In the construction of a reliable TB model for graphene-MoS2-graphene heterostructure, we are guided by first by the principle of density functional theory (DFT) calculations that will provide the reference fronm which to calibrate the TB model. The DFT calculation is performed with Quantum Espresso code[13]. The generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) is used to approximate the electronic exchange and correlation. The structure is relaxed until the energy has converged to within 〖10〗^(-4) eV. In this calculation, we consider the most stable configuration, which contains two , 5×5 lateral periodicities of graphene layers and a 4×4 lateral periodicity of the MoS2 monolayer. Fig. 2 presents the geometrics of the top- and side -view of graphene-MoS2-graphene heterostructure. In this supercell, there are 100 carbon (C), 32 sulfur (S), and 16 molybdenum (Mo) atoms. After structure relaxation, graphene keeps its original planar and hexagonal atomic network, maintaining 3.65 Å distance from MoS2 layer. The orbital composition is of fundamental importance ftor building ofthe TB model. The bandstructure orbital compositions are calculated using PROJWFC module of Quantum Espresso package [13].