Observation of bulk-dislocation correspondence in photonic crystals

The emergence of topological edge states is a key feature of various topological phases. This phenomenon, termed the bulk-edge correspondence, is regarded as the major experimental signature of topological materials. Recent theoretical studies reveal that topological defects, such as dislocations, can reveal more information about the topological properties of the hosting materials. Here, we observe such a phenomenon in experiments by engineering dislocations in topological photonic crystals. Instead of the topological edge states, we show that a fractional topological number and a local mode bound to the dislocation can emerge as the experimental manifestation of the underlying topology. The fractional topological number depends on both the photonic band topology in momentum space and the geometry of the dislocation in real space and, thus, it serves as a versatile probe of the band topology. We confirm with experiments that the photonic band topology can indeed be inferred from the fractional topological numbers at various dislocations, uncovering the underlying bulk-defect correspondence. Moreover, the geometry of the dislocation can be engineered, which in turn affects the fractional topological number, indicating the role of the real-space topology of the dislocation. Our work serves as a stepping stone toward probing topological phases with dislocations, especially for crystalline materials and metamaterials with time-reversal symmetry.