  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.
