Quantized spin Hall effect and high-order van Hove singularities in square-octagonal MA₂Z₄ compounds

Quantum spin Hall (QSH) insulators are versatile platforms for exploring exotic quantum phases, especially when combined with high-order van Hove singularities (VHSs) that enhance electron correlations. However, perfect spin Hall quantization is often hindered by spin mixing from strong spin-orbit coupling, and the emergence of such VHSs is highly sensitive to material-specific electronic structures. Here, we predict a class of seven-layered square-octagonal MA₂Z₄(M = Mo/W, A = Si/Ge, Z = Pnictogen) isomers that host a robust, large-gap QSH phase with nearly quantized spin Hall conductivity (SHC) and intrinsic high-order VHSs. Topological and symmetry analyses reveal that compounds with Z = P, As, and Sb are Z₂ nontrivial with spin Chern number C_s = 1 and support S_z-polarized edge states, while those with Z = N are trivial insulators. The QSH phase features an S_z-conserving spin Hamiltonian consistent with an emergent spin U(1) quasi-symmetry, yielding SHC ~2e²/h. Notably, MA₂(As,Sb)₄ compounds exhibit quasi-flat bands near the Fermi level in the inverted regime, with WSi₂Sb₄ additionally hosting four high-order VHSs at generic momentum points. These results position square-octagonal MA₂Z₄ materials as robust QSH insulators for realizing quantized SHC and correlated topological phases, including fractionalized states and possibly non-Abelian anyons.