Defects induce phase transition from dynamic to static rippling in graphene

Two-dimensional (2D) materials display nanoscale dynamic ripples that significantly impact their properties. Defects within the crystal lattice are the elementary building blocks to tailor the material's morphology. While some studies have explored the link between defective structures and rippling dynamics in 2D materials, a comprehensive understanding of this relationship has yet to be achieved. Here, we address this using machine learning-driven molecular dynamics simulations. Specifically, we find that above a critical concentration of defects, free-standing graphene sheets undergo a dynamic transition from freely propagating to static ripples. Our computational approach captures the dynamics with atomic resolution, \cs{and reveals that the transition is driven by elastic interactions between defects. The strength of these interactions is found to vary across defect types and we identify a unifying set of principles driving the dynamic-to-static transition in 2D materials. Our work not only rationalises puzzling experimental results for defective 2D materials, but also paves the way to design two-dimensional devices with tailored rippling dynamics. These insights could lay the foundations for a new class of disorder-based catalytic and interfacial materials.