Modulation of electronic properties from stacking orders and spin-orbit coupling for 3R-type MoS2

Two-dimensional crystals stacked by van der Waals coupling, such as twisted graphene and coupled graphene-BN layers with unusual phenomena have been a focus of research recently. As a typical representative, with the modulation of structural symmetry, stacking orders and spin-orbit coupling, transitional metal dichalcogenides have shown a lot of fascinating properties. Here we reveal the effect of stacking orders with spin-orbit coupling on the electronic properties of few-layer 3R-type MoS2 by first principles methods. We analyze the splitting of states at the top of valence band and the bottom of conduction band, following the change of stacking order. We find that regardless of stacking orders and layers' number, the spin-up and spin-down channels are evidently separated and can be as a basis for the valley dependent spin polarization. With a model Hamiltonian about the layer's coupling, the band splitting can be effectively analyzed by the coupling parameters. It is found that the stacking sequences, such as abc and abca, have the stronger nearest-neighbor coupling which imply the popular of periodic abc stacking sequence in natural growth of MoS2.