Coulomb scattering cross-section in a 2D electron gas and production of entangled electrons

TL;DR

This paper calculates Coulomb scattering in a 2D electron gas, explores entangled electron pair production, and compares phonon-mediated interactions to Coulomb forces, concluding certain pairing instabilities are negligible.

Contribution

It provides a detailed calculation of Coulomb scattering amplitudes in a 2DEG including many-body effects and assesses the feasibility of generating entangled electron pairs.

Findings

Entangled electron pairs can be produced at specific scattering angles.

Phonon-mediated interactions are weaker than Coulomb interactions in this system.

Kohn-Luttinger pairing instability is negligible in GaAs 2DEG.

Abstract

We calculate the Coulomb scattering amplitude for two electrons injected with opposite momenta in an interacting 2DEG. We include the effect of the Fermi liquid background by solving the 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.