A model for pairing in two-dimensional electron gases

If the bare interaction between two electrons is dressed in the two-dimensional (2D) electron gas by the many-body environment, pairing may occur. Here, we study numerically the existence and character of bound states in cases where the basic dressing is described by superimposing normalized holes centered around both electrons. Beyond this modeling, a possible modification of the interaction energy at short range is considered by a repulsive potential term. The effect of the ionic polarizability on pair interaction is approximated by a static dielectric constant. A many-body analysis of pairing, employing the spherical harmonics representation of the Bethe-Salpeter ladder-solution for the two-particle scattering amplitude in 2D, is given as well. Pairing occurs due to attractive spherical harmonics in our interparticle potential.