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Derivation of the Carbon Nanotube Susceptibility Tensor Using Lattice Dynamics Formalism
By
Progress In Electromagnetics Research B, Vol. 9, 1-26, 2008
Abstract
We develop in this paper a theoretical approach to describe the electrodynamics of carbon nanotubes (CNTs). A lattice dynamics formalism is employed to model the mechanical response of matter to the radiation field. We start first by deriving the normal modes of the free lattice. Then, a simple and general microscopic model for light-matter interaction is proposed and the resulting mechanical equation of motion is derived using a suitable Lagrangian formalism. The symmetry group of the CNT is employed to explicitly probe the nonlocal structure of the fields and to carefully insure that higher-order Floquet modes are included in the derivation. The normal modes are then employed to perform an eigenmode expansion for the solution of the mechanical equation of motion, leading to the susceptibility tensor of the CNT medium. The final expression of this tensor describes the electrodynamics in the CNT viewed as a low-dimensional surface and is shown to be reduced effectively to a one-dimensional response function.
Citation
Said Mikki, and Ahmed Kishk, "Derivation of the Carbon Nanotube Susceptibility Tensor Using Lattice Dynamics Formalism," Progress In Electromagnetics Research B, Vol. 9, 1-26, 2008.
doi:10.2528/PIERB08082301
References

1. Poole, C. P. and F. J. Owens, Introduction to Nanotechnology, Wiley-Interscience, 2003.

2. Talele, K. and D. S. Patil, "Analysis of wave function, energy and transmission coefficients in GaN/ALGaN superlattice nanostructures," Progress In Electromagnetics Research, Vol. 81, 237-252, 2008.
doi:10.2528/PIER08011102

3. Kong, F. M., K. Li, B.-I. Wu, H. Huang, H. S. Chen, and J. A. Kong, "Propagation properties of the SPP modes in nanoscale narrow metallic gap, channel, and hole geometries," Progress In Electromagnetics Research, Vol. 76, 449-466, 2007.
doi:10.2528/PIER07070203

4. Iijima, S., "Helical microtabules of graphitic carbon," Nature, Vol. 354, 56-58, 1991.
doi:10.1038/354056a0

5. Anantram, M. and F. Leonard, "Physics of carbon nanotube electronic devices," Reports on Progress in Physics, Vol. 69, 507-561, February 2006.
doi:10.1088/0034-4885/69/3/R01

6. Smalley, R. E., M. S. Dresselhaus, G. Dresselhaus, and P. Avouris, Carbon Nanotubes: Synthesis, Structure, Properties and Applications, Springer, 2001.

7. Wooten, F., Optical Properties of Solids, Academic Press, 1972.

8. Jackson, J. D., Classical Electrodynamics, 3rd Edition, John Wiley & Sons, 1999.

9. Toyozawa, Y., "Optical Processes in Solids," Cambridge University Press, 2003.

10. Brillouin, L., Wave Propagation in Periodic Structures, 1956.

11. Born, M. and K. Haung, Dynamical Theory of Crystal Lattices, 1st edition, Oxford University Press, London, 1954.

12. Mikki, S. M. and A. A. Kishk, "A symmetry-based formalism for the electrodynamics of nanotubes," submitted to PIERS.

13. Grosso, G. and G. Parravicini, Solid-State Physics, Academic Press, 2000.

14. White, C. T., D. H. Robertson, and J. W. Mintmire, "Helical and rotational symmetries of nanoscale graphitic tubules," Phys. Rev. B, Vol. 47, No. 9, 5485-5488, March 1993.
doi:10.1103/PhysRevB.47.5485

15. Damnjanovic, M., I. Milosevic, T. Vukovic, and R. Sredanovic, "Full-symmetry, optical activity, and potentials of single-wall and multi-wall nanotubes," Phys. Rev. B, Vol. 60, No. 4, 2728-2739, July 1999.
doi:10.1103/PhysRevB.60.2728

16. Damnjanovic, M., I. Milosevic, T. Vukovic, and R. Sredanovic, "Symmetry and lattices of single-wall nanotubes," J. Phys. A, Vol. 32, 4097-4104, 1999.
doi:10.1088/0305-4470/32/22/310

17. Popov, V. N. and V. E. van Doren, "Elastic properties of singlewalled carbon nanotubes," Phys. Rev. B, Vol. 61, No. 4, 3078-3084, January 2000.
doi:10.1103/PhysRevB.61.3078

18. Cohen-Tannoudjii, C., J. Dupont-Roc, and G. Grynberg, Photons and Atoms: Introduction to Quantum Electrodynamics, Wiley, 1989.

19. Pekar, S. I., "Theory of electromagnetic waves in a crystal in which excitons are produced," Sov. Phys. JETP, Vol. 6, 785, 1957.

20. Agranovich, V. M. and V. L Ginsburg, Crystal Optics and Spatial Dispersion, and Excitons, Springer, 1984.

21. Halevi, P. (ed.), Spatial Dispersion in Solids and Plasmas, Springer, 1992.

22. Cho, K., "Nonlocal theory of radiation-matter interaction: Boundary-condition-less treatment of Maxwell equations," Prog. Theor. Phys. Suppl., Vol. 106, 225-233, 1991.
doi:10.1143/PTPS.106.225