Strong structural asymmetry is actively explored in two-dimensional (2D) materials, because it can give rise to many interesting physical properties. Motivated by the recent synthesis of monolayer $\mathrm{Si_2Te_2}$, we explore a family of 2D materials, termed as the Janus Si dichalcogenides (JSD), which parallel the Janus transition metal dichalcogenides and exhibit even stronger inversion asymmetry. Using first-principles calculations, we demonstrate excellent stability of these materials. We show that their strong structural asymmetry leads to pronounced intrinsic polar field, sizable spin splitting due to spin-orbit coupling, and large piezoelectric response. The spin splitting involves an out-of-plane component, which is beyond the linear Rashba model. The piezoelectric tensor has large value in both in-plane $d_{11}$ coefficient and out-of-plane $d_{31}$ coefficient, making the monolayer JSDs distinct among the existing 2D piezoelectrics. In addition, we find interesting strain-induced phase transitions in these materials. Particularly, there are multiple valleys in the conduction band that compete for the conduction band minimum, which will lead to notable changes in optical and transport properties under strain. Our work reveals a new family of Si based 2D materials, which could find promising applications in spintronic and piezoelectric devices.
8 pages, 8 figures