BCS instability of a two-layer system of composite fermions

Pairing instability is considered for a two-layer electron system in a strong magnetic field with an even-fractional filling ν=1/(2m) (m is an integer) of the lowest Landau level in each of the layers. The limit of large distance d between the layers is analyzed. Microscopic analysis is carried out in the eikonal approximation in the composite-fermion formalism. It is found that the condition for pairing instability in this model is independent of d. Due to the marginal character of the composite-fermion system, pairing instability in the particle-particle (BCS) channel arises only for η<2 or η=2, but Mv ₀>43, where η and v ₀ are the parameters of the assumed electron-electron interaction, v∝v ₀/r ^η, and M is the band electron mass. In the particle-hole (isospin density wave) channel, instability is not observed.