New metallic quasi-two-dimensional structures of graphene and molybdenum disulfide layers with embedded rhenium atoms

New metallic structures in the system of graphene and molybdenum disulfide layers with embedded rhenium atoms, in which the graphene layer is rotated by $30^\circ$ to the molybdenum disulfide layer and the Re atom either substitutes the molybdenum atom in the MoS$_2$ layer or is located between the layers mainly interacting with three sulfur atoms and six carbon atoms, are examined. In the latter case, a high electron density of states has been found in the Fermi level, which indicates a high metallicity of the graphene$30^\circ$-(Re)-MoS$_2$ bilayer in comparison with other bilayer structures considered earlier. All proposed structures are energetically stable. Possible applications of the studied bilayers have been considered as well.