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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.