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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 non-contact 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 (DFT). 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 2D structures with varying chemical reactivity.

Controlled defect creation is a prerequisite for the detailed study of disorder effects in materials. Here, we irradiate a graphene/Ir(111)-interface with low-energy Ar+ to study the induced structural changes. Combining computer simulations and scanning-probe microscopy, we show that the resulting disorder manifests mainly in the forms of intercalated metal adatoms and vacancy-type defects in graphene. One prominent feature at higher irradiation energies (from 1 keV up) is the formation of line-like depressions, which consist of sequential graphene defects created by the ion channeling within the interface -- much like a stone skipping on water. Lower energies result in simpler defects, down to 100 eV where more than one defect in every three is a graphene single vacancy.

We study the electronic structure of finite armchair graphene nanoribbons using density-functional theory and the Hubbard model, concentrating on the states localized at the zigzag termini. We show that the energy gaps between end-localized states are sensitive to doping, and that in doped systems, the gap between the end-localized states decreases exponentially as a function of the ribbon length. Doping also quenches the antiferromagnetic coupling between the end-localized states leading to a spin-split gap in neutral ribbons. By comparing dI/dV maps calculated using the many-body Hubbard model, its mean-field approximation and density-functional theory, we show that the use of a single-particle description is justified for graphene {\pi} states. Furthermore, we study the effect of structural defects in the ribbons on their electronic structure. Defects at one ribbon termini do not significantly modify the electronic states localized at the intact end. This provides further evidence for the interpretation of a multi-peaked structure in a recent scanning tunneling spectroscopy (STS) experiment resulting from inelastic tunneling processes [J. van der Lit et al., Nature Commun., in press (2013)]. Finally, we show that the hydrogen termination at the flake edges leaves identifiable fingerprints on the positive bias side of STS measurements, thus possibly aiding the experimental identification of graphene structures.

Despite the enormous interest in the properties of graphene and the potential of graphene nanostructures in electronic applications, the study of quantum confined states in atomically well-defined graphene nanostructures remains an experimental challenge. Here, we study graphene quantum dots (GQDs) with well-defined edges in the zigzag direction, grown by chemical vapor deposition (CVD) on an iridium(111) substrate, by low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS). We measure the atomic structure and local density of states (LDOS) of individual GQDs as a function of their size and shape in the range from a couple of nanometers up to ca. 20 nm. The results can be quantitatively modeled by a relativistic wave equation and atomistic tight-binding calculations. The observed states are analogous to the solutions of the text book "particle-in-a-box" problem applied to relativistic massless fermions., Comment: accepted for publication in Phys. Rev. Lett

Epitaxial graphene grown on transition metal surfaces typically exhibits a moir\'e pattern due to the lattice mismatch between graphene and the underlying metal surface. We use both scanning tunneling microscopy (STM) and atomic force microscopy (AFM) experiments to probe the electronic and topographic contrast of the graphene moir\'e on the Ir(111) surface. While STM topography is influenced by the local density of states close to the Fermi energy and the local tunneling barrier height, AFM is capable of yielding the 'true' surface topography once the background force arising from the van der Waals (vdW) interaction between the tip and the substrate is taken into account. We observe a moir\'e corrugation of 35$\pm$10 pm, where the graphene-Ir(111) distance is the smallest in the areas where the graphene honeycomb is atop the underlying iridium atoms and larger on the fcc or hcp threefold hollow sites., Comment: revised version