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Abstract Recently, the studies of topological corner states (TCSs) have been extended from crystals to quasicrystals, which are referred to as higher‐order topological quasicrystalline insulators (HOTQIs). However, the TCSs of complete quasi‐periodic structure in photonic systems have yet to be demonstrated. Moreover, there is only one TCS in each corner region in higher‐order topological insulators (HOTIs). Increasing the number of TCS is expected to increase the application potential of TCSs. In this work, HOTQIs in photonic systems are experimentally observed. It is found that HOTQIs possess TCS arrays, and each TCS array contains several TCSs. Furthermore, the universal theoretical framework of the multimer analysis method is improved, and the difference in the average charge density is proposed as a real‐space topological index. These results will open up new ideas for investigating highly integrated, multi‐region localized TCSs and are expected to provide new ways to explore topological phenomena and the applications of photonic quasicrystals.
Shi et al. (Mon,) studied this question.