Half-metallic quantum valley Hall effect in biased zigzag-edge bilayer graphene nanoribbons

We have investigated electron-electron interaction effects on gapless edge states in the antiferromagnetic phase of zigzag-edge bilayer graphene nanoribbons under a voltage bias between the layers by using a tight-binding model with on-site Coulomb interactions. We found that a zigzag-edge bilayer graphene nanoribbon can have gapless edge states corresponding to peculiar topologically nontrivial insulator phases, such as a half-metallic quantum valley Hall phase. The half-metallicity was found to be due to the on-site Coulomb interactions through which excess charges produced by the voltage bias between the layers give rise to the potential difference between the opposite edges. A topological phase diagram in the antiferromagnetic phase of a zigzag-edge bilayer graphene nanoribbon was determined as a function of the bias voltage and the ribbon width. The quantum confinement effect, which was found to be graphene-like for narrow ribbons and to be bilayer graphene-like for wide ribbons, was also confirmed to play an important role in determining the topologically nontrivial insulator phases.