Limits of Lateral Expansion in Two-Dimensional Materials with Line Defects

TL;DR

This paper investigates the intrinsic limits of lateral expansion in 2D materials with line defects, revealing that rippling constrains expansion to below one percent and highlighting implications for strain engineering and pseudomagnetic fields.

Contribution

The study introduces a multiscale modeling approach to quantify the maximum lateral expansion of 2D materials with line defects, linking it to elastic properties and defect density.

Findings

Lateral expansion is limited by rippling onset.

Maximum expansion is approximately 2.1 times the square of thickness times defect density.

Potential for giant pseudomagnetic fields in graphene due to strain engineering.

Abstract

The flexibility of two-dimensional (2D) materials enables static and dynamic ripples that are known to cause lateral contraction, shrinking of the material boundary. However, the limits of 2D materials' \emph{lateral expansion} are unknown. Therefore, here we discuss the limits of intrinsic lateral expansion of 2D materials that are modified by compressive line defects. Using thin sheet elasticity theory and sequential multiscale modeling, we find that the lateral expansion is inevitably limited by the onset of rippling. The maximum lateral expansion $\chi_{max}\approx 2.1\cdot t^2\sigma_d$, governed by the elastic thickness $t$ and the defect density $\sigma_d$, remains typically well below one percent. In addition to providing insight to the limits of 2D materials' mechanical limits and applications, the results highlight the potential of line defects in strain engineering, since for graphene they suggest giant pseudomagnetic fields that can exceed $1000$~T.