Abstract
The distinctive properties of graphene sheets may be significantly influenced by the presence of corrugation structures. Our understanding of these graphene structures has been limited to the mesoscopic scale. Here we characterize angstrom-scale periodic buckling structures in free-standing graphene bilayers produced by liquid-phase processing in the absence of specific substrates. Monochromated, aberration-corrected transmission electron microscopy with sub-angstrom resolution revealed that the unit structures in the major buckling direction consist of only two and three unit cells of graphene's honeycomb lattice, resulting in buckling wavelengths of 3.6 ± 0.5 and 6.4 ± 0.8 Å, respectively. The buckling shows a strong preference of chiral direction and spontaneously chooses the orientation of the lowest deformation energy, governed by simple geometry rules agreeing with Euler buckling theory. Unexpectedly, the overall buckled structures demonstrate geometric complexity with cascaded features. First-principles calculations suggest that significant anisotropic changes in the electronic structure of graphene are induced by the buckling.