Inter-band and intra-band reflections in graphene-insulator-superconductor junctions with zigzag or armchair edge

We analyze electron-electron and Andreev reflections (AR) for a graphene-insulator-superconductor junction for zigzag and armchair edges, where the insulator is modeled as a potential barrier characterized by a strength. We calculate the reflection probabilities and differential conductance using the Bogoliubov-de Gennes-Dirac (BdGD) equations. For low doping values and zigzag edge the reflection coefficients have the same behavior that in a graphene-superconductor junction. However for high doping values the reflection probabilities have a periodicity of pi with the strength barrier values. For high doping values and armchair edge the electron-electron reflections associated to K' valley increase and AR associated to K valley decrease. We compare our results with the differential conductance obtained by the Green formalism. We show that the effect of barrier strength for high doping resembles the behavior when a hopping between graphene and superconductor interfaces is considered. (C) 2014 Elsevier B.V. All rights reserved.