  Topological phonics has emerged as a novel approach to engineer the flow of
light and provides unprecedented means for developing diverse photonic
elements, including robust optical waveguides immune to structural
imperfections. However, the development of nanoscale standing-wave cavities in
topological photonics is rather slow, despite its importance when building
densely-integrated photonic integrated circuits. In this Letter, we report a
photonic crystal nanocavity based on a topological corner state, supported at a
90-degrees-angled rim of a two dimensional photonic crystal. A combination of
the bulk-edge and edge-corner correspondences guarantees the presence of the
higher-order topological state in a hierarchical manner. We experimentally
observed a corner mode that is tightly localized in space while supporting a
high Q factor over 2,000, verifying its promise as a nanocavity. These results
cast new light on the way to introduce nanocavities in topological photonics
platforms.
