  Field emission (FE) and the electronic-states origin of graphitic
nanostructures were investigated by first-principles calculations based on
time-dependent density-functional theory. We find that the FE current from
graphitic ribbons changes remarkably depending on the hydrogen termination and
the direction of the applied electric field. Also, the FE current from graphene
sheets shows a dramatic increase around vacancy defects. We verified, through
the analysis of local electronic structures and energy distributions of emitted
electrons, that the dangling-bond (or $\sigma$) character is responsible for
these results and governs the nature of the FE of graphitic nanostructures.
