On the Edge of Bilayered Graphene: Unexpected Atomic Geometry and Specific Electronic Properties

The tendency of bilayered graphene edges to connect with each other allows to create hollow sp²-hybridized material with specific electronic properties. However, the unknown geometry of the formed edges hinders further investigation. Here we show that a closed bigraphene edge can be represented as a connection of generally misoriented graphene domains with topological defects and can be further described by grain boundary theory. The energy dependence of closed edges of commensurate twisted bilayered graphene is derived for any twist angle and edge orientation. Our findings allow to predict what particular edge types appear in the bilayered graphene holes and explain the structure of the connected bilayered graphene edges, which are often observed in the experiment.