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As a typical transition-metal dichalcogenide material,MoS2 has attracted intense research interest among two-dimensional materials due to its promising electronic and optical properties.In this talk,I will present our recent results on thin MoS2 nanosheets obtained within the framework of density functional theory calculations: 1)hopping transport through defect-induced localized states in MoS2 ; 2)electronic structure of twisted bilayer of graphene and MoS2 and MoS2/MoS2)and 3)Pattern magnetic Co-doping on MoS2 nanosheet.Our calculations revealed that i)charge transport of few-layer MoS2 in low carrier density regime can be explained by hopping through defect-induced localized states; 2)The twist of interlayers leads to significant variations in the band structure for both Gr/MoS2 and MoS2/MoS2 and the former shows clearly dependence on the rotation angle which is indeed from the twisted resultant lattice mismatch; 3)we predict a new 2D half-metallic Co/MoS2 heterojunction with robust ferromagnetic ground spin state and 100%spin current polarization and it is synthesizable via wetting deposition of Co on MoS2 by electron-beam evaporation technique.