Geometrical optics limit of phonon transport in a channel of disclinations

  • Sébastien Fumeron
  • Bertrand Berche
  • Fernando Moraes
  • Fernando A. N. Santos
  • Erms Pereira
Regular Article
  • 26 Downloads

Abstract

The presence of topological defects in a material can modify its electrical, acoustic or thermal properties. However, when a group of defects is present, the calculations can become quite cumbersome due to the differential equations that can emerge from the modeling. In this work, we express phonons as geodesics of a 2 + 1 spacetime in the presence of a channel of dislocation dipoles in a crystalline environment described analytically in the continuum limit with differential geometry methods. We show that such a simple model of 1D array of topological defects is able to guide phonon waves. The presence of defects indeed distorts the effective metric of the material, leading to an anisotropic landscape of refraction index which curves the path followed by phonons, with focusing/defocusing properties depending on the angle of the incident wave. As a consequence, using Boltzmann transfer equation, we show that the defects may induce an enhancement or a depletion of the elastic energy transport. We comment on the possibility of designing artificial materials through the presence of topological defects.

Keywords

Solid State and Materials 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Sébastien Fumeron
    • 1
  • Bertrand Berche
    • 1
  • Fernando Moraes
    • 2
    • 3
  • Fernando A. N. Santos
    • 4
  • Erms Pereira
    • 5
  1. 1.Statistical Physics Group, IJL, UMR Université de Lorraine – CNRS 7198 BP 70239Vandœuvre les NancyFrance
  2. 2.Departamento de Física, CCEN, Universidade Federal da ParaíbaJoão PessoaBrazil
  3. 3.Departamento de Física, Universidade Federal Rural de PernambucoRecifeBrazil
  4. 4.Departamento de Matemática Universidade Federal de PernambucoRecifeBrazil
  5. 5.Escola Politécnica de Pernambuco, Universidade de PernambucoRecifeBrazil

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