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The transition metal dichalcogenides MX 2 /Chromium Trihalides CrX 3  van der Waals heterostructure, which can control the valley polarization of MX 2  effectively, has promising potential application in valleytronics. The present work investigated the stacking order and electronic structure of MoSe 2 /CrI 3 , MoSe 2 /CrBr 3  and WS 2 /CrBr 3  based on First-principle calculation and k-projection band unfolding method. The underlying mechanism of valley splitting was also explored. The stacking energy surfaces were calculated and the stable stacking configurations were determined. The effect of time-symmetry and spatial-symmetry broken on electronic structure was also revealed. Since the orbital hybridization, the conduction band of heterostructure became complicated and the valence band maximum changed drastically. It is thus difficult to compare the electronic structure of vdW heterostructure and free-standing MX 2  directly. Through the unfolding energy band, the change of electronic structure of MX 2  induced by CrX 3  was revealed clearly, and the valley splitting of MX 2  were obtained quantificationally. Moreover, the interlayer distance and strain were found to tune the valley splitting effectively. When the interlayer distance reduced to 2.6 Å, the valley splitting of MoSe 2 /CrI 3  with AB stacking enhanced to 10.713meV, which is 8.8 times as large as the value of equilibrium structure. Our work overcame the limit of the complex electronic structure in supercell, which provide a important reference to other magnetic vdW heterostructure.

Study of transition metal dichalcogenides/chromium trihalides van der Waals heterostructure by band unfolding method