Effects of van der Waals interaction and electric field on the electronic structure of bilayer MoS2

The modification of the electronic structure of bilayer MoS₂by an external electric field can have potential applications in optoelectronics and valleytronics. Nevertheless, the underlying physical mechanism is not clearly understood, especially the effects of the van der Waals interaction. In this study, the spin orbit-coupled electronic structure of bilayer MoS₂has been investigated using the first-principle density functional theory. We find that the van der Waals interaction as well as the interlayer distance has significant effects on the band structure. When the interlayer distance of bilayer MoS₂increases from 0.614 nm to 0.71 nm, the indirect gap between the Γ and Λ points increases from 1.25 eV to 1.70 eV. Meanwhile, the energy gap of bilayer MoS₂transforms from an indirect one to a direct one. An external electric field can shift down (up) the energy bands of the bottom (top) MoS₂layer and also breaks the inversion symmetry of bilayer MoS₂. As a result, the electric field can affect the band gaps, the spin-orbit interaction and splits the valance bands into two groups. The present study can help us understand more about the electronic structures of MoS₂materials for potential applications in electronics and optoelectronics.