  Recently, the quantum anomalous Hall (QAH) insulators are predicted in
Lithium-decorated iron-based superconductor monolayer materials (LiFeX (X=S, Se
and Te)) with very high Curie temperature (\textcolor[rgb]{0.00,0.00,1.00}{PRL
125, 086401 (2020)}), which combines the topological and ferromagnetic (FM)
orders. It is interesting and useful to achieve coexistence of intrinsic
piezoelectricity, ferromagnetism and nontrivial band topology in single
two-dimensional (2D) material, namely 2D piezoelectric quantum anomalous hall
insulator (PQAHI). In this work, 2D Janus monolayer $\mathrm{Li_2Fe_2SSe}$ is
predict to be a room-temperature PQAHI, which possesses dynamic, mechanical and
thermal stabilities. It is predicted to be a half Dirac semimetal without
spin-orbit coupling (SOC). It is found that the inclusion of SOC opens up a
large nontrivial gap, which means the nontrivial bulk topology (QAH insulator),
confirmed by the calculation of Berry curvature and the presence of two chiral
edge states (Chern number C=2). Calculated results show that monolayer
$\mathrm{Li_2Fe_2SSe}$ possesses robust QAH states against biaxial strain and
electronic correlations. Compared to LiFeX, the glide mirror $G_z$ of
$\mathrm{Li_2Fe_2SSe}$ disappears, which will induce only out-of-plane
piezoelectric response. The calculated out-of-plane $d_{31}$ of monolayer
$\mathrm{Li_2Fe_2SSe}$ is -0.238 pm/V comparable with ones of other 2D known
materials. Moreover, very high Curie temperature (about 1000 K) is predicted by
using Monte Carlo (MC) simulations, which means that the QAH effect can be
achieved at room temperature in Janus monolayer $\mathrm{Li_2Fe_2SSe}$. Similar
to monolayer $\mathrm{Li_2Fe_2SSe}$, the PQAHI can also be realized in the
Janus monolayer $\mathrm{Li_2Fe_2SeTe}$.
