An all-dielectric photonic crystal with unconventional higher-order topology

Abstract: Photonic crystals 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 photonic crystals which are yet to be explored. Here, we propose a dielectric photonic crystal with 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 photonic crystal 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 band filling anomaly in electronic systems. Furthermore, we show that by introducing a disclination in the proposed photonic crystal, localized states and a 2/3 fractional spectral charge emerge around the disclination core, as the manifestation of the bulk disclination correspondence. 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.