Singular structure and enhanced Friedel oscillations in the two-dimensional electron gas

We evaluate the leading-order corrections (in rₛ) to the static polarization Π* $(q,0),$ of the two-dimensional electron gas with dynamically screened interactions. The corresponding diagrams all exhibit singular logarithmic behavior in their derivatives about q=2kF and provide significant enhancement of the proper polarization particularly at low densities. At a density of rₛ=3, the contribution from the leading-order fluctuational diagrams exceeds both the zeroth-order (Lindhard) response and the self-energy and exchange contributions. The importance of these diagrams in two-dimensions is demonstrated by comparison to those of an equivalent three-dimensional electron gas; we also consider the impact these findings have on Π* $(q,0)$ computed to all orders in perturbation theory.