Observation of monopole topological mode

Among the many far-reaching consequences of the potential existence of a magnetic monopole, it induces a topological zero mode in the Dirac equation, which was derived by Jackiw and Rebbi 48 years ago and has been elusive ever since. Here, we show that the monopole and multi-monopole solutions can be constructed in the band theory by gapping the three-dimensional Dirac points in hedgehog mass configurations. We then experimentally demonstrate such a monopole bound state in an optimized Dirac acoustic crystal structurally modulated in full solid angles. The monopole mode exhibits the optimal scaling behavior — whose modal spacing is inversely proportional to the cubic root of the modal volume. This work completes the kink-vortex-monopole zero-mode trilogy and paves the way for exploring higher-dimensional bulk-topological-defect correspondence. Researchers have achieved the elusive monopole topological defect modes in 3D Dirac crystals with hedgehog mass configurations, completing the bulk topological-defect correspondence in full three dimensions and providing an optimal single mode resonance for future exploration.