Eur. Phys. J. B (2017) 90: 95
https://doi.org/10.1140/epjb/e2017-70384-5

Regular Article

Geometrical optics limit of phonon transport in a channel of disclinations

¹ Statistical Physics Group, IJL, UMR Université de Lorraine – CNRS 7198 BP 70239, 54506 Vandœuvre les Nancy, France
² Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900 João Pessoa, PB, Brazil
³ Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900 Recife, PE, Brazil
⁴ Departamento de Matemática Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil
⁵ Escola Politécnica de Pernambuco, Universidade de Pernambuco, Rua Benfica, 455, Madalena, 50720-001 Recife, PE, Brazil

^a e-mail: fernando.jsmoraes@ufrpe.br

Received: 17 June 2016
Received in final form: 21 February 2017
Published online: 17 May 2017

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.