Fig. 1. (Color online) (a, b) Top and side views of SL VXY. The illustrations in (a) indicate VXY trigonal prismatic geometry. (c) The 2D Brillouin zone of VXY.

Fig. 2. (Color online) (a) Calculated electronic band structures of the VBrSe monolayer without and with SOC. (b) The projected band structures of the VbrSe monolayer without and with SOC, respectively.

Fig. 3. (Color online) (a, b) In-plane spin-polarization components of two bands around Γ. (c) Magnified view of the band structure around Γ. (d) Spin texture of Janus VBrSe.

Fig. 4. (Color online) Comparison of Rashba parameters of VXY structure with MoSSe, MoSTe and WSSe.

Fig. 5. (Color online) (a) Valley and spin coupling in VXY optical selection rules. Discrete valleys coupled to different circular helicities (σ⁺, σ⁻) with transition frequencies (ω_u, ω_d). (b) Photoinduced valley Hall effect when circularly polarized light incident on it, in which the charge Hall current is spin and valley polarized. (c) Spin and valley Hall effects under linearly polarized optical field. (d) Valley polarization with opposite circular polarization having a frequency ω_u and ω_d.

Fig. 6. (Color online) Berry curvature of Janus VBrSe (a) in the full Brillouin zone and (c) along high-symmetry points. (b) Berry curvature value of VXY. (d) Diagrammatic sketch of valley Hall effects and rapid carrier transfer in Janus VBrSe.

Fig. 7. (Color online) (a) Changes in Berry curvature of VBrSe with external strain. (b) The relevance between strain and the value of berry curvature.

Table 1. The structural parameters, band gaps, total magnetic moments ( ) and local magnetic moments ( ) of VXY monolayers are calculated. The lattice constant ( = b), bond length of V–X(l₁) and V–Y(l₂) are presented. In each VXY system, the atomic number of Y is greater than that of X, so that l₁ < l₂.

Table 2. Band structure analysis of VXY. ΔC and ΔV are the magnitude of the energy band split between the conduction band and the valence band at point K. E_g is the band gap at K point. and K_r are the splitting of the energy and wave vector. is the Rashba parameter.