Vacuum potential barrier and field emission characteristic of graphene edges

We investigated the vacuum potential barriers of various graphene edges. It is found that the exchange-correlation potential correction is significant to the edge structures with electronegativity higher than carbon. The correction leads to the local work function decreased by more than 1 eV for the O terminated edge. An extraordinary low vacuum barrier height of 2.0 eV has been found on the zigzag-edge of graphene terminated with the secondary amine via the ab initio calculation. This edge structure has a flat band of edge states attached to the gamma point where the transversal kinetic energy is vanishing. We show that the field electron emission is dominated by the flat band. The edge states pin the Fermi level to a constant, leading to an extremely narrow emission energy width. The graphene with such edge is a promising line field electron emitter that can produce highly coherent emission current.