| Peer-Reviewed

Acoustical Phonons Transport through a Stepped Quantum Wire

Received: 29 November 2014     Accepted: 4 December 2014     Published: 16 December 2014
Views:       Downloads:
Abstract

This work presents a theoretical approach for the study of phonon dynamics and scattering properties of an infinite linear atomic chain perturbed by a mono atomic step. The coherent transmittance scattering cross-sections for incident phonons on the atomic waveguide structure are calculated using the Landauer-Buttiker electron scattering description and the matching method formalism with the nearest and next nearest neighbour interactions. Numerical results for different configurations yield an understanding of the chain dynamical properties and the effects on phonon transmittance due to incoming phonons. The reflectance and transmittance coefficients show spectral characteristic features depending on the cut-off frequencies for the propagating phonons. They illustrate the occurrence of Fano resonances in the scattering spectra that result from degeneracy of step localized modes and propagating continuum modes due to the breakdown of the translation symmetry in the propagating direction. Furthermore, the interferences between diffused and reflected waves in the step regions generate Fabry-Pérot oscillations whose number is determined by the distance between steps and the number of terraces.

Published in American Journal of Physics and Applications (Volume 2, Issue 6)
DOI 10.11648/j.ajpa.20140206.14
Page(s) 135-144
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Reticular Dynamics, Disordered Mesoscopic Systems, Crystallographic Waveguides, Matching Procedure, Phonon Scattering

References
[1] B. Kramer, Quantum Coherence in Mesoscopic Systems, (plenum, New York, 1991).
[2] E. Tekman and P. F. Bagwell, Phys. Rev. B48 (1993) 18 299.
[3] Yu A. Kosevich, Prog. Surf. Sci. vol 55 (1997) 1.
[4] R. Landauer, Z. Phys. B 68 (1987) 217; J. Phys. Condens. Matter 1 (1989) 8099.
[5] M. Büttiker, Phys. Rev. Lett. 57 (1986) 1761.
[6] E. S. Syrkin, P.A. Minaev, A. G. Shkorbatov and A. Feher, Microelec. Eng. vol. 81, (2005) 503.
[7] J. Szeftel and A. Khater, J. Phys C 20 (1987) 4725.
[8] A. Fellay, F. Gagel, K. Maschke, A. Virlouvet and A. Khater, Phys.Rev. B 55 (1997) 1707.
[9] M. S. Rabia, J. Mol. Struc-Theochem 777 (2006) 131-138.
[10] A. Khater, N. Auby and D. Kechrakos, J. Phys. Condens. Matter 4 (1992) 3743-3752.
[11] C. Berthold, F. Gagel and K. Maschke, Phys. Rev. B 50 (1994) 18299.
[12] F. Gagel and K. Maschke, Phys. Rev. B 52 (1995) 2013.
[13] H. Ibach and D. L. Mills, Electron Energy Loss Spectroscopy and Surface Vibrations, (New York: Academic, 1982)
[14] P. F. Bagwell, Phys. Rev. B 41 (1990) 10354; J. Phys. Condens. Matter 2 (1993) 6179.
[15] R. E. Allen, G. P. Alldrege and F. W. Wette, Phys. Rev. B 4 (1971) 1648.
[16] P. Knipp, Phys. Rev. B 43 6908 (1991).
[17] G. M. Watson, D. Gibbs and D. M. Zehner, Phys. Rev. Lett. 71 (1954) 3166.
[18] V. Pouthier and C. Girardet, Phys. Rev. B 66 (2002) 115322.
[19] M. S. Rabia, 10ème Congrès Français d’Acoustique, Lyon (2010), France.
[20] M. Born and K. Huang, Dynamical Theory and Crystal Lattices (Oxford University Press, New York, 1954).
[21] G. Lubfried and W. Ludwig, Solid State Physics, vol. 12 edited by F. Seitz and Turnbull (Academic Press Inc., New York, 1961).
[22] L. M. Lifshitz and L. N. Rosenzweig, Ekperim. Theor. Fiz. 18 (1948) 1012.
[23] Maradudin A. A., Montroll E. W., Weiss G. H. and Ipatova, Theory of lattice Dynamic in the Harmonic Approximation, Academic Press New York and London (1971).
[24] M. S. Rabia, H. Aouchiche and O. Lamrous, Eur. Phys. J. – A. P. 23 (2003) 95-102.
[25] M. S. Rabia, J. Phys. Condens. Matter 20 (2008) 465218.
[26] H. Ibach and D. Bruchmann, Phys. Rev. Lett. 41 (1978) 958.
[27] M. Mostoller and U. Landmann, Phys. Rev. B 20 (1979) 1755.
[28] M. Wutting, C. Oshima, T. Aizawa, R. Souda, S. Otami and Y. Ishizawa, Surf. Sci. 193 (1988) 180.
[29] L. Van Hove, Phys. Rev. 89 (1953) 1189.
[30] C. Kittel, Introduction to solid state physics, 8th ed., (Wiley, 2005).
[31] W. Kress, F. W. De Wette (Eds), Surface Phonons, (Springer-Verlag, Berlin, 1991).
[32] M. S. Rabia, Physica E 42 (2010) 307-1318.
Cite This Article
  • APA Style

    Mohammed Saïd Rabia. (2014). Acoustical Phonons Transport through a Stepped Quantum Wire. American Journal of Physics and Applications, 2(6), 135-144. https://doi.org/10.11648/j.ajpa.20140206.14

    Copy | Download

    ACS Style

    Mohammed Saïd Rabia. Acoustical Phonons Transport through a Stepped Quantum Wire. Am. J. Phys. Appl. 2014, 2(6), 135-144. doi: 10.11648/j.ajpa.20140206.14

    Copy | Download

    AMA Style

    Mohammed Saïd Rabia. Acoustical Phonons Transport through a Stepped Quantum Wire. Am J Phys Appl. 2014;2(6):135-144. doi: 10.11648/j.ajpa.20140206.14

    Copy | Download

  • @article{10.11648/j.ajpa.20140206.14,
      author = {Mohammed Saïd Rabia},
      title = {Acoustical Phonons Transport through a Stepped Quantum Wire},
      journal = {American Journal of Physics and Applications},
      volume = {2},
      number = {6},
      pages = {135-144},
      doi = {10.11648/j.ajpa.20140206.14},
      url = {https://doi.org/10.11648/j.ajpa.20140206.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20140206.14},
      abstract = {This work presents a theoretical approach for the study of phonon dynamics and scattering properties of an infinite linear atomic chain perturbed by a mono atomic step. The coherent transmittance scattering cross-sections for incident phonons on the atomic waveguide structure are calculated using the Landauer-Buttiker electron scattering description and the matching method formalism with the nearest and next nearest neighbour interactions. Numerical results for different configurations yield an understanding of the chain dynamical properties and the effects on phonon transmittance due to incoming phonons. The reflectance and transmittance coefficients show spectral characteristic features depending on the cut-off frequencies for the propagating phonons. They illustrate the occurrence of Fano resonances in the scattering spectra that result from degeneracy of step localized modes and propagating continuum modes due to the breakdown of the translation symmetry in the propagating direction. Furthermore, the interferences between diffused and reflected waves in the step regions generate Fabry-Pérot oscillations whose number is determined by the distance between steps and the number of terraces.},
     year = {2014}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Acoustical Phonons Transport through a Stepped Quantum Wire
    AU  - Mohammed Saïd Rabia
    Y1  - 2014/12/16
    PY  - 2014
    N1  - https://doi.org/10.11648/j.ajpa.20140206.14
    DO  - 10.11648/j.ajpa.20140206.14
    T2  - American Journal of Physics and Applications
    JF  - American Journal of Physics and Applications
    JO  - American Journal of Physics and Applications
    SP  - 135
    EP  - 144
    PB  - Science Publishing Group
    SN  - 2330-4308
    UR  - https://doi.org/10.11648/j.ajpa.20140206.14
    AB  - This work presents a theoretical approach for the study of phonon dynamics and scattering properties of an infinite linear atomic chain perturbed by a mono atomic step. The coherent transmittance scattering cross-sections for incident phonons on the atomic waveguide structure are calculated using the Landauer-Buttiker electron scattering description and the matching method formalism with the nearest and next nearest neighbour interactions. Numerical results for different configurations yield an understanding of the chain dynamical properties and the effects on phonon transmittance due to incoming phonons. The reflectance and transmittance coefficients show spectral characteristic features depending on the cut-off frequencies for the propagating phonons. They illustrate the occurrence of Fano resonances in the scattering spectra that result from degeneracy of step localized modes and propagating continuum modes due to the breakdown of the translation symmetry in the propagating direction. Furthermore, the interferences between diffused and reflected waves in the step regions generate Fabry-Pérot oscillations whose number is determined by the distance between steps and the number of terraces.
    VL  - 2
    IS  - 6
    ER  - 

    Copy | Download

Author Information
  • Sections