Theory of a superfluid Fermi liquid. I. General formalism and static properties

The microscopic theory of a superfluid Fermi liquid at finite temperature is developed for the case of a pure system with S-wave pairing, and applied to the calculation of the static properties. As a function of TTc these properties are determined entirely by the Landau parameters F0, F1, Z0, etc., characterizing quasiparticle interactions in the normal phase. In particular the spin susceptibility and the density of the normal component n are given by ()(1)=(1+14Z0)f()[1+14Z0f()], n=(1+13F1)f()[1+13F1f()], where the universal function f()-[(0)]-1p(dndEp) is the "effective density of states near the Fermi surface" relative to its value (0) in the normal phase. Thus the often-quoted expression n=13pp2(dndEp) is valid for an interacting system only in the limit T0. In the latter part of the paper a simple phenomenological theory of "Fermi-liquid" effects on and n is developed for arbitrary conditions (including the presence of impurities and pairing with l 0); it is found that under most circumstances explicit expressions for and n may be obtained which involve only the Landau parameters and a suitably generalized effective density of states. The theory should apply to the possible superfluid phase of He3 and to most superconductors. It is suggested that the Knight shift in nontransition-metal superconductors should display some "Fermi- liquid" effects. The weak-field dc penetration depth (T) is shown to be insensitive to such effects both in the Pippard limit and near Tc; however, in a London superconductor at lower temperatures the correction to (T) should be observable and yield a direct estimate of F1.