Abstract
We theoretically study the topological effects of zigzag-edged ribbons on the motion of collective excitations. Pristine geometries resembling those of narrow graphene nanoribbons as well as edge structures with dangling bonds are considered with the help of photonic lattices and/or Bose-Einstein condensates trapped in deep optical lattices. We observe an irrational fractionalization of the excitations when moving under the action of an external field. This effect is discussed in terms of the interband dynamics associated with the systems in consideration.