The relevance of electrostatics for scanning-gate microscopy

Scanning-probe techniques have been developed to extract local information from a given physical system. In particular, conductance maps obtained by means of scanning-gate microscopy (SGM), where a conducting tip of an atomic-force microscope is used as a local and movable gate, seem to present an intuitive picture of the underlying physical processes. Here, we argue that the interpretation of such images is complex and not very intuitive under certain circumstances: scanning a graphene quantum dot (QD) in the Coulomb-blockaded regime, we observe an apparent shift of features in scanning-gate images as a function of gate voltages, which cannot be a real shift of the physical system. Furthermore, we demonstrate the appearance of more than one set of Coulomb rings arising from the graphene QD. We attribute these effects to screening between the metallic tip and the gates. Our results are relevant for SGM on any kind of nanostructure, but are of particular importance for nanostructures that are not covered with a dielectric, e.g. graphene or carbon nanotube structures.