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We investigate, in the framework of macroscopic Dirac model, the spectrum,charge density and conductivity of metallic armchair graphene nanoribbons inpresence of different mass terms. We reveal the conditions and symmetriesgoverning the presence of edge modes in the system. Depending on the mass termspresent they are exponentially localized gapless or gapped modes. The lattersituation is realized, in particular, for a full Kekule distortion. For thiscase, we calculate the mean charge and conductivity of the ribbon, and derivethe traces of the presence of edge modes suitable for experimentalverification.

To gap or not to gap? Mass distortions and edge modes in graphene armchair nanoribbons