Elastic Theory of Defects in Toroidal Crystals

TL;DR

This paper develops an elastic theory framework to analyze the defect structures in toroidal crystals, examining how curvature and material properties influence their ground states and structural features.

Contribution

It introduces a comprehensive elastic theory for defects on curved surfaces, specifically applied to toroidal crystals, and compares theoretical predictions with numerical simulations.

Findings

Curvature influences defect arrangements significantly.

As the aspect ratio approaches one, amorphization occurs.

The elastic theory aligns well with numerical results.

Abstract

We report a comprehensive analysis of the ground state properties of axisymmetric toroidal crystals based on the elastic theory of defects on curved substrates. The ground state is analyzed as a function of the aspect ratio of the torus, which provides a non-local measure of the underlying Gaussian curvature, and the ratio of the defect core-energy to the Young modulus. Several structural features are discussed,including a spectacular example of curvature-driven amorphization in the limit of the aspect ratio approaching one. The outcome of the elastic theory is then compared with the results of a numerical study of a system of point-like particles constrained on the surface of a torus and interacting via a short range potential.