  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 (LDOS) 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-pi transitions
are predicted.
