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The -electron excitations are studied for a multiwall carbon nanotube, a single-wall carbon nanotube bundle with finite nanotubes, and graphite layers. The loss spectra of the nanotube systems exhibit several plasmon peaks. The most prominent one is the plasmon, and the others are the interband plasmons. The latter are absent in graphite layers. The plasmon depends on the number of carbon nanotubes or graphite layers ͑N͒, the transferred momentum ͑q͒, and the transferred angular momentum ͑L͒. The intertube or interlayer Coulomb interactions clearly enhance -plasmon frequency and oscillator strength as N increases. A multiwall carbon nanotube can exhibit L-decoupled plasmons. For the Lϭ0 plasmon, the multiwall nanotube behaves like graphite layers, but not like a single-wall carbon nanotube bundle. The radius dependence is negligible for a multiwall nanotube, while it is strong for a single-wall nanotube bundle. Furthermore, the former exhibits stronger collective excitations, higher -plasmon frequency, and relatively rapid increase of plasmon frequency with q. The calculated results are compared with experimental measurements.

Magnetoelectronic and optical properties of carbon nanotubes are, respectively, studied within the sp 3 tight-binding model and the gradient approximation. They strongly depend on the magnitude and the direction of the magnetic field, the nanotube geometry ͑radius and chiral angle͒, and the Zeeman splitting. The magnetic field would lead to the change of energy gap, the destruction of state degeneracy, and the coupling of different angular momenta. Hence there are magnetic-field-dependent absorption frequencies and more absorption peaks. The types of carbon nanotubes predominate in the band structure and thus the range of absorption frequencies and the number of absorption peaks. The Zeeman splitting makes the semiconductor-metal transition occur at lower magnetic flux. It metalizes armchair carbon nanotubes in the presence of the perpendicular magnetic field. However, it does not affect the optical excitations except for metallic carbon nanotubes.

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Graphene ripples possess peculiar essential properties owing to the strong chemical bonds, as an investigation using first principle calculations clearly revealed. Various charge distributions, bond lengths, energy bands, and densities of states strongly depend on the corrugation structures, ripple curvatures and periods. Armchair ripples belonging to a zero-gap semiconductor display split middle-energy states, while the zigzag ripples exhibit highly anisotropic energy bands, semi-metallic behavior implicated by the destruction of the Dirac cone, and the newly created critical points.Their density of states exhibit many low-lying prominent peaks and can explain the experimental measurements. There exist certain important similarities and differences between graphene ripples and carbon nanotubes.

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