Rotation-dependent epitaxial relations between graphene and the Si-terminated SiC substrate

We study the rotation-dependent epitaxial relations between graphene nanoflake and the Si-terminated 4H-SiC(0001) substrate. Depending on the rotation angle between the nanoflake and substrate surface, we find that Si-C bonds formed between the C atoms in the nanoflake and Si atoms on the SiC surface exhibit complicated two-dimensional patterns. Among the various patterns formed, we reveal a finite-size epitaxial domain with a perfectly regular triangular lattice. We further identify the lattice constant of 12.3 angstrom and the maximal size of the perfect lattice domain is about 70 angstrom. It is found that the maximal lattice domain size is set by the lattice mismatch between the common hexagonal lattices of the graphene nanoflake and its underlying substrate.