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.

中文翻译：

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具有非常规高阶拓扑的全电介质光子晶体

光子晶体（PhC）已被证明是研究拓扑现象的多功能平台。高阶拓扑绝缘子的最新发现引入了拓扑PhC的新方面，尚待探索。在这里，我们提出了具有非常规高阶带拓扑的全电介质PhC。除了带隙边缘状态和带内拐角状态的常规频谱特征外，拓扑带理论还预测，高阶拓扑绝缘子的拐角边界将承载2/3的分数电荷。我们证明，在PhC中，由于电子系统中的谱带填充异常，可以通过局部光谱电荷作为局部电荷的类似物的概念，从光子的局部状态密度验证这种分数电荷。此外，我们表明，通过在拟议的PhC中引入旋错，在旋错核心周围会出现局部状态和2/3分数谱电荷。但是，这里的分数谱电荷和拓扑边界模式的出现与已知情况截然不同。特别是通过2/3分数谱电荷和独特的拓扑指数。可以在最先进的实验中轻松观察到预期的效果，并可能导致其在集成和量子光子学中的潜在应用。特别是通过2/3分数谱电荷和独特的拓扑指数。可以在最先进的实验中轻松观察到预期的效果，并可能导致其在集成和量子光子学中的潜在应用。特别是通过2/3分数谱电荷和独特的拓扑指数。可以在最先进的实验中轻松观察到预期的效果，并可能导致其在集成和量子光子学中的潜在应用。