Hybrid systems consisting of graphene and various two-dimensional materials would provide more opportunities for achieving desired electronic and optoelectronic properties. Here, we focus on a superlattice composed of graphene and monolayer MoS2. The geometric and electronic structures of the superlattice have been studied by using density functional theory. The possible stacking models, which are classified into four types, are considered. Our results revealed that all the models of graphene/MoS2 superlattices exhibit metallic electronic properties. Small band gaps are opened up at the K-point of the Brillouin zone for all the four structural models. Furthermore, a small amount of charge transfer from the graphene layer to the intermediate region of C–S layers is found. The band structure and the charge transfer together with the buckling distortion of the graphene layer in the superlattice indicate that the interaction between the stacking sheets in the superlattice is more than just the van der Waals interaction.

Study of heterostructured bilayer systems is an essential prerequisite for developing twodimensional nano-electronic devices. Using ab initio density functional theory calculations, we investigated the atomic and electronic properties of hetero-bilayers composed of silicene and germanene layers with monolayer MoS2. Our results show that both Silicene-MoS2 and Germanene-MoS2 hetero-bilayers are direct band gap semiconductors. The band gaps of silicene and germanene in hetero-bilayers are opened due to the sublattice symmetry breaking induced by the introduction of the MoS2 monolayer, indicating that the monolayer MoS2 makes a good complement to silicene and germanene. Moreover, tunable band gaps in silicene and germanene can be realized by changing the interlayer distance or employing inplane compressing/stretching. Especially, through compressing or stretching, the Germanene-MoS2 bilayers realize a transformation from an indirect band gap semiconductor to a direct band gap semiconductor, while the Silicene-MoS2 bilayers can keep the direct band gaps.Our results in this work provide a new way for designing applications in future MoS2-based nano devices with controllable band gaps.