All-dielectric photonic crystal with unconventional higher-order topology

Photonic crystals(PhCs) have been demonstrated as a versatile platform for the study of topological phenomena.The recent discovery of higher-order topological insulators introduces new aspects of topological PhCs that are yet to be explored. Here, we propose an all-dielectric PhC with an unconventional higher-order band topology.Besides the conventional spectral features of gapped edge states and in-gap corner states, topological band theory predicts that the corner boundary of the higher-order topological insulator hosts a 2/3 fractional charge. We demonstrate that in the PhC such a fractional charge can be verified from the local density-of-states of photons,through the concept of local spectral charge as an analog of the local electric charge due to the band filling anomaly in electronic systems. Furthermore, we show that by introducing a disclination in the proposed PhC, localized states and a 2/3 fractional spectral charge emerge around the disclination core. The emergence of the fractional spectral charges and topological boundary modes here, however, is distinct from the known cases;particularly by the 2/3 fractional spectral charges and the unique topological indices. The predicted effects can be readily observed in the state-of-the-art experiments and may lead to potential applications in integrated and quantum photonics.