All the calculations are performed in the framework of the density functional theory with the projector augmented plane-wave method, as implemented in the Vienna ab initio simulation package. The generalized gradient approximation proposed by Perdew-Burke-Ernzerhof (PBE) is selected for the exchange-correlation potential. The cut-off energy for the plane wave is set to 480 eV and the Monkhorst-Pack k-point grid of 3 × 2 × 3 is adopted. The energy criterion is set to 10-5 eV in the iterative solution of the Kohn-Sham equation. All the structures are relaxed until the residual forces on the atoms have declined to less than 0.05 eV/Å. The heterostructure has a size of 4 × 3 rectangular computational cell of the graphene. The cohesive energy (Ecoh) is expressed as