Multifold bulk-boundary correspondence in a gyromagnetic photonic crystal

In topological photonics, the bulk-boundary correspondence (BBC) predicts the existence of boundary states through bulk topological invariants, typical examples being quantum anomalous Hall (QAH) phases responsible for boundary optical robust transport and second-order topological phases capable of corner local field enhancement. However, achieving multifold BBC, i.e., the coexistence of first-order and higher-order topological phases in a single photonic system, remains a critical unresolved scientific question. Here, we report the first experimental observation in a gyromagnetic photonic crystal, in which the QAH phase is induced by breaking the time-reversal symmetry and the second-order topological insulator phase is protected by the fourfold rotational symmetry. The photonic chiral edge and magnetic corner modes are confirmed by measuring the field distribution. This work not only enriches the classification of topological matter, but also provides new possibilities for the application of photonic crystals in the field of low-energy information processing.