▎ 摘　　要

By using first-principles calculations, we demonstrate the influence of proximity effect on the band structures of heterostructures formed by graphene stacking on a two dimensional (2D) topological insulator (TI) 1T'-MX2. The interlayer distance d between graphene and TI decreases with the enhancement of the intrinsic lattice anisotropy of 1T'-MX2, which determines different strength of the interlayer proximity interaction. The bandgap can be opened by the proximity exchange. The weak anisotropic symmetry of heterostructure (large d) only results in a small band gap (similar to 50 meV) in graphene/MoTe2. However, a large energy gap (up to similar to 200 meV) can be obtained in graphene/MoS2, which is attributed to the interintralayer charge transfer due to the strong p(r)oximity interaction of the hetero-interface (small d). In addition, the 1T'-MX2 of heterostructure still possesses the topological feature of Z(2) = 1, since the graphene has a negligible effect on the band structure of the system.