Electron transport through pair of Graphene-Superconductor junctions

Electron transport across Graphene-Superconductor (GS) junctions have recently attracted a lot of attention [1] after it was pointed out that the Andreev processes in such junction holds distinct features as compared to Andreev processes in Normal metal-Superconductor junction because of the ultra relativistic dispersion of the charge carriers in Graphene. In this work we analyze transport properties through a pair of such junctions that can be either GSG or SGS formdue to Andreev and normal processes. In one part of the work we compare such transport with certain optical phenomena such as Goos-Hanchen shift [2] and discuss its experimentally verifiable features. We also investigate the formation of the Andreev Bound States(ABS) in hetero-junctions like SGS, and explore its connection with the transport properties; Josephson current.
References:
[1] C. W. J. Beenakker, PRL 97, 067007, 2006
[2] C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydlo, PRL 102, 146804, (2009)