  We investigate, in the framework of macroscopic Dirac model, the spectrum,
charge density and conductivity of metallic armchair graphene nanoribbons in
presence of different mass terms. We reveal the conditions and symmetries
governing the presence of edge modes in the system. Depending on the mass terms
present they are exponentially localized gapless or gapped modes. The latter
situation is realized, in particular, for a full Kekule distortion. For this
case, we calculate the mean charge and conductivity of the ribbon, and derive
the traces of the presence of edge modes suitable for experimental
verification.
