Zigzag graphene nanoribbon edge reconstruction with stone-wales defects

tight-binding method, with parameters determined by ab-initio calculations of very narrow ribbons. We explore the characteristics of the electronic band structure with a focus on the nature of edge states. Edge reconstruction allows the appearance of a new type of egde states. They are dispersive, with non-zero amplitudes in both sub-lattices; furthermore, the amplitudes have two components that decrease with dierent decay lengths with the distance from the edge; at the Dirac points one of these lengths diverges, whereas the other remains nite, of the order of the lattice parameter. We trace this curious eect to the doubling of the unit cell along the edge, brought about by the edge reconstruction. In the presence of a magnetic eld, the zero-energy Landau level is no longer degenerate with edge states as in the case of pristine zigzag ribbon.