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

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.

19 pages, 10 figures

References in corpus (4)

• Production and detection of entangled electron-hole pairs in a degenerate electron gas
• Semiconductor few-electron quantum dot operated as a bipolar spin filter
• Lower bound for electron spin entanglement from beamsplitter current correlations
• Coulomb scattering in a 2D interacting electron gas and production of EPR pairs

Cited by in corpus (6)

• Magnetic Ordering of Nuclear Spins in an Interacting 2D Electron Gas
• Entanglement of Two Impurities through Electron Scattering
• Singlet-triplet filtering and entanglement in a quantum dot structure
• Momentum dependence of the spin susceptibility in two dimensions: nonanalytic corrections in the Cooper channel
• Clauser-Horne inequality and decoherence in mesoscopic conductors
• Measuring statistics-induced entanglement entropy with a Hong-Ou-Mandel interferometer