Excitation loss spectra of finite carbon nanotubes

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The sp 3 and 2 p z tight-binding models are, respectively, used to calculate electronic states. The static dielectric function is evaluated from the gradient approximation. Electronic states have differences within the sp 3 and the 2 p z tight-binding models. The former (latter) exhibits asymmetric (symmetric) energy dispersions about Fermi level with an angular momentum. The imaginary and the real parts of the dielectric function, respectively, exhibit the special peaks and dips. The prominent π and π + σ plasmon peaks exist at ω < 4 γ 0 and ω > 4 γ 0 ( γ 0 is the nearest-neighbor overlap integral), respectively. Prominent peak energies are almost independent of length for sufficiently long carbon nanotubes (CNTs). These results illustrate the quasi-zero-dimensional character. Moreover, for different nanotube lengths, they reveal a common feature—prominent plasmon structures at 2 γ 0 ≈ 6 eV and 6.5 γ 0 ≈ 18 eV . This result follows the fact that all CNTs are derived their states from those of a graphene sheet. On the other hand, for ω < 2 γ 0 the prominent peaks of the finite CNTs are associated with the standing waves. The predicted loss spectra could be verified by electron energy loss spectra (EELS).