Interactions and Magnetism in Graphene Boundary States

We analyze interaction effects on boundary states of single layer graphene. Near a half filled band, both short- and long-ranged interactions lead to a fully spin-polarized configuration. In addition, the band of boundary states acquires a finite dispersion as a function of the momentum parallel to the edge, induced by the interactions. Away from half filling the wave function develops charge correlations similar to those in a Wigner crystal, and the spin strongly alternates with the occupation of the boundary states. For certain fillings the ground state has a finite linear momentum, leading to the formation of persistent currents.