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Motivated by recent scanning tunneling experiments on zigzag-terminatedgraphene this paper investigates an interplay of evanescent and extendedquasiparticle states in the local density of states (LDOS) near a zigzag edgeusing the Green's function of the Dirac equation. A model system is consideredwhere the local electronic structure near the edge influences transport of bothnormal and superconducting electrons via a Fano resonance. In particular, thetemperature enhancement of the critical Josephson current and 0-pi transitionsare predicted.

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