  Topological photonics provides a new paradigm in studying cavity quantum
electrodynamics with robustness to disorder. In this work, we demonstrate the
coupling between single quantum dots and the second-order topological corner
state. Based on the second-order topological corner state, a topological
photonic crystal cavity is designed and fabricated into GaAs slabs with quantum
dots embedded. The coexistence of corner state and edge state with high quality
factor close to 2000 is observed. The enhancement of photoluminescence
intensity and emission rate are both observed when the quantum dot is on
resonance with the corner state. This result enables the application of
topology into cavity quantum electrodynamics, offering an approach to
topological devices for quantum information processing.
