  Most natural and artificial materials have crystalline structures from which
abundant topological phases emerge [1-6]. The bulk-edge correspondence,
widely-adopted in experiments to determine the band topology from edge
properties, however, becomes inadequate in discerning various topological
crystalline phases [7-17], leading to great challenges in the experimental
classification of the large family of topological crystalline materials [4-6].
Theories predict that disclinations, ubiquitous crystallographic defects,
provide an effective probe of crystalline topology beyond edges [18-21], which,
however, has not yet been confirmed in experiments. Here, we report the
experimental discovery of the bulk-disclination correspondence which is
manifested as the 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). Meanwhile, 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 those hallmark features via pump-probe and near-field
detection measurements. Both the fractional charge and the localized states are
demonstrated to emerge at the disclination in the TCI phase but vanish in the
trivial phase. The experimental discovery of bulk-disclination correspondence
unveils a novel fundamental phenomenon and a new paradigm for exploring
topological materials.
