Topological confinement effect of edge potentials in zigzag-edge graphene nanoribbons under a staggered bulk potential

We have investigated topological confinement effects of edge potentials on gapless edge states in zigzag-edge graphene nanoribbons (ZGNRs) under a staggered bulk potential. A variety of gapless edge states were predicted with the concept of topological confinement effect alone, which was confirmed by using tight-binding model calculations. Half-metallicity of ZGNR, which has been semiclassically described, was revealed to fundamentally result from a topological confinement effect. Edge potentials were found to allow an infinitesimal staggered bulk potential to result in gapless edge states, regardless of the ribbon width. A uniform or staggered potential applied to the boundary region narrower than a critical width was found to play a role of the edge potentials, and the critical width was estimated.