Newly synthesized Janus transition-metal dichalcogenides MXY ($M=\mathrm{Mo}$, W; $X\ne Y=\mathrm{S}$, 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 $\mathrm{\Gamma }$ point, which can be greatly affected by interlayer interactions. The high-symmetry AA′ 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.

In this research, we demonstrate the large spin and valley splittings in Janus monolayer WSSe brought by the interaction with a magnetic substrate. The MnO(111) substrate plays the role of ferromagnet since the importance lies in the magnetism of the surface Mn atoms. The responses of both in-plane and out-of-plane spin splittings with the magnetic direction of the substrate are investigated. It is indicated that a large valley splitting of about 410 meV at the $K$ and $K^{\prime }$ points can be produced by the magnetic substrate, which is positively correlated with the vertical magnetic moments of the surface Mn atoms. In addition, a helical gap is opened and the Rashba spin-orbit coupling induced dispersion relation is also significantly modified under the action of proximity coupling with the substrate. Through the effective Hamiltonian method, the derived effective Zeeman fields from the $K/K^{\prime }$ point and the $\mathrm{\Gamma }$ point are greatly different, due to the combination with other factors, such as the difference of the $g$ factor, the existence of charge transfer, or electrostatic interaction with the substrate. The greatly manipulated asymmetric electronic structure and spin/valley splittings can be realized in the spin- and valley-polarized transmission, which are of some significance for the realization of spintronic and valleytronic devices using magnetic substrates and Janus two-dimensional materials.

Monolayer $\mathrm{Cu}M{\mathrm{P}}_2{X}_6$ $(M=\mathrm{Cr},\mathrm{V};X=\mathrm{S},\mathrm{Se})$ has been attracting increasing attention due to the ferromagnetism derived from the indirect exchange interaction between Cr (V) atoms and the ferroelectricity originating from the spontaneous displacement of Cu atoms. Using first-principles calculations, we predicted the intrinsic valley splittings and anomalous valley Hall effect in $\mathrm{Cu}M{\mathrm{P}}_2{X}_6$ monolayers. In addition, the valley splittings and Berry curvature are independent of the orientation of out of plane (OOP) ferroelectric polarization, which makes it a promising storage device with dual degrees of freedom in ferroelectric polarization and ferrovalleys. Due to the variations in the energy of the spin-dependent valence-band maximum (VBM) and orbital compositions of the valleys, the magnitude of valley splitting at VBM can be effectively tuned by the biaxial strain and external electric field. Large OOP magnetic anisotropy can be obtained by changing the energy and occupation (unoccupation) states of $d$ orbital compositions through strain and charge doping, respectively, and the magnetic anisotropy of $\mathrm{Cu}M{\mathrm{P}}_2{X}_6$ increases with increasing tensile biaxial strain from −5% to 5%. Our research results are expected to tune the valley splittings and magnetic anisotropy of $\mathrm{Cu}M{\mathrm{P}}_2{X}_6$ and to help understand the physical mechanism.

Lateral heterostructures built from an armchair MoS₂ nanoribbon (AMoS₂NR) and an armchair NbS₂ nanoribbon (ANbS₂NR) were studied based on first-principles calculations and a non-equilibrium Green's function method. It is found that the work function of the AMoS₂NR shows substantial oscillation with increasing nanoribbon width, which is different from the work functions of other kinds of nanoribbons. The AMoS₂NR–ANbS₂NR lateral heterostructure exhibits an anomalous transport gap that is much larger than the bandgap of the AMoS₂NR. As a result, a field effect transistor with AMoS₂NR as the channel and ANbS₂NRs as electrodes has high on–off ratios of 10⁶–10⁷ and a tiny leakage current of the order of 10⁻⁸ μA. These results suggest that lateral metal–semiconductor heterostructures of transition metal dichalcogenides may have potential applications in nanodevices with low energy consumption.