Topological Surface State by Hierarchical Concatenation of Photonic Stopbands

We have designed, investigated, and experimentally realized a topological surface state (TSS) localized at the interface of two stratified photonic media. The manifested state is protected by the spatial inversion symmetry of the constituents, which permits the assignment of quantized topological invariants to them. The genesis of the surface state can be traced to the characteristic difference in the bulk topological behavior of the underlying stopbands. Specifically, in the present realization of TSS, we have resorted to a concatenation of topologically inequivalent first and second-order stopbands of two planar photonic crystals and established the disparity in their stopband characteristics.