Tunable valley-spin splitting in a Janus XMSiN2 monolayer (X=S, Se; M

Exploring spin-valley coupling in two-dimensional (2D) materials with strong spin-orbit coupling (SOC) is of great significance for fundamental physics and practical applications. Using first-principles calculations, we investigate the valley-related properties of Janus $XM{\mathrm{SiN}}_{2}$ $(X=\mathrm{S}, \mathrm{Se}; M=\mathrm{Mo}, \mathrm{Cr})$ monolayer. The Janus $XM{\mathrm{SiN}}_{2}$ monolayer forms a pair of nonequivalent valleys, and the conduction and valence bands are degenerated at the valleys. The inversion symmetry breaking and the SOC effect induce remarkable valley spin splitting and Rashba spin splitting. Our calculations indicate that not only valley-contrasting transport properties but also optical selection rules with spin-valley coupling result in the coexistence of spin and valley Hall effects in the Janus $XM{\mathrm{SiN}}_{2}$ monolayer. Moreover, we demonstrate that the valley-spin physics of the Janus $XM{\mathrm{SiN}}_{2}$ monolayer can be modulated by in-plane biaxial strains, allowing its extraordinary potential for spintronics and valleytronic applications. We also show that V-doped ${\mathrm{SMoSiN}}_{2}$ monolayer can exhibit giant valley polarization of 89.51 meV $(\ensuremath{-}24.48 \mathrm{meV})$ for the valence (conduction) band. These findings could be helpful for the valleytronic applications of the Janus $XM{\mathrm{SiN}}_{2}$ monolayer.