Square-root higher-order topological insulators (HOTIs) are recently discovered new topological phases, with intriguing topological properties inherited from a parent lattice Hamiltonian. Different from conventional HOTIs, the square-root HOTIs typically manifest two paired nonzero energy corner states. In this work, we experimentally demonstrate the second-order square-root HOTIs in photonics for the first time to our knowledge, thereby unveiling such distinct corner states. The specific platform is a laser-written decorated honeycomb lattice (HCL), for which the squared Hamiltonian represents a direct sum of the underlying HCL and breathing Kagome lattice. The localized corner states residing in different bandgaps are observed with characteristic phase structures, in sharp contrast to the discrete diffraction in a topologically trivial structure. Our work illustrates a scheme to study fundamental topological phenomena in systems with the coexistence of spin-1/2 and spin-1 Dirac-Weyl Fermions and may bring about new possibilities in topology-driven photonic devices.

中文翻译：

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二阶光子平方根拓扑绝缘体的实现

平方根高阶拓扑绝缘体 (HOTI) 是最近发现的新拓扑相，具有从父晶格哈密顿量继承的有趣拓扑特性。与传统的 HOTI 不同，平方根 HOTI 通常表现出两个成对的非零能量角状态。在这项工作中，我们首次通过实验证明了光子学中的二阶平方根 HOTI，从而揭示了这种不同的角态。特定平台是激光书写的装饰蜂窝晶格 (HCL)，其平方哈密顿量表示底层 HCL 和呼吸 Kagome 晶格的直接和。观察到存在于不同带隙中的局部角态具有特征相结构，与拓扑微不足道结构中的离散衍射形成鲜明对比。