2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143706Motivated 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.5 pages, 5 figures, to be published in Phys. Rev. BMesoscale and Nanoscale PhysicsSuperconductivitytext