Edge plasmons in graphene nanostructures

Plasmon modes in graphene are influenced by the unusual dispersion relation of the material. For bulk plasmons this results in a n(1/4) dependence of the plasma frequency on the charge density, as opposed to the n(1/2) dependence in two-dimensional electron gas (2DEG); yet, bulk plasmon dispersion in graphene follows a similar q(1/2) behavior as for other two-dimensional materials. In this work we consider finite graphene nanostructures, semi-infinite sheets, and circular disks and study edge plasmons that are confined to the boundaries of the structures. We find that, for abrupt edges, graphene edge plasmons behave analogously to those in 2DEGs, but, for gradual edge profiles, important distinctions arise. In particular, we show that for a linear edge profile, graphene supports fewer edge modes than a 2DEG at a given q, and the edge monopole plasmon dispersion in graphene follows a q(1/4) law in contrast to the q(0) behavior seen in 2DEGs.