  An extraordinary low vacuum barrier height of 2.30 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.
