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

Abstract

The transition metal dichalcogenides <i>MX</i><sub>2</sub>/Chromium Trihalides Cr<i>X</i><sub>3</sub> van der Waals heterostructures can control the valley polarization of of <i>MX</i><sub>2</sub> effectively, which makes them possess promising potential applications in valleytronics. In the present work, the stacking order and electronic structure of MoSe<sub>2</sub>/CrI<sub>3</sub>, MoSe<sub>2</sub>/CrBr<sub>3</sub> and WS<sub>2</sub>/CrBr<sub>3</sub> are investigated based on the first-principle calculation and k-projection band unfolding method. The underlying mechanism of valley splitting is also explored. The stacking energy surfaces are calculated and the stable stacking configurations are determined. The effects of the breaking of time-symmetry and spatial-symmetry on electronic structure are also revealed. Because of the orbital hybridization, the conduction band of heterostructure becomes complicated and the valence band maximum changes drastically. It is thus difficult to compare the electronic structure of vdW heterostructure with that of free-standing <i>MX</i><sub>2</sub> directly. Through the unfolding energy band, the electronic structure change of <i>MX</i><sub>2</sub> induced by Cr<i>X</i><sub>3</sub> is revealed clearly, and the valley splitting of <i>MX</i><sub>2</sub> is obtained quantitatively. Moreover, the interlayer distance and strain are found to be able to tune the valley splitting effectively. When the interlayer distance reduces to 2.6 Å, the valley splitting of MoSe<sub>2</sub>/CrI<sub>3</sub> is enhanced to 10.713 meV with the increase of <i>AB</i> stacking, which is 8.8 times as large as the value of equilibrium structure. This work breaks through the limit of the complex electronic structure in supercell, providing an important reference for studying other magnetic vdW heterostructure.