Pair formation temperature in jelliumlike two-dimensional electron gases

A standard many-body method, based on the spherical-harmonics representation of the Bethe-Salpeter ladder solution for the two-particle scattering amplitude in two-dimensional jellium electron gases, is applied to determine a pair formation temperature $T_p$ from the pole of the pairing vertex. In this method, pairing may occur due to attractive spherical harmonics in the input interparticle interaction. The comparative study was performed with parametrized models for this interaction obtained by considering the real-space aspects of screening holes around moving electrons. The theoretical, maximal pair formation temperatures are in the $\sim 100\text{K}$ range and appear at small values of the density of the jellium system.