Intercalated architecture of MA2Z4 family layered van der Waals materials with emerging topological, magnetic and superconducting properties

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 $\alpha_i$- and $\beta_i$-$MA_2Z_4$ 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 $\alpha_1$-MoSi$_2$N$_4$, $\alpha_1$-WSi$_2$N$_4$ and $\beta_5$-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 $\alpha_2$-WSi$_2$P$_4$ for the spin-valley polarization, $\alpha_1$-TaSi$_2$N$_4$ for Ising superconductor and $\beta_2$-SrGa$_2$Se$_4$ for topological insulator.