Tuning the chemical potential of a solid to the vicinity of a Van Hove singularity (VHS) is a well-established route to discovering emergent quantum phases. In monolayer graphene, the use of electron-donating metal layers has recently emerged as a method to dope the chemical potential to the nearest VHS, as evidenced by Angle-Resolved Photoemission Spectroscopy (ARPES) measurements. In this work, we study the spatial uniformity of the doping from this process using spectroscopic imaging scanning tunneling microscopy (SI-STM). Using molecular beam epitaxy, we achieve electron doping of graphene on silicon carbide using Ytterbium (Yb-Graphene). We show using in situ ARPES that the chemical potential is shifted to within 250 meV of the VHS. Using insitu SI-STM, we establish that there exists significant inhomogeneity in the VHS position in overdoped graphene. We find two separate reasons for this. First, the spatial inhomogeneity of the intercalated Yb leads to local variations in the doping, with a length scale of inhomogeneity set by the screening length of $\sim 3$ nm. Second, we observe the presence of substitutional Yb dopants in the graphene basal plane. These Yb dopants cause a strong local shift of the doping, along with a renormalization of the quasiparticle amplitude. Theoretical calculations confirm that the Yb impurities effectively change the local potential, thus energetically shifting the position of the Van Hove singularity. Our results point to the importance of considering the spatial structure of doping and its inextricable link to electronic structure.

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• Density of states
• Electronic structure
• Fermi surface
• Flat bands
• Graphene