Coulomb edge effects in graphene nanoribbons

Coulomb effects in graphene nanoribbons with arbitrary edges are investigated with the use of a mean-field Hubbard model. It was recently shown that chiral ribbons with minimal edges, characterized by the translation vector (n,m), have a similar structure of bands localized around the Fermi energy as pure zigzag ribbons (n−m,0). Here we show that these flat bands in both ribbon cases differ in detail due to the perturbation induced by armchair edge nodes. For chiral ribbons the edge bands split at the zone boundary, where the corresponding bands of (n−m,0) zigzag ribbons are degenerate. Coulomb interactions enhance strongly this splitting and at the same time they bring spin into play. We modify each edge keeping global sublattice balance to find that spin degeneracy can be partially lifted. The breaking of spin-degeneracy depends on the asymmetry between the edges and in some cases leads to spin-polarized currents.