Topological Insulators are a novel state of matter where spectral bands are characterized by quantized topological invariants. This unique quantized nonlocal property commonly manifests through exotic bulk phenomena and corresponding robust boundary effects. In our work we study a system where the spectral bands are associated with non-quantized indices, but nevertheless possess robust boundary states. We present a theoretical analysis, where we show that the square of the Hamiltonian exhibits quantized indices. The findings are experimentally demonstrated by using photonic Aharonov-Bohm cages.

中文翻译：

---

通过光子Aharonov-Bohm笼实现具有非量化索引的平方根拓扑绝缘子。

拓扑绝缘子是一种新型的物质状态，其中光谱带的特征是量化的拓扑不变性。这种独特的量化的非局部属性通常通过奇异的体积现象和相应的鲁棒边界效应来体现。在我们的工作中，我们研究了一个谱带与非量化指标相关联的系统，但是该系统具有强大的边界状态。我们提供了一种理论分析，其中我们证明了哈密顿量的平方具有量化指标。通过使用光子Aharonov-Bohm笼实验证明了这一发现。