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.