Prevalence of Two-Dimensional Photonic Topology

Despite intense research in topological photonics for more than a decade, the basic question of whether photonic band topology is rare or abundant - i.e., its relative prevalence - remains open. Here, we use symmetry analysis and a dataset of 550 000 synthetic two-dimensional photonic crystals to determine the prevalence of stable, fragile, and higher-order topology across 11 plane groups and find a general abundance of nontrivial band topology. Below the first band gap and with time-reversal symmetry, stable topology is more prevalent in the transverse electric polarization, is weakly dependent on contrast, and fragile topology is nearly absent. In time-reversal broken settings, Chern insulating phases are also abundant, albeit less so in threefold symmetric settings. Our results elucidate the role of symmetry, dielectric contrast, polarization, and time-reversal breaking in engendering topological photonic phases and may inform new design principles for their experimental realization.