Graphene intercalation is a novel way to control graphene's band structure and generate two-dimensional quantum materials with unusual spintronic and electronic properties. Despite its importance, information about the intercalation mechanism is lacking, especially the role of low density domain boundaries between regions of graphene of different thickness. With high resolution surface diffraction we have systematically studied Pb intercalation on epi-graphene grown on SiC, with domain boundaries between buffer and single layer graphene. By examining the evolution of different diffraction spots as a function of tempertature, the location of Pb and stability of the intercalated phases underneath were determined.

Metal intercalation of graphene is a promising method to tune its electronic band structure and generate novel electronic and topological phases. The tuning depends critically on the ability to bond the intercalated atoms at predesigned, subsurface interlayer locations because the emerging band structure depends on metal location. We have studied Dy intercalation under single-layer graphene (SLG) on SiC using spot profile analysis–low-energy electron diffraction and scanning tunneling microscopy (STM). The experimental work is complemented with density-functional theory (DFT) analysis. Because different diffraction spots originate from different subsurface interlayer regions, it is possible to identify changes in the intercalation location by monitoring the spot intensity as a function of growth conditions. DFT calculations of the chemical potential as a function of intercalated Dy coverage support the variation of the stability of the intercalated phase at different intercalated locations. The preferred location is confirmed from STM studies showing the removal of the $6\times 6$ moiré corrugation at the preferred location, observed at higher Dy coverage.

The realization of the unusual properties of two-dimensional (2D) materials requires the formation of large domains of single-layer thickness, extending over the mesoscale. It is found that the formation of uniform graphene on SiC, contrary to textbook diffraction, is signaled by a strong bell-shaped component (BSC) around the (00) and G(10) spots (but not around the substrate spots). The BCS is also seen on graphene grown on metals, because a single uniform graphene layer can be also grown with large lateral size. It is only seen by electron diffraction but not with x-ray or He scattering. Although the origin of such an intriguing result is unclear, its presence in the earlier literature (but never mentioned) points to its robustness and significance. A likely mechanism relates to the the spatial confinement of the graphene electrons, within a single layer. This leads to large spread in their wave vector which is transferred by electron-electron interactions to the elastically scattered electrons to generate the BSC.