Superconductivity at low carrier density beyond leading order in the coupling constant

We present results for the onset pairing instability temperature for superconductivity mediated by an Einstein phonon in a 2D electron gas with a parabolic dispersion, in the regime of low carrier density. We go beyond the leading order in the electron-phonon coupling and include contributions to the pairing kernel from fermionic self-energy and from Kohn-Luttinger processes. We then compute the phase stiffness and obtain the actual critical temperature Tc. We analyze thermodynamic properties of our system, such as the specific heat jump across Tc.