Structural, electronic, vibrational, and elastic properties of graphene/ MoS2 bilayer heterostructures

Graphene/MoS$_2$ van der Waals (vdW) heterostructures have promising technological applications due to their unique properties and functionalities. Many experimental and theoretical research groups across the globe have made outstanding contributions to benchmark the properties of graphene/MoS$_2$ heterostructures. Even though some research groups have already made an attempt to model the graphene/MoS$_2$ heterostructures using {\it first-principles} calculations, there exists several discrepancies in the results from different theoretical research groups and the experimental findings. In the present work, we revisit this problem by first principles approach and address the existing discrepancies about the interlayer spacing between graphene and MoS$_2$ monolayers in graphene/MoS$_2$ heterostructures, and the location of Dirac points near Fermi-level. We find that the Tkatchenko--Scheffler method efficiently evaluates the long-range vdW interactions and accurately predicts interlayer spacing between graphene and MoS$_2$ sheets. We further investigate the electronic, mechanical and vibrational properties of the optimized graphene/MoS$_2$ heterostructures created using 5$\times$5/4$\times$4 and 4$\times$4/3$\times$3 supercell geometries having different magnitudes of lattice mismatch. The effect of the varying interlayer spacing on the electronic properties of heterostructures is discussed. Our phonon calculations reveal that the interlayer shear and breathing phonon modes, which are very sensitive to the weak vdW interactions, play vital role in describing the thermal properties of the studied systems. The thermodynamic and elastic properties of heterostructures are further discussed. A comparison between our results and the results reported from other research groups is presented.