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 πwith the strength barrier values. For high doping values and armchair   edge the electron–electron reflections associated to K′K′ valley increase and AR associated to KK 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.