Realization of second-order photonic square-root topological insulators.

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 non-zero 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 discrete diffraction in a topologically trivial structure. Our work illustrates a scheme to study fundamental topological phenomena in systems with coexistence of spin-1/2 and spin-1 Dirac-Weyl fermions, and may bring about new possibilities in topology-driven photonic devices.