Effect of Electron-Electron Interactions on the Topological Properties of Graphene Armchair Nanoribbons

When tensile strain is applied transversely to a finite region of a graphene armchair ribbon topological gap states can appear. The probability density of such a state can be fractionalized into two parts such that one half of the overall probability density is on a zigzag edge consisting of A carbon atoms while the other half is on a zigzag edge consisting of B carbon atoms. Here we investigate how the on-site repulsive electron-electron interaction U affects this charge fractionalization in the smallest width armchair ribbon. When the bonds are cut partially by the tensile strain, the charge fractionalization remains intact. However, when the bonds are cut completely, the edges no longer display charge fractionalization. We find that a spin-up electron resides on one zigzag edge while as pin-down electron resides on the opposite zigzag edge.