# Geometrical optics limit of phonon transport in a channel of disclinations

## TL;DR

This paper models phonon transport in a material with dislocation defects using differential geometry, revealing how topological defects influence phonon paths and energy transport, with implications for designing materials with tailored thermal properties.

## Contribution

It introduces a geometric approach to analyze phonon transport in defect-laden materials, highlighting the impact of topological defects on phonon guiding and energy flow.

## Key findings

- Dislocation defects create an anisotropic refraction landscape for phonons.
- Defects can focus or defocus phonon paths depending on incident angles.
- Energy transport can be enhanced or depleted by defect configurations.

## 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.