Microwave hinge states in a simple-cubic-lattice photonic crystal insulator

We numerically and experimentally demonstrated a higher-order topological state in a three-dimensional (3D) photonic crystal (PhC) with a complete photonic bandgap. Two types of cubic lattices were designed with different topological invariants, which were theoretically and numerically confirmed by the finite difference of their Zak phases. Topological boundary states in the two-dimensional interfaces and hinge states in the one-dimensional corners were formed according to the higher-order of bulk-boundary correspondence. Microwave measurements of the fabricated 3D PhC containing two boundaries and one corner showed a localized intensity, which confirmed the boundary and hinge states.