Novel electronic states in graphene ribbons—competing spin and charge orders

In a nanographene ring with zigzag edges, the spin-polarized state and the charge-polarized state are stabilized by the on-site and the nearest-neighbor Coulomb repulsions, U and V, respectively, within the extended Hubbard model under the mean-field approximation. In a Möbius strip of the nanographene with a zigzag edge, U stabilizes two magnetic states, the domain wall state and the helical state. Both states have ferrimagnetic spins localized along the zigzag edge while the former connects the opposite ferrimagnetic orders resulting in a magnetic frustration forced by the topology and the latter rotates the ferrimagnetic spins uniformly to circumvent the frustration. The helical state is lower in energy than the domain wall state. On the other hand, V stabilizes another domain wall state connecting the opposite charge orders.