Theoretical prediction of electronic, transport, optical, and thermoelectric properties of Janus monolayers <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>In</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mi>X</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math> (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">S</mml:mi><mml:mo>,</mml:mo><mml:mi>Se</mml:mi><mml:mo>,</mml:mo><mml:mi>Te</mml:mi></mml:mrow></mml:math>)

The breaking of the vertical symmetry in Janus monochalcogenides gave rise to many properties that were not present in the original monochalcogenide monolayers. However, recent papers have often focused only on Janus monochalcogenides containing S, Se, and Te elements despite that O is also one of the group VI chalcogen elements. In this paper, we systematically investigate the electronic, transport, optical, and thermoelectric properties of Janus monolayers ${\mathrm{In}}_{2}X\mathrm{O}$ ($X=\mathrm{S},\mathrm{Se},\mathrm{Te}$) using first-principles calculations. Based on phonon spectrum analysis and ab initio molecular dynamics simulations at room temperature, ${\mathrm{In}}_{2}X\mathrm{O}$ monolayers were reported to be stable. Our calculations reveal that, while ${\mathrm{In}}_{2}\mathrm{SO}$ is an indirect semiconductor, ${\mathrm{In}}_{2}\mathrm{SeO}$ exhibits a direct semiconducting characteristic, and biaxial strain can lead to the semiconductor-metal phase transition in ${\mathrm{In}}_{2}\mathrm{SeO}$. Monolayer ${\mathrm{In}}_{2}\mathrm{TeO}$ is metal at equilibrium, and its metallic characteristics are prevented under biaxial strains. Calculations for transport properties show that the carrier mobilities of ${\mathrm{In}}_{2}\mathrm{SO}$ and ${\mathrm{In}}_{2}\mathrm{SeO}$ monolayers are highly anisotropic, and electron mobility of ${\mathrm{In}}_{2}\mathrm{SO}$ exceeds $3\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}/\mathrm{Vs}$. In this paper, the optical and thermoelectric properties of ${\mathrm{In}}_{2}\mathrm{SO}$ and ${\mathrm{In}}_{2}\mathrm{SeO}$ monolayers are also investigated and discussed in detail. Finally, the electronic properties of all four possible stacking configurations of the Janus bilayers are briefly calculated. Our findings not only contribute to a more general view of the physical properties of the Janus group III monochalcogenides but also recommend them as potential nanomaterials for applications in optoelectronic and thermal devices.