  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.
