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Journal of Nanomaterials
Volume 2013 (2013), Article ID 525070, 4 pages
Research Article

On the Phononic Bandgap of Carbon Nanotubes

1Institute of Applied Physics and Tsukuba Research Center for Interdisciplinary Materials Science, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba, Ibaraki 305-8573, Japan
2Green Innovation Research Laboratory, NEC Corporation, 34 Miyukigaoka, Tsukuba, Ibaraki 305-8501, Japan

Received 14 April 2013; Accepted 4 June 2013

Academic Editor: Nadya Mason

Copyright © 2013 Kohei Yamamoto et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


On the phononic bandgap of carbon nanotubes (CNTs), we show in what chirality CNTs have phononic bandgaps and its dependence on the diameters of CNTs. We find that, though the rule where CNTs have phononic bandgaps is the same as in the electronic structure case, the diameter dependence is different. The phononic bandgaps of the zigzag-CNTs reveal “three” kinds of diameter dependence due to the anisotropy of graphene phonon band around the K point in k-space. We also show the crossover from one- to two-dimensional characteristics in phononic bandgaps.