Dynamics and Instabilities of Defects in Two-Dimensional Crystals on Curved Backgrounds

TL;DR

This paper analyzes how defects behave in two-dimensional crystals on curved surfaces, revealing their stability, elastic properties, and differences from flat crystals through continuum elasticity theory.

Contribution

It provides an analytical framework for defect dynamics in curved 2D crystals, including elastic constants and stability analysis of vacancies and interstitials.

Findings

Dislocations' elastic spring constants match experimental data.

Vacancies and interstitials are unstable in curved geometries.

Curved backgrounds influence defect stability and behavior.

Abstract

Point defects are ubiquitous in two dimensional crystals and play a fundamental role in determining their mechanical and thermodynamical properties. When crystals are formed on a curved background, finite length grain boundaries (scars) are generally needed to stabilize the crystal. We provide a continuum elasticity analysis of defect dynamics in curved crystals. By exploiting the fact that any point defect can be obtained as an appropriate combination of disclinations, we provide an analytical determination of the elastic spring constants of dislocations within scars and compare them with existing experimental measurements from optical microscopy. We further show that vacancies and interstitials, which are stable defects in flat crystals, are generally unstable in curved geometries. This observation explains why vacancies or interstitials are never found in equilibrium spherical crystals. We finish with some further implications for experiments and future theoretical work.