Kohn-Luttinger effect and the instability of a two-dimensional repulsive Fermi liquid atT=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≤2{p}F$. 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 ³He adsorbed on the free surface of ⁴He is discussed.