Fine structure of the local pseudogap and Fano effect for superconducting electrons near a zigzag graphene edge

Motivated by recent scanning tunneling experiments on zigzag-terminated graphene, this paper investigates an interplay of evanescent and extended quasiparticle states in the local density of states near a zigzag edge using the Green's function of the Dirac equation. A model system is considered where the local electronic structure near the edge influences transport of both normal and superconducting electrons via a Fano resonance. In particular, the temperature enhancement of the critical Josephson current and 0-π transitions are predicted.