Crossed, or nonlocal, Andreev reflection as a means of entanglement production is an intruiging new side of the ongoing efforts to model the electronic transport in normal metal – superconductor heterostructures.
The quasiclassical Keldysh Green’s functions formalism is applied to a variety of systems to study non-equilibrium, non-stationary and multiband phenomena in SN, SNS, SINIS and NISIN structures, often in the diffusive limit. A review can be found in:
Microscopic nonequilibrium theory of double-barrier Josephson junctions,
A. Brinkman, A.A. Golubov, H. Rogalla, F. Wilhelm, and M.Yu. Kupriyanov,
Phys. Rev. B. 68, 224513 (2003).
In an exploratory study, the quasiclassical techniques have been applied to the concept of crossed Andreev reflection in:
Crossed Andreev reflection in diffusive contacts: quasiclassical Keldysh-Usadel formalism,
A. Brinkman and A.A. Golubov,
Phys. Rev. B 74, 214512 (2006).
One proposed solution to achieve 100% pure entangled electrons from Crossed Andreev reflection is by employing forbidden energy gaps in semiconductors:
Nonlocal Cooper pair splitting in a pSn-junction
M. Veldhorst and A. Brinkman
Phys. Rev. Lett. 105, 107002 (2010).