  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.
