Defects in solids commonly limit the material performance by acting as weak points under external loads or perturbations to propagating waves. However, here we will discuss the roles of defects in graphene, or in general two-dimensional (2D) crystals, from a constructive viewpoint. We will show the topological and geometrical aspects of defects in graphene, including the pre-strain and warping effects. These dual roles of defects modulate both local and global properties of the material in unexpected ways. For example, we will demonstrate that in some cases local response of 2D crystals can even be stiffened and strengthened by the presence of defects. These new findings not only shed lights on the characterization of 2D material properties, but also add a new dimension to material design, in the scenario of defect-based geometrical and topological engineering.

Defects in solids commonly limit the material performance by acting as weak points under external loads or perturbations to propagating waves. However, here we will discuss the roles of defects in graphene, or in general two-dimensional (2D) crystals, from a constructive viewpoint. We will show the topological and geometrical aspects of defects in graphene, including the pre-strain and warping effects. These dual roles of defects modulate both local and global properties of the material in unexpected ways. For example, we will demonstrate that in some cases local response of 2D crystals can even be stiffened and strengthened by the presence of defects. These new findings not only shed lights on the characterization of 2D material properties, but also add a new dimension to material design, in the scenario of defect-based geometrical and topological engineering.