  The combination of piezoelectricity with other unique properties (like
topological insulating phase and intrinsic ferromagnetism) in two-dimensional
(2D) materials is much worthy of intensive study. In this work, the
piezoelectric properties of 2D topological insulators InXO (X=Se and Te) from
monolayer InX (X=Se and Te) with double-side oxygen functionalization are
studied by density functional theory (DFT). The large piezoelectric strain
coefficients (e.g. $d_{11}$=-13.02 pm/V for InSeO and $d_{11}$=-9.64 pm/V for
InTeO) are predicted, which are comparable and even higher than ones of many
other familiar 2D materials. Moreover, we propose two strategies to enhance
piezoelectric response of monolayer InXO (X=Se and Te). Firstly, the biaxial
strain (0.94-1.06) is applied, and the $d_{11}$ (absolute value) is increased
by 53\%/56\% for monolayer InSeO/InTeO at 1.06 strain, which is due to
increased $e_{11}$ (absolute value) and reduced $C_{11}-C_{12}$. In considered
strain range, InXO (X=Se and Te) monolayers are always 2D topological
insulators, which confirm the coexistence of piezoelectricity and nontrivial
band topology. Secondly, a Janus monolayer $\mathrm{In_2SeTeO_2}$ is designed
by replacing the top Se/Te atomic layer in monolayer InSeO/InTeO with Te/Se
atoms, which is dynamically and mechanically stable. More excitingly, Janus
monolayer $\mathrm{In_2SeTeO_2}$ is also a 2D topological insulator with
sizeable bulk gap up to 0.158 eV, confirming the coexistence of intrinsic
piezoelectricity and topological nature. The calculated $d_{11}$ is -9.9 pm/V,
which is in the middle of ones of InSeO and InTeO monolayers.

Materials Science