Higher-Order Topological States in Photonic Thue-Morse Quasicrystals: Quadrupole Insulator and the Origin of Corner States

Abstract

Corner states (CSs) in higher-order topological insulators (HOTIs) have recently been of great interest in both crystals and quasicrystals. In contrast to electronic systems, HOTIs have not been found in photonic quasicrystals (PQCs). Here, we systemically study the higher-order topology in the two-dimensional Thue-Morse photonic quasicrystals (TM PQCs). Not only the topological phase transition and the nontrivial CSs with fractional charge induced by multipole moments, but also another type of CSs are found due to the complex structure of TM PQCs near corners. The different origins of these CSs are also analyzed based on the tight-binding model. Our work opens the door to explore richer HOT physics beyond photonic crystals and the robustness of CSs in PQC shows the potential for applications.