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

We present electronic transport measurements through short and narrow (30 x 30 nm) single-layer graphene constrictions on a hexagonal boron nitride substrate. While the general observation of Coulomb blockade is compatible with earlier work, the details are not: We show that the area on which charge is localized can be significantly larger than the area of the constriction, suggesting that the localized states responsible for the Coulomb blockade leak out into the graphene bulk. The high bulk mobility of graphene on hexagonal boron nitride, however, seems to be inconsistent with the short bulk localization length required to see Coulomb blockade. To explain these findings, charge must instead be primarily localized along the imperfect edges of the devices and extend along the edge outside of the constriction. In order to better understand the mechanisms, we compare the experimental findings with tight-binding simulations of such constrictions with disordered edges. Finally, we discuss previous experiments in the light of our findings.