Phonon Energy Spectra and Stationary Elastic Waves in Single-Walled Carbon Nanotubes and Graphite Bulk Crystals

  • V. V. Strelchuk V.E. Lashkaryov Institute of Semiconductor Physics, Nat. Acad. of Sci. of Ukraine
  • A. S. Nikolenko V.E. Lashkaryov Institute of Semiconductor Physics, Nat. Acad. of Sci. of Ukraine
  • Yu. Yu. Stubrov V.E. Lashkaryov Institute of Semiconductor Physics, Nat. Acad. of Sci. of Ukraine
  • A. E. Belyaev V.E. Lashkaryov Institute of Semiconductor Physics, Nat. Acad. of Sci. of Ukraine
  • V. O. Gubanov Faculty of Physics, Taras Shevchenko National University of Kyiv
  • M. M. Biliy Faculty of Physics, Taras Shevchenko National University of Kyiv
  • L. A. Bulavin Faculty of Physics, Taras Shevchenko National University of Kyiv
Keywords: micro-Raman spectroscopy, arc-discharge method, stationary elastic waves, double Davydov splitting, macromolecular class

Abstract

Micro-Raman spectra of single-walled carbon nanotubes, graphite bulk crystals, one-layer and two-layer graphenes are investigated in detail. The structure of Davydov multiplets in the energy spectra of electronic states of one-layer and two-layer graphenes and Bernal graphite bulk crystals is established. The energy spectra of vibrational and electronic states of nanotubes and graphite bulk crystals are shown to be described by the dispersion curves, which pairwise joint at points A of the Brillouin zones of these structures. The forms of stationary elastic waves in single-walled carbon nanotubes at Γ and A points of their Brillouin zones and in one-layer and two-layer graphenes and bulk graphite at Γ, K, and M points of their Brillouin zones are analytically calculated.

References

K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, and A.A. Firsov, Science 306, 666 (2004).

http://dx.doi.org/10.1126/science.1102896

L.M. Malard, M.A. Pimenta, G. Dresselhaus, and M.S. Dresselhaus, Phys. Rep. 473, 51 (2009).

http://dx.doi.org/10.1016/j.physrep.2009.02.003

B. Partoens and F.M. Peeters, Phys. Rev. B 74, 075404 (2006).

http://dx.doi.org/10.1103/PhysRevB.74.075404

A.C. Ferrari and J. Robertson, Phys. Rev. B 61, 14095 (2000).

http://dx.doi.org/10.1103/PhysRevB.61.14095

M.A. Pimenta, G. Dresselhaus, M.S. Dresselhaus, L.G. Cancado, A. Jorio, and R. Saito Phys. Chem. Chem. Phys. 9, 1276 (2007).

http://dx.doi.org/10.1039/B613962K

M.S. Dresselhaus, G. Dresselhaus, A. Jorio, A.G. Souza Filho, M.A. Pimenta, and R. Saito, Acc. Chem. Res. 35, 1070 (2002).

http://dx.doi.org/10.1021/ar0101537

P. Blakea, E.W. Hill, A.H. Castro Neto, K.S. Novoselov, D. Jiang, R. Yang, T.J. Booth, and A.K. Geim, Appl. Phys. Lett. 91, 063124 (2007).

http://dx.doi.org/10.1063/1.2768624

A.C. Ferrari, J.C. Mayer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K.S. Novoselov, S. Roth, and A.K. Geim, Appl. Phys. Lett. 97, 187401 (2006).

http://dx.doi.org/10.1103/PhysRevLett.97.187401

T. Michel, M. Paillet, A. Zahab, D. Nakabayashi, V. Jourdain, R. Parret, and J.-L. Sauvajol, Adv. Nat. Sci.: Nanosci. Nanotechnol. 1, 045007 (2010).

L.M. Malard, M.H.D. Guimar˜aes, D.L. Mafra, M.S.C. Mazzoni, and A. Jorio, Phys. Rev. B 79, 125426 (2009).

http://dx.doi.org/10.1103/PhysRevB.79.125426

M.C. Schabel, and J.L. Martins, Phys. Rev. B 46, 7185 (1992).

http://dx.doi.org/10.1103/PhysRevB.46.7185

G.L. Bir and G.E. Pikus Symmetry and Strain-Induced Effects in Semiconductors (Wiley, New York, 1974).

L.G. Cancado, A. reina, J. Kong, and M.S. Dresselhaus, Phys. Rev. Lett. 77, 245408 (2008).

M. Damnjanovi’c, T. Vukovi’c, I. Miloˇsevi’c, and B. Nikoli’c, Acta Crystallogr. A 57, 304 (2001).

http://dx.doi.org/10.1107/S0108767300018857

O.E. Alon, Phys. Rev. B 63, 201403 (2001).

http://dx.doi.org/10.1103/PhysRevB.63.201403

E.A. Wood, Bell System Techn. J. 43, 541 (1964).

http://dx.doi.org/10.1002/j.1538-7305.1964.tb04077.x

T. Hahn, International Tables for Crystallography (Reidel, Dordrecht, 1987), Vol. A, Space-group symmetry.

V.O. Gubanov, L.O. Komarova, M.M. Biliy, and S.V. Kovrygin, Nanosyst., Nanomater., Nanotechn. 5, 307 (2007).

Published
2019-01-15
How to Cite
Strelchuk, V., Nikolenko, A., Stubrov, Y., Belyaev, A., Gubanov, V., Biliy, M., & Bulavin, L. (2019). Phonon Energy Spectra and Stationary Elastic Waves in Single-Walled Carbon Nanotubes and Graphite Bulk Crystals. Ukrainian Journal of Physics, 60(9), 925. https://doi.org/10.15407/ujpe60.09.0925
Section
Solid matter

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