Superconductivity in Engineered Two-Dimensional Electron Gases

TL;DR

This paper investigates how superconductivity can arise in engineered two-dimensional electron gases through the Kohn-Luttinger mechanism, highlighting conditions that favor non-s-wave pairing and estimating the critical temperature's dependence on system parameters.

Contribution

It demonstrates the emergence of non-s-wave superconductivity in a two-band 2D electron gas and analyzes how system parameters influence the pairing symmetry and transition temperature.

Findings

Non-s-wave superconductivity can occur in 2D electron gases with two occupied subbands.

p-wave pairing is typically the dominant superconducting channel.

The estimated coupling constant suggests potential for higher $T_c$ at larger Coulomb correlations.

Abstract

We consider Kohn-Luttinger mechanism for superconductivity in a two-dimensional electron gas confined to a narrow well between two metallic planes with two occupied subbands with Fermi momenta $k_{FL} > k_{FS}$. 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 $T_c$ as a function of the distance to the metallic planes, the ratio $k_{FL}/k_{FS}$, and $r_s$, 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 $r_s = O(1)$ we estimate that the dimensionless coupling $\lambda \approx 10^{-1}$, but it likely continues increasing for larger $r_s$ (where we lose theoretical control).