Midgap states and band gap modification in defective graphene/h-BN   heterostructures
  The role of defects in van der Waals heterostructures made of graphene and hexagonal boron nitride (h-BN) is studied by a combination of ab initio and model calculations. Despite the weak van der Waals interaction between layers, defects residing in h-BN, such as carbon impurities and antisite defects, reveal a hybridization with graphene p$_{\rm z}$ states, leading to midgap state formation. The induced midgap states modify the transport properties of graphene and can be reproduced by means of a simple effective tight-binding model. In contrast to carbon defects, it is found that oxygen defects do not strongly hybridize with graphene's low-energy states. Instead, oxygen drastically modifies the band gap of graphene, which emerges in a commensurate stacking on h-BN lattices. 
B. Sachs, T. O. Wehling, M. I. Katsnelson, and A. I. Lichtenstein
cond-mat.mtrl-sci cond-mat.mes-hall