▎ 摘　　要

The emerging interest in van der Waals heterostructures as new materials for optoelectronics and photonics poses questions about their stability and structure-property relations. In the framework of density-functional and many-body perturbation theory, we investigate the structural, electronic, and optical properties of periodic heterostructures formed by graphene and hexagonal boron nitride (h-BN). To understand how the constituents affect each other depending on the layer stacking, we examine 12 commensurate arrangements. We find that interaction with graphene improves the stability of bulk h-BN also in those configurations that are predicted to be energetically metastable. In return, the interaction with h-BN can open a band gap of a few hundred meV in graphene. Its actual size can be tuned by the arrangement of the layers. In the semiconducting configurations, the character and spatial distribution of optical excitations are affected by the specific stacking that determines the electronic states involved in the transitions. Remarkably, six out of the 12 explored heterostructures remain semimetallic.