Kohn-Luttinger effect and the instability of a two-dimensional repulsive Fermi liquid at T=0

We consider the possibility for a pairing in a two-dimensional (2D) repulsive Fermi liquid due to the singularity in the scattering amplitude Γ(q) at the momentum transfer q≤2pF (Kohn-Luttinger effect). A common belief based on perturbative calculations up to second order in the s-wave scattering amplitude is that this effect is absent in two dimensions. I show that this is not the case. For an arbitrary Fermi liquid, Γ(q) is found to have a singular part, Γsing(q)∼ 1-q2/(2pF)2, for q≤2pF. For large 2D orbital momentum l, this term gives a dominant attractive contribution to the scattering amplitude and leads to a pairing instability in a 2D Fermi liquid with arbitrary short-range repulsion. In the dilute limit, numerical studies show that the effect survives down to l=1 and gives rise to a p-wave pairing. The relevance of these results to experiments on He3 adsorbed on the free surface of He4 is discussed.