Finite-size effects on electronic structure and local properties in passivated AA-stacked bilayer armchair-edge graphene nanoribbons.

Based on the tight-binding model and dual-probe scanning tunneling microscopy technology, we theoretically investigate the electronic structure and local property in the passivated AA-stacked bilayer armchair-edge graphene nanoribbons (AABLAGNRs). We show that they are highly sensitive to the size of the ribbons, which is evidently different from the single-layer armchair-edge graphene nanoribbons. The '3p' rule only applies to the narrow AABLGNRs. Namely, in the passivated 3p- and (3p  +  1)-AABLGNRs, the narrow ribbons are semiconducting while the medium and wide ribbons are metallic. Although the passivated (3p  +  2)-AABLGNRs are metallic, the '3j' rule only applies to the narrow and medium ribbons. Namely, electrons are in the semiconducting states at sites of line 3j while they are in the metallic states at other sites. This induces a series of parallel and discrete metallic channels, consisting of lines 3j  -  1 and 3j  -  2, for the low-energy electronic transports. In the passivated wide (3p  +  2)-AABLGNRs, all electrons are in the metallic states. Additionally, the '3p' and '3j' rules are controllable to disappear and reappear by applying an external perpendicular electric field. Resultantly, an electric filed-driven current switch can be realized in the passivated narrow and medium (3p  +  2)-AABLGNRs.