Quantum interference on electron scattering in graphene by carbon impurities in underlying h -BN

Abstract

Electronic structures and transport properties of graphene on $h$-BN with carbon impurities are investigated by first-principles calculation and the tight-binding model. We show that the coupling between the impurity level and the graphene's Dirac cone sensitively depends on the impurity position, and in particular, it nearly vanishes when the impurity is located right below the center of the six membered ring of graphene. The Bloch phase factor at the Brillouin zone edge plays a decisive role in the cancellation of the hopping integrals. The impurity position dependence on the electronic structures of graphene on $h$-BN is investigated by the first-principles calculation, and its qualitative feature is well explained by a tight-binding model with graphene and a single impurity site. We also propose a simple one-dimensional chain-impurity model to analytically describe the role of the quantum interference in the position-dependent coupling.