Coulomb scattering cross section in a two-dimensional electron gas and production of entangled electrons

We calculate the Coulomb scattering amplitude for two electrons injected with opposite momenta in an interacting two-dimensional electron gas (2DEG). We include the effect of the Fermi-liquid background by solving the two-dimensional (2D) Bethe-Salpeter equation for the two-particle Green function vertex in the ladder and random phase approximations. This result is used to discuss the feasibility of producing spin-EPR pairs in a 2DEG by collecting electrons emerging from collisions at a pi/2 scattering angle, where only the entangled spin singlets avoid the destructive interference resulting from quantum indistinguishability. Furthermore, we study the effective 2D electron-electron interaction due to the exchange of virtual acoustic and optical phonons and compare it to the Coulomb interaction. Finally, we show that the 2D Kohn-Luttinger pairing instability for the scattering electrons is negligible in a GaAs 2DEG.