Dual-band topological Bott insulators in Ammann–Beenker-tiling square photonic quasicrystals - Yingfang Zhang; Zhihao Lan; Weicheng Chen; Jianqing Li (JPhys Photonics)
In this work, we study topological states in Ammann–Beenker-tiling photonic quasicrystals made of magneto-optical materials. While conventional topological states in photonic systems with crystalline symmetry are characterized by topological invariants associated with bulk Bloch bands in momentum space, photonic systems in quasicrystal geometries typically lack exact periodicity and translational symmetry. As a result, conventional topological invariants defined in momentum space for photonic crystals, such as Chern number, are not applicable for photonic quasicrystals. Instead, a topological invariant called Bott index defined in real space could be employed for characterizing the topological properties of photonic quasicrystals, which we term as topological Bott insulators. In specific, we investigate the topological properties of photonic quasicrystals made of gyromagnetic dielectric cylinders arranged in a two-dimensional Ammann–Beenker tiling quasicrystalline lattice and find that this system supports dual-band chiral topological edge states, where the topological nature of both bandgaps is unambiguously confirmed by explicit calculations of the Bott index. Our work not only provides new insights on topological states in photonic quasicrystals based on the Ammann–Beenker-tiling, the results may also offer promising potentials for robust multiband photonic devices and applications not constrained by crystalline symmetries.