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

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.