Non-uniform square–octagon lattice: a new platform for quantum spin Hall insulator

Abstract The tight-binding model of the non-uniform square–octagon lattice is investigated, with two kinds of spin–orbit couplings denoted as λ so 1 and λ so 2 . The topological invariant Z 2 is evaluated numerically using the Fukui-Hatsugai method. A comprehensive analysis is conducted on the influence of two spin–orbit couplings λ so 1 and λ so 2 on the electronic band structure and the associated topological phase transition. Both λ so 1 and λ so 2 are observed to induce band gap closure and reopening, indicative of topological phase transition. In particular, at 1/8 and 3/8 filling fractions, the spin–orbit coupling λ so 1 drives the system into a quantum spin Hall (QSH) phase. In contrast, λ so 2 only stabilizes the QSH phase at 3/8 filling. The presence of topologically protected edge state is further verified, providing robust evidence of the nontrivial topological character of the system. These findings demonstrate that the non-uniform square–octagon lattice can serve as a promising platform for realizing nontrivial topological phases, expanding the family of two-dimensional materials capable of hosting the QSH effect.