Graphene  Vol.3 No.2 , April 2014
Phonon Dispersion for Armchair and Zigzag Carbon Nanotubes
ABSTRACT

In this paper we present calculations of phonon dispersion of different types of single walled carbon nanotubes (SWCNT). In these calculations, the starting point has been the phonon dispersion of graphene. Zone folding scheme is then applied to obtain the phonon dispersion of CNT from that of graphene. Since the radial breathing modes in the phonon dispersion are not obtained by the zone-folding method, certain modifications are made in the lower branches to obtain these modes. These modifications produce results similar to those obtained by more sophisticated ab-initio methods.


Cite this paper
Sahoo, R. and Mishra, R. (2014) Phonon Dispersion for Armchair and Zigzag Carbon Nanotubes. Graphene, 3, 14-19. doi: 10.4236/graphene.2014.32003.
References
[1]   Iijima, S. (1991) Helical Microtubules of Graphitic Carbon. Nature, 354, 56-58.
http://dx.doi.org/10.1038/354056a0

[2]   Dubay, O. and Kresse, G. (2003) Accurate Density Functional Calculations for the Phonon Dispersion Relations of Graphite Layer and Carbon Nanotubes. Physical Review B, 67, 035401. http://dx.doi.org/10.1103/PhysRevB.67.035401

[3]   Maultzsch, J., Reich, S., Thomsen, C., Dobardzic, E., Milosevic, I. and Damnjanovic, M. (2002) Phonon Dispersion of Carbon Nanotubes. Solid State Communication, 121, 471-474.
http://dx.doi.org/10.1016/S0038-1098(02)00025-X

[4]   Saito, R., Dresselhaus, M.S. and Dresselhaus, G. (1998) Physical Properties of Carbon Nanotubes. Imperial College Press, London.

[5]   Portal, D.S., Artacho, E., Soler, J.M., Rubio, A. and Ordejon, P. (1999) Ab Initio Structural, Elastic, and Vibrational Properties of Carbon Nanotubes. Physical Review B, 59, 12678-12688. http://dx.doi.org/10.1103/PhysRevB.59.12678

[6]   Kurti, J., Kresse, G. and Kuzmany, H. (1998) First-Principles Calculations of the Radial Breathing Mode of Single-Wall Carbon Nanotubes. Physical Review B, 58, R8869-R8872.
http://dx.doi.org/10.1103/PhysRevB.58.R8869

[7]   Sahoo, R. and Mishra, R.R. (2012) Phonon Dispersion of Graphene Revisited. Journal of Experimental and Theoretical Physics, 114, 805-809. http://dx.doi.org/10.1134/S1063776112040152

[8]   Zimmermann, J., Pavone, P. and Cuniberti, G. (2008) Vibrational Modes and Low-Temperature Thermal Properties of Graphene and Carbon Nanotubes: Minimal Force-Constant Model. Physical Review B, 78, 045410.

[9]   Lazzeri, M., Piscanec, S., Mauri, F., Ferrari, A.C. and Robertson, J. (2005) Electron Transport and Hot Phonons in Carbon Nanotubes. Physical Review Letters, 95, 236802.
http://dx.doi.org/10.1103/PhysRevLett.95.236802

[10]   Kauser, M.Z. and Ruden, P.P. (2007) Effects of Chirality and Diameter on the Transport Properties of Semiconducting Carbon Nanotubes. Journal of Applied Physics, 102, 033712.
http://dx.doi.org/10.1063/1.2767224

 
 
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