Boundary scattering in quasi-ballistic graphene/hexagonal boron nitride mesoscopic wires

In a quasi-ballistic transport regime where the mean free path is larger than the width of conduction channel, diffusive boundary scattering results in an anomalous positive magnetoresistance due to a megnetic commensurability effect between cyclotron motion and sample width. In this work, we fabricate a high-mobility two terminal graphene mesoscopic wire on hexagonal boron nitride with a mean free path comparable to sample width $\sim $ 1 $\mu $m. Magnetoresistance of the graphene mesoscopic wire shows a peak structure at a magnetic field which scales with the ratio of the cyclotron radius $R_{c}$ to the wire width $w$. The peak field increases with back-gate voltage as a consequence that the ratio $w$/$R_{c}$ is modified due to the change in $R_{c}$. These results indicate the quasi-ballistic transport and diffusive boundary scattering in graphene on hexagonal boron nitride.