Recently, a group of MAX phases, (Mo$_{2/3}$Y$_{1/3}$)$_2$AlC, (Mo$_{2/3}$Sc$_{1/3}$)$_2$AlC, (W$_{2/3}$Sc$_{1/3}$)$_2$AlC, (W$_{2/3}$Y$_{1/3}$)$_2$AlC, and (V$_{2/3}$Zr$_{1/3}$)$_2$AlC, with in-plane ordered double transition metals, named iMAX phases, have been synthesized. Experimentally, some of these MAX phases can be chemically exfoliated into two-dimensional (2D) single- or multilayered transition metal carbides, so-called MXenes. Accordingly, the 2D nanostructures derived from iMAX phases are named iMXenes. Here, we investigate the structural stabilities and electronic structures of the experimentally discovered iMAX phases and their possible iMXene derivatives. We show that the iMAX phases and their pristine, F, or OH-terminated iMXenes are metallic. However, upon O termination, (Mo$_{2/3}$Y$_{1/3}$)$_2$C, (Mo$_{2/3}$Sc$_{1/3}$)$_2$C, (W$_{2/3}$Y$_{1/3}$)$_2$C, and (W$_{2/3}$Sc$_{1/3}$)$_2$C iMXenes turn into semiconductors. Owing to the absence of centrosymmetry, the semiconducting iMXenes may find applications in piezoelectricity. Our calculations reveal that the semiconducting iMXenes possess giant piezoelectric coefficients as large as 45$times10^{-10}$~C/m.
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