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 θ≡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 χ and the density of the normal component ρₙ are given by χ(θ)χ(1)=(1+1/4Z₀)f(θ)[1+1/4Z₀f(θ)], ρₙρ=(1+1/3F₁)f(θ)[1+1/3F₁f(θ)], where the universal function f(θ)≡-[ν(0)]^-1Σₚ(dndEₚ) is the "effective density of states near the Fermi surface" relative to its value ν(0) in the normal phase. Thus the often-quoted expression ρₙ=1/3Σₚp²(dndEₚ) is valid for an interacting system only in the limit T→0. In the latter part of the paper a simple phenomenological theory of "Fermi-liquid" effects on χ and ρₙ 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 χ and ρₙ 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 λ(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 λ(T) should be observable and yield a direct estimate of F₁.