Electron energy loss spectra of finite carbon nanotubes

The s p3 tight-binding model and the gradient approximation are, respectively, used to calculate electronic states and the loss function of finite carbon nanotubes. The study results show that the loss spectra of finite carbon nanotubes are strongly dependent on the nanotube geometric structure (length, radius, and chiral angle) and the magnetic flux. The prominent peaks at ω<4 γ0 (γ0 is the nearest-neighbor overlap integral) mainly result from the π states, while the peaks at ω>4 γ0 result from the π + states. For ω<4 γ0, most loss spectra contain four peaks in the different finite carbon nanotubes (CNTs) systems. The peak energy versus length graph is a monotonous curve for zigzag nanotubes, while the one for armchair nanotubes is oscillatory. Prominent peak energies are almost independent of length for sufficiently long CNTs. These results illustrate the quasi-zero-dimensional character. Moreover, finite armchair CNTs reveal dominating π and π + plasmon peaks at ∼2 γ0 ≈6 eV and ∼6.5 γ0 ≈18 eV, respectively. Yet, for finite zigzag CNTs plasmon peaks exist at ∼2.15 γ0 and ∼6.6 γ0, due to special localized states at the outermost zigzag positions. The predicted loss spectra and the plasmon frequencies could be verified by electron energy loss spectra.