Transport properties of graphene nanoroads in boron nitride sheets.

We demonstrate that the one-dimensional (1D) transport channels that appear in the gap when graphene nanoroads are embedded in boron nitride (BN) sheets are more robust when they are inserted at AB/BA grain boundaries. Our conclusions are based on ab initio electronic structure calculations for a variety of different crystal orientations and bonding arrangements at the BN/C interfaces. This property is related to the valley Hall conductivity present in the BN band structure and to the topologically protected kink states that appear in continuum Dirac models with position-dependent masses.