Superconductivity in engineered two-dimensional electron gases

We consider Kohn-Luttinger mechanism for superconductivity in a two-dimensional electron gas confined to a narrow well between two grounded metallic planes with two occupied subbands with Fermi momenta kFL>kFS. On the basis of a perturbative analysis, we conclude that non-s-wave superconductivity emerges even when the bands are parabolic. We analyze the conditions that maximize Tc as a function of the distance to the metallic planes, the ratio kFL/kFS, and rₛ, which measures the strength of Coulomb correlations. The largest attraction is in p-wave and d-wave channels, of which p wave is typically the strongest. For rₛ=O(1) we estimate that the dimensionless coupling λ≈10^-1, but it likely continues increasing for larger rₛ (where we lose theoretical control).