Self-assisted growth of InAs nanowires on graphene by molecular beam epitaxy is reported. Nanowires with diameter of ~50 nm and aspect ratio of up to 100 were achieved. The morphological and structural properties of the nanowires were carefully studied by changing the substrate from bilayer graphene through buffer layer to quasi-free-standing monolayer graphene. The positional relation of the InAs NWs with the graphene substrate was determined. A 30{deg} orientation configuration of some of the InAs NWs is shown to be related to the surface corrugation of the graphene substrate. InAs NW-based devices for transport measurements were fabricated, and the conductance measurements showed a semi-ballistic behavior. In Josephson junction measurements in the non-linear regime, Multiple Andreev Reflections were observed, and an inelastic scattering length of about 900 nm was derived.
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