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).
Bibliographical noteFunding Information:
We thank S. Raghu, R.-R. Du, and L. N. Pfeiffer for useful discussions. This work was supported by the NSF DMR-1523036 (A.V.C.) and DMR-1608055 (S.A.K.). The authors are thankful to KITP at UCSB, where part of the work has been done. KITP is supported by NSF Grant No. PHY-1125915.
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