| Summary: | Conventional three-dimensional crystal lattices are terminated by surfaces, which can demonstrate complex rebonding and rehybridisation, localised strain and dislocation formation. Two-dimensional crystal lattices, of which graphene is the archetype, are terminated by lines. The additional available dimension at such interfaces opens up a range of new topological interface possibilities. We show that graphene sheet edges can adopt a range of topological distortions depending on their nature. Rehybridisation, local bond reordering, chemical functionalisation with bulky, charged, or multi-functional groups can lead to edge buckling to relieve strain, folding, rolling and even tube formation. We discuss the topological possibilities at a two-dimensional graphene edge, and under what circumstances we expect different edge topologies to occur. Density functional calculations are used to explore in more depth different graphene edge types.
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