Graphene nanoribbons: Photonic crystal waveguide analogy and minigap stripes

Graphene nanoribbons are one-dimensional multimode systems with quasilinear electron dispersion. We discuss why they are direct analogs of broad photonic crystal waveguides. Three kinds of dispersion regions found in band structure of the latter (Fabry-Perot region, mini-stopband region, and coupled-zone-edge regions) are traced to their equivalent in zigzag graphene nanoribbons whose edges are periodically modified. For a superperiod of similar to 1 nm, the zone folding arising across the nearly linear low-energy part of the electronic dispersion induces these equivalent band structures. A last analogy is the capability to induce a form of localization characterized by minigap stripes and collective flatband edges through a limited modification localized within a pair of edge rows of the nanoribbon, representing typically less than 1% of the ribbon atoms.