  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.
