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

Abstract

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′ 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.