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Graphene quantum dots probed by scanning tunneling spectroscopy and transport spectroscopy after local anodic oxidation

Graphene quantum dots are considered as promising alternatives to quantum dots in III-V semiconductors, e.g., for the use as spin qubits due to their consistency made of light atoms including spin-free nuclei which both imply relatively long spin decoherene times. However, this potential has not been realized in experiments so far, most likely, due to a missing control of the edge configurations of the quantum dots. Thus, a more fundamental investigation of Graphene quantum dots appears to be necessary including a full control of the wave function properties most favorably during transport spectroscopy measurements. Here, we review the recent success in mapping wave functions of graphene quantum dots supported by metals, in particular Ir(111), and show how the goal of probing such wave functions on insulating supports during transport spectroscopy might be achieved.