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Janus two-dimensional (2D) materials have attracted much attention due topossessing unique properties caused by their out-of-plane asymmetry, which havebeen achieved in many 2D families. In this work, the Janus monolayers arepredicted in new 2D $\mathrm{MA_2Z_4}$ family by means of first-principlescalculations, $\mathrm{MoSi_2N_4}$ and $\mathrm{WSi_2N_4}$ of which have beensynthesized in experiment(\textcolor[rgb]{0.00,0.00,1.00}{Science 369, 670-674(2020)}). The predicted $\mathrm{MSiGeN_4}$ (M=Mo and W) monolayers exhibitdynamic, thermodynamical and mechanical stability, and they are indirectband-gap semiconductors. The inclusion of spin-orbit coupling (SOC) gives riseto the Rashba-type spin splitting, which is observed in the valence bands,being different from common conduction bands. Calculated results show valleypolarization at the edge of the conduction bands due to SOC together withinversion symmetry breaking. It is found that $\mathrm{MSiGeN_4}$ (M=Mo and W)monolayers have high electron mobilities. Both in-plane and much weakout-of-plane piezoelectric polarizations can be observed, when a uniaxialstrain in the basal plane is applied. The values of piezoelectric straincoefficient $d_{11}$ of the Janus $\mathrm{MSiGeN_4}$ (M=Mo and W) monolayersfall between those of the $\mathrm{MSi_2N_4}$ (M=Mo and W) and$\mathrm{MGe_2N_4}$ (M=Mo and W) monolayers, as expected. It is proved thatstrain can tune the positions of valence band maximum (VBM) and conduction bandminimum (CBM), and enhance the the strength of conduction bands convergencecaused by compressive strain. It is also found that tensile biaxial strain canenhance $d_{11}$ of $\mathrm{MSiGeN_4}$ (M=Mo and W) monolayers, and thecompressive strain can improve the $d_{31}$ (absolute values).

Predicted septuple-atomic-layer Janus $\mathrm{MSiGeN_4}$ (M=Mo and W) monolayers with Rashba spin splitting and high electron carrier mobilities