Pathways to controlled 3D deformation of graphene: Manipulating the motion of topological defects

Functional properties of 2D materials like graphene can be tailored by designing their 3D structure at the Angstrom to nanometer scale. While there are routes to tailoring 3D structure at larger scales, achieving controllable sub-micron 3D deformations has remained an elusive goal since the original discovery of graphene. In this contribution, we summarize the state-of-the-art in controllable 3D structures, and present our perspective on pathways to realizing atomic-scale control. We propose an approach based on strategic application of mechanical load to precisely relocate and position topological defects that give rise to curvature and corrugation to achieve a desired 3D structure. Realizing this approach requires establishing the detailed nature of defect migration and pathways in response to applied load. From a computational perspective, the key needed advances lie in the identification of defect migration mechanisms. These needed advances define new forward and inverse problems: when a fixed stress or strain field is applied, along which pathways will defects migrate?, and vice versa. We provide a formal statement of these forward and inverse problems, and review recent methods that may enable solving them. The forward problem is addressed by determining the potential energy surface of allowable topological configurations through Monte Carlo and Gaussian process models to determine defect migration paths through dynamic programming algorithms or Monte Carlo tree search. Two inverse models are suggested, one based on genetic algorithms and another on convolutional neural networks, to predict the applied loads that induce migration and position defects to achieve desired curvature and corrugation. The realization of controllable 3D structures enables a vast design space at multiple scales to enable new functionality in flexible electronics, soft robotics, biomimetics, optics, and other application areas.