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We present electronic transport measurements through short and narrow (30x30nm) single layer graphene constrictions on a hexagonal boron nitride substrate.While the general observation of Coulomb-blockade is compatible with earlierwork, the details are not: we show that the area on which charge is localizedcan be significantly larger than the area of the constriction, suggesting thatthe localized states responsible for Coulomb-blockade leak out into thegraphene bulk. The high bulk mobility of graphene on hexagonal boron nitride,however, seems not consistent with the short bulk localization length requiredto see Coulomb-blockade. To explain these findings, charge must instead beprimarily localized along the imperfect edges of the devices and extend alongthe edge outside of the constriction. In order to better understand themechanisms, we compare the experimental findings with tight-binding simulationsof such constrictions with disordered edges. Finally we discuss previousexperiments in the light of these new findings.

Characterizing wave functions in graphene nanodevices: electronic transport through ultrashort graphene constrictions on a boron nitride substrate