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Structure-driven intercalated architecture of septuple-atomic-layer $MA_2Z_4$ family with diverse properties from semiconductor to topological insulator to Ising superconductor

Motivated by the fact that septuple-atomic-layer MnBi$_2$Te$_4$ can be structurally viewed as the combination of double-atomic-layer MnTe intercalating into quintuple-atomic-layer Bi$_2$Te$_3$, we present a general approach of constructing twelve septuple-atomic-layer $α_i$- and $β_i$-$MA_2Z_4$ monolayer family (\emph{i} = 1 to 6) by intercalating MoS$_2$-type $MZ$$_2$ monolayer into InSe-type A$_2$Z$_2$ monolayer. Besides reproducing the experimentally synthesized $α_1$-MoSi$_2$N$_4$, $α_1$-WSi$_2$N$_4$ and $β_5$-MnBi$_2$Te$_4$ monolayer materials, another 66 thermodynamically and dynamically stable $MA_2Z_4$ were predicted, which span a wide range of properties upon the number of valence electrons (VEC). $MA_2Z_4$ with the rules of 32 or 34 VEC are mostly semiconductors with direct or indirect band gap and, however, with 33 VEC are generally metal, half-metal ferromagnetism, or spin-gapless semiconductor upon whether or not an unpaired electron is spin polarized. Moreover, we propose $α_2$-WSi$_2$P$_4$ for the spin-valley polarization, $α_1$-TaSi$_2$N$_4$ for Ising superconductor and $β_2$-SrGa$_2$Se$_4$ for topological insulator.