Structure and Local Variations of the Graphene Moiré on Ir(111)

We have studied the incommensurate moir\'e structure of epitaxial graphene grown on iridium(111) by dynamic low-energy electron diffraction [LEED $I$($V$)] and noncontact atomic force microscopy (AFM) with a CO-terminated tip. Our LEED $I$($V$) results yield the average positions of all the atoms in the surface unit cell and are in qualitative agreement with the structure obtained from density functional theory. The AFM experiments reveal local variations of the moir\'e structure: The corrugation varies smoothly over several moir\'e unit cells between 42 and 56 pm. We attribute these variations to the varying registry between the moir\'e symmetry sites and the underlying substrate. We also observe isolated outliers, where the moir\'e top sites can be offset by an additional 10 pm. This study demonstrates that AFM imaging can be used to directly yield the local surface topography with pm accuracy even on incommensurate two-dimensional structures with varying chemical reactivity.