Electronic and valley properties of Janus $\mathrm{Te}M\mathrm{Si}{X}_2$ ($M=\mathrm{Mo},W$; $X=P,\mathrm{As}$) monolayers and $\mathrm{Te}M\mathrm{Si}{X}_2/{\mathrm{CrI}}_3$ heterostructures

In this study, we investigate $\mathrm{Te}M\mathrm{Si}{X}_2$ ($M=\mathrm{Mo}$ and W; $X=P$ and As) Janus monolayers, identifying them as direct band-gap semiconductors exhibiting two distinctive valley within both the conduction and valence bands. $\mathrm{Te}M\mathrm{Si}{X}_2$ exhibits significant valley spin splitting (VSS) in the valence band, especially in ${\mathrm{TeWSiP}}_2$ and ${\mathrm{TeWSiAs}}_2$ (up to 0.48 and 0.53 eV). Furthermore, the construction of $\mathrm{Te}M\mathrm{Si}{X}_2/{\mathrm{CrI}}_3$ heterostructure introduces valley polarization, with magnitudes ranging from 2.9 meV for ${\mathrm{TeMoSiP}}_2/{\mathrm{CrI}}_3$ to up to 26.1 meV for ${\mathrm{TeWSiAs}}_2/{\mathrm{CrI}}_3$. Manipulating the magnetization direction of ${\mathrm{CrI}}_3$ or the interlayer spacing results in alterations of valley polarization in $\mathrm{Te}M\mathrm{Si}{X}_2/{\mathrm{CrI}}_3$. These findings provide valuable guidance for the further development of valleytronic devices based on $\mathrm{Te}M\mathrm{Si}{X}_2$ Janus monolayers.