Focused electron beam from open-tip single-wall carbon nanotubes

Open-tip single-wall carbon nanotubes can produce focused electron spot in the field emission. We calculate direct evolution of the nanotube wavefunction under applied electric field by solving the time dependent Shr\"{o}dinger equation in the first principles scheme. (5,5), (10,10), and (12,12) carbon nanotubes are investigated and We obtain the focused spot size of a few angstroms. The spot size of electron beam from the (10,10) tube is smaller than that of the (5,5) or (12,12) tube. We also find that s-like state near the Fermi level contributes most to the field emission current.