Edge properties in a flat graphene monolayer

The lattice relaxation and the change of atomic vibrations, as well as the excess energy near both the armchair and zigzag edges of a flat graphene monolayer are calculated using the unsymmetrized self-consistent field theory of strongly anharmonic solids in the lowest order of anharmonicity. A comparison is given of these properties in each of the two types of edge. •An analytical method is developed to study edges in graphene.•The structure, dynamics, and thermodynamics of graphene are investigated.•Anharmonicity effects have significant influence on the properties.