Geometrical optics limit of phonon transport in a channel of disclinations

Sébastien Fumeron, Bertrand Berche, Fernando Moraes (), Fernando A. N. Santos and Erms Pereira
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Sébastien Fumeron: Statistical Physics Group, IJL, UMR Université de Lorraine – CNRS 7198 BP 70239
Bertrand Berche: Statistical Physics Group, IJL, UMR Université de Lorraine – CNRS 7198 BP 70239
Fernando Moraes: Departamento de Física, CCEN, Universidade Federal da Paraíba
Fernando A. N. Santos: Departamento de Matemática Universidade Federal de Pernambuco
Erms Pereira: Escola Politécnica de Pernambuco, Universidade de Pernambuco

The European Physical Journal B: Condensed Matter and Complex Systems, 2017, vol. 90, issue 5, 1-8

Abstract: 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 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1140/epjb/e2017-70384-5

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