I will discuss our recent progress in the preparation and study of high mobility devices based on suspended graphene or based graphene on a boron nitride (BN) substrate. We observed that by current annealing of suspended graphene constrictions can be formed, with very high mobility and very low background doping [1]. They allowed the observation of conductance quantization in the absence of a magnetic field due to quantum confinement. This conductance quantization in units of 2e2/h gradually evolves into the regular quantum Hall effect for graphene when a perpendicular magnetic field is applied. In the second part of the talk I discuss spin transport in high mobility devices. We observed that in high quality graphene on BN [2] the spin relaxation length increased to about 5 micrometer at room temperature. For similar devices prepared with suspended graphene the actual spin relaxation could not yet be determined, because the spin relaxation is dominated by the lower mobility regions close to, or underneath the contacts. Implications for the mechanisms for spin relaxation in graphene will be discussed.

[1] N. Tombros et al., Quantized conductance of a suspended graphene nanoconstriction, Nat. Phys. 7, 697 (2011).

[2] P.J. Zomer at al., A transfer technique for high mobility graphene devices on commercially available hexagonal boron nitride, Appl. Phys. Lett. 99, 232104 (2011)

[3] P.J. Zomer and M. Guimaraes, in preparation