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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, unknown geometry of the formed edges hinders the further investigation. Here we show that closed bigraphene edge can be represented as connection of generally misoriented graphene domains with topological defects and further described by grain boundary theory. 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.