Acoustical Phonons Transport through a Stepped Quantum Wire

Mohammed Saïd Rabia

doi:doi:10.11648/j.ajpa.20140206.14

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Acoustical Phonons Transport through a Stepped Quantum Wire

Mohammed Saïd Rabia

Published in American Journal of Physics and Applications (Volume 2, Issue 6)

Received: 29 November 2014 Accepted: 4 December 2014 Published: 16 December 2014

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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), 2024. Published by Science Publishing Group

Keywords

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

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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

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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

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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

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@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}
}

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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  -

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Mohammed Saïd Rabia

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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

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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

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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

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@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  -

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