Dynamic screening-driven superconductivity in a two-dimensional electron gas

We establish the ultra-low temperature phase diagram of a two-dimensional (2D) electron gas in the dense limit where the random phase approximation (RPA) is controlled. Such a 2D Fermi gas at the RPA level cannot be a Kohn-Luttinger superconductor due to the absence of emergent attractive interaction from the back-scattering channel. Nevertheless, we develop a Cooper-pair linear response approach and identify a series of exotic superconductivity with the ultra-low superconducting temperature of 10^-200~10^-10 times Fermi temperature. Our results show that dynamic screening-driven superconductivity exists in the 2D electron gas, where the long-range character of Coulomb interaction is essential, and indicate a broad reconsideration of the widely used static approximation in the context of 2D superconductivity from repulsive interactions.