects of the Coulomb and electron-phonon interaction in metals are treated by completely parallel techniques, and explicit expressions are given for the electronic correlation functions in the limits ω 2> ωD and ω ≪ ωD. Results for the static properties, etc., are in agreement with the recent work of Prange and Sachs. It is shown that the electron-phonon interaction can only enhance the "dynamic effective mass" m* (1 + 1 3F1), and that the enhancement tends to zero for forward electron-phonon scattering. It is also shown explicitly that phonon effects on the Landau parameters can affect the static properties in the superconducting state even though they cannot in the normal state. The inequalities obtained are compared as far as possible with experiment, and it is shown that the rough value of Z1 12(≡B1) recently obtained for Na from CESR experiments is almost certainly not compatible with the optical data. Tentative application is also made to the recently observed Knight shift in superconducting Al.

Original languageEnglish (US)
Pages (from-to)76-113
Number of pages38
JournalAnnals of Physics
Volume46
Issue number1
DOIs
StatePublished - Jan 1968

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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