  This work presents a novel approach to describe spectral properties of
graphene layers with well defined edges. We microscopically analyze the
boundary problem for the continuous Bogoliubov-de Gennes-Dirac (BdGD) equations
and derive the Green functions for normal and superconducting graphene layers.
Importing the idea used in tight-binding (TB) models of a microscopic hopping
that couples different regions, we are able to set up and solve an algebraic
Dyson's equation describing a graphene-superconductor junction. For this
coupled system we analytically derive the Green functions and use them to
calculate the local density of states and the spatial variation of the induced
pairing correlations in the normal region. Signatures of specular Andreev
reflections are identified.
