Coexistence of intrinsic piezoelectricity, ferromagnetism and nontrivial band topology in Li-decorated Janus monolayer $\mathrm{Fe_2SSe}$ with high Curie temperature

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 $\mathrm{Li_2Fe_2SeTe}$.