Geometry and electronic structure of monolayer, bilayer, and multilayer Janus WSSe

Newly synthesized Janus transition-metal dichalcogenides MXY ($M=\mathrm{Mo}$, W; $X\ensuremath{\ne}Y=\mathrm{S}$, Se, Te) possess intrinsic Rashba spin splitting and out-of-plane dipole moment due to the breaking of mirror symmetry. Taking WSSe as an example, we present a first-principles investigation of the structural stability and electronic properties of mono-, bi-, and multilayer MXY. Results show that S atoms contribute more than Se atoms in the valence-band maximum at the $\mathrm{\ensuremath{\Gamma}}$ point, which can be greatly affected by interlayer interactions. The high-symmetry AA\ensuremath{'} stacking is still the most stable pattern, but there are various orders of chalcogen atomic layers in each stacking. The most preferred order of two adjacent layers is S-Se-Se-S, followed by Se-S-Se-S. The Se-S-Se-S--ordered WSSe bilayer is found to have significant layer splitting due to the net dipole moment, which has great potential for solar cells. Layer-dependent Rashba splittings exist in asymmetry-ordered WSSe bilayers, that can be tuned by changing the interlayer distance, originating from the regulation of interlayer electrostatic interaction. However, there is not layer splitting in a symmetrically stacked WSSe bilayer and opposite Rashba splitting appears in the two layers at a sufficiently large interlayer distance. The electronic structures and spin splittings can be easily modulated by controlling the chalcogen atomic-layer order, so that we can obtain the desired properties from mono-, bi-, and multilayer MXY.