Abstract
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.
Highlights
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
The single-layer of hexagonal transition metal dichalcogenides (h-TMDs) is formed by the quasi-2D sheet of chemical bonded X-M-X, and with space group P-6m2
The formation of trigonal structure results in the absence of inversion symmetry which makes the demonstration of spin-orbit coupling in h-TMDs possible
Summary
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. The weak screening due to the low dimensional limitation has lead to tightly-bound excitons and enhanced electron-electron interactions[14,15,16] These with the direct band gap in single-layer h-TMDs, give rise to a lot of fascinating optical phenomena[17,18,19,20], such as surface sensitive luminescence[21,22] and strain-control of optical band gap[23,24,25,26,27]. Its unit cell is composed of a double-layer with space group P63/mmc In this way, the inversion symmetry which is broken in single-layer. The unit cell of 3R phase is composed of a triple-layer stacked In this way, the inversion symmetry is broken in the bulk form which is different from 2H phase. The modulation of band splitting by LC was found to be changed, following the change of stacking orders
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