Role of the localized states in field emission of carbon nanotubes

We have performed $\mathrm{ab}$ $\mathrm{initio}$ pseudopotential electronic structure calculations for various edge geometries of the $\mathrm{}(n,n)\mathrm{}$ single-wall nanotube with or without applied fields. Among the systems studied, the one with a zigzag edge exposed by a slant cut is found to be the most favorable for emission due to the existence of unpaired dangling bond states around the Fermi level. The next most favorable geometry is the capped nanotube where $\pi$-bonding states localized at the cap and pointing in the tube axis direction occur at the Fermi level. A scaling rule for the induced field linear in the aspect ratio of the tube is also obtained.