Twinning and twisting of tri- and bilayer graphene.

The electronic, optical, and mechanical properties of bilayer and trilayer graphene vary with their structure, including the stacking order and relative twist, providing novel ways to realize useful characteristics not available to single layer graphene. However, developing controlled growth of bilayer and trilayer graphene requires efficient large-scale characterization of multilayer graphene structures. Here, we use dark-field transmission electron microscopy for rapid and accurate determination of key structural parameters (twist angle, stacking order, and interlayer spacing) of few-layer CVD graphene. We image the long-range atomic registry for oriented bilayer and trilayer graphene, find that it conforms exclusively to either Bernal or rhombohedral stacking, and determine their relative abundances. In contrast, our data on twisted multilayers suggest the absence of such long-range atomic registry. The atomic registry and its absence are consistent with the two different strain-induced deformations we observe; by tilting the samples to break mirror symmetry, we find a high density of twinned domains in oriented multilayer graphene, where multiple domains of two different stacking configurations coexist, connected by discrete twin boundaries. In contrast, individual layers in twisted regions continuously stretch and shear independently, forming elaborate Moiré patterns. These results, and the twist angle distribution in our CVD graphene, can be understood in terms of an angle-dependent interlayer potential model.