Superconductivity and acoustic plasmons in the two-dimensional electron gas

We calculate the superconducting transition temperature $T_c$ for the two-dimensional, two-component electron gas. We use an effective interaction which approximates vertex corrections by means of local-field factors, which are obtained self-consistently; this interaction includes but is not limited to the "acoustic plasmon" (AP) mode. The gap equation, which gives $T_c$, includes the full frequency dependence of the interaction. We find two main results: (i) the $T_c\text{'}\mathrm{s}$ obtained are low (mK); (ii) the AP itself essentially does not contribute to the pairing transition, which is rather due to low-frequency electron-hole pair excitations.