In order to examine the excitation of intrinsic localized modes (ILMs) in a three-dimensional material, we conducted molecular dynamics numerical simulations on (12, 0), (10, 0), and (8, 0) zigzag carbon nanotubes (CNTs) and (7, 7), (6, 6), and (5, 5) armchair CNTs based on the Brenner potential. While energy localization is observed in several regions in the zigzag CNTs, it is not seen in the armchair CNTs. In the former, fairly constant modes, where two neighboring atoms vibrate in the opposite direction along the axial direction, are found in the energy-localized region, and their frequencies exceed the upper bound of the phonon band. In the armchair CNTs, atomic vibrations in the circumferential direction within high-energy regions cannot last a long time. These results indicate that the ILM is excited in the three zigzag CNTs but not in the three armchair ones. This is because the bond along the tube-axial direction has stronger nonlinearity under vibrations than that in the circumferential one, and the bond direction depends on the structure of the CNT.
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