Bulk-disclination correspondence in topological crystalline insulators.

Most natural and artificial materials have crystalline structures from which abundant topological phases emerge1–6. However, the bulk–edge correspondence—which has been widely used in experiments to determine the band topology from edge properties—is inadequate in discerning various topological crystalline phases7–16, leading to challenges in the experimental classification of the large family of topological crystalline materials4–6. It has been theoretically predicted that disclinations—ubiquitous crystallographic defects—can provide an effective probe of crystalline topology beyond edges17–19, but this has not yet been confirmed in experiments. Here we report an experimental demonstration of bulk–disclination correspondence, which manifests as fractional spectral charge and robust bound states at the disclinations. The fractional disclination charge originates from the symmetry-protected bulk charge patterns—a fundamental property of many topological crystalline insulators (TCIs). Furthermore, the robust bound states at disclinations emerge as a secondary, but directly observable, property of TCIs. Using reconfigurable photonic crystals as photonic TCIs with higher-order topology, we observe these hallmark features via pump–probe and near-field detection measurements. It is shown that both the fractional charge and the localized states emerge at the disclination in the TCI phase but vanish in the trivial phase. This experimental demonstration of bulk–disclination correspondence reveals a fundamental phenomenon and a paradigm for exploring topological materials. It is experimentally shown that topological states exist at crystallographic defects in the bulk and that disclination defects trap fractional charges characteristic of topological crystalline insulators.