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

The tight-binding model of the non-uniform square-octagon lattice is investigated, with two kinds of spin-orbit couplings denoted asλso1andλso2. The topological invariant<i>Z</i>₂is evaluated numerically using the Fukui-Hatsugai method. A comprehensive analysis is conducted on the influence of two spin-orbit couplingsλso1andλso2on the electronic band structure and the associated topological phase transition. Bothλso1andλso2are 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 couplingλso1drives the system into a quantum spin Hall (QSH) phase. In contrast,λso2only 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.