Structural and electronic properties of graphene/MoS${}_2$ bilayer heterostructures

Graphene and two-dimensional materials based on transition metal dichalcogenides have gained increasing attention because of their fascinating features in electronics and optical properties. Combining a single layer of graphene with a transition metal dichalcogenide layer in a Van der Waals heterostructure offers an intriguing means of controlling the electronic properties through these bilayer heterostructures. Here, we report the structural and electronic properties of graphene/MoS${}_2$ bilayer heterostructures. For the theoretical calculations, we use Density Functional Theory with Van der Waals corrections, as implemented in the Abinit package. We analyze the interlayer spacing between the graphene and MoS${}_2$ layers and also the location of Dirac points near the Fermi level. In particular, we focus on the structural and electrical properties of bilayer heterostructures with different supercell geometries and give particular attention to the effect of relaxing the lattice structure. These heterostructures are based on different supercell geometries (4:3, 5:4, and 9:7), having different magnitudes of the lattice mismatch.