Emergent Spin Hall Quantization and High-Order van Hove singularities in Square-Octagonal MA2Z4

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.