Optical excitations of finite carbon nanotubes

Optical excitations of finite carbon nanotubes by the cross polarized light are studied within the gradient approximation. They are dominated by the quantum size effects. The absorption spectra exhibit rich absorption peaks, mainly owing to many zero-dimensional discrete states. They strongly depend on the length, the radius, the chiral angles, and the magnetic flux. The absorption peaks gradually group together as the length increases. The threshold excitation energy (ω_th) decreases in the increasing of radius. The dependence of ω_th on length is monotonous for zigzag nanotubes, while it is oscillatory for armchair nanotubes. The threshold excitation energy is constant for the sufficiently long carbon nanotubes. Chiral carbon nanotubes exhibit very complicated optical spectra, compared with achiral carbon nanotubes. The magnetic flux reduces the threshold excitation energy and increases the number of absorption peaks.