Phonon dispersion of carbon nanotubes |
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| Institution: | 1. Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany;2. Faculty of Physics, University of Beograd, P.O. Box 368, Beograd 11001, Yugoslavia;1. Zhytomyr State Technological University, 103 Chernyakhovsky Street, Zhytomyr 10005, Ukraine;2. Institute of Physics of Semiconductors, National Academy of Science of Ukraine, Nauky Avenue 41, Kyiv 03028, Ukraine;1. School of Science, Hunan Institute of Technology, Hengyang, 421002, People''s Republic of China;2. School of Physics and Electronics, Hunan Normal University, Changsha, 410081, People''s Republic of China;1. Photonics Research Centre, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia;2. Department of Electrical Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia;3. Faculty of Applied Sciences, MARA University of Technology, 40450, Shah Alam, Selangor, Malaysia;4. Fuel Cell Centre, Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia;5. Faculty of Applied Science, MARA University of Technology, Jengka Campus, 26400, Bandar Tun Razak, Pahang, Malaysia;6. Low Dimensional Material Research Center, Department of Physics, University Malaya, 50603, Kuala Lumpur, Malaysia;7. Department of Electronics and Communication, Marwadi University, Rajkot, 360003, India;8. School of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications Xianlin Campus, Nanjing, Jiangsu Province, 210023, China |
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| Abstract: | We present the phonon dispersion relations of single-wall carbon nanotubes calculated within a force-constants approach. By using the full symmetry group of the tubes, we are able to calculate the dispersion relations for any chirality starting from one single carbon atom. We find an overbending in the highest optical branch between 6 and 12 cm−1 independent of the tube diameter. The order of the high-energy modes at the Γ-point differs from the results derived from simple zone folding. The splitting between the two Raman active optical modes with A1 symmetry at the Γ-point of chiral tubes is ≈4 cm−1 for typical diameters; it increases with decreasing tube diameter. |
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