Effect of sulphur vacancy and interlayer interaction on the electronic structure and spin splitting of bilayer MoS₂

Molybdenum disulfide (MoS₂) is one of the candidate materials for nanoelectronics and optoelectronics devices in the future. The electronic and magnetic properties of MoS₂ can be regulated by interlayer interaction and the vacancy effect. Nevertheless, the combined effect of these two factors on MoS₂ is not clearly understood. In this study, we have investigated the impact of a single S vacancy combined with interlayer interaction on the properties of bilayer MoS₂. Our calculated results show that an S vacancy brings impurity states in the band structure of bilayer MoS₂, and the energy level of the impurity states can be affected by the interlayer distance, which finally disappears in the bulk state when the layer distance is relatively small. Moreover, during the compression of bilayer MoS₂, the bottom layer, where the S vacancy stays, gets an additional charge due to interlayer charge transfer, which first increases, and then decreases due to gradually forming the interlayer S-S covalent bond, as interlayer distance decreases. The change of the additional charge is consistent with the change of the total magnetic moment of the bottom layers, no magnetic moment has been found in the top layer. The distribution of magnetic moment mainly concentrates on the three Mo atoms around the S vacancy, for each of which the magnetic moment is very much related to the Mo-Mo length. Our conclusion is that the interlayer charge transfer and S vacancy co-determine the magnetic properties of this system, which may be a useful way to regulate the electronic and magnetic properties of MoS₂ for potential applications.