Nature of topological protection in photonic spin and valley Hall insulators

Recent interest in optical analogs to the quantum spin Hall and quantum valley Hall effects is driven by the promise to establish topologically protected photonic edge modes at telecommunication and optical wavelengths on a simple platform suitable for industrial applications. While first theoretical and experimental efforts have been made, these approaches so far both lack a rigorous understanding of the nature of topological protection and the limits of backscattering immunity. We here use a generic group theoretical methodology to fill this gap and obtain general design principles for purely dielectric two-dimensional topological photonic systems. The method comprehensively characterizes possible two-dimensional hexagonal designs and reveals their topological nature, potential, and limits.