Magnetic-field tunable Möbius and higher-order topological insulators in three-dimensional layered octagonal quasicrystals

The authors demonstrate here that layered magnetic quasicrystals with eightfold rotational symmetry can host a series of magnetic field tunable topological phases. By combining canted antiferromagnetic order and octagonal warping effect, they reveal the emergence of a glide symmetry protected M"obius insulator and multiple higher-order topological insulator (HOTI) phases, distinguished by their hinge-mode configurations. Their findings establish quasicrystals as a fertile platform for realizing symmetry-protected topological phenomena beyond periodic lattices, and offer a new route for magnetic control of higher-order topology.