Emergent Spin Hall Quantization and High‐Order van Hove singularities in Square‐Octagonal MA ₂ Z ₄

ABSTRACT 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 sensitive to material‐specific electronic structures. Here, we predict a class of seven‐layered square‐octagonal (M = Mo/W, A = Si/Ge, Z = Pnictogen) isomers that host a large‐gap QSH phase with nearly quantized spin Hall conductivity and intrinsic high‐order VHSs. Topological and symmetry analyses reveal that compounds with Z = P, As, and Sb are nontrivial with spin Chern number and support ‐polarized edge states, while those with Z = N are trivial insulators. The QSH phase features an ‐conserving spin Hamiltonian consistent with an emergent spin quasi‐symmetry, yielding spin Hall conductivity . Notably, (As, Sb) compounds exhibit quasi‐flat bands near the Fermi level in the inverted regime, with additionally hosting four high‐order VHSs at generic momentum points. These results position square‐octagonal materials as robust QSH insulators for realizing quantized spin Hall conductivity and correlated topological phases, including fractionalized states and possibly non‐Abelian anyons.