Topology of the Valley-Chern Effect*

In this talk, we investigate the quantum valley-Hall effect (QVHE) using a versatile experimental platform based on magnetically coupled spinners. We demonstrate that this regime is not suitable for metamaterial applications due to the delocalization of the interface modes. The enlargement of the bulk gap needs to be accompanied by a Berry curvature engineering that keeps it localized near the valleys. This is a new effect which we call the valley-Chern effect (VCE). By establishing an exact relation between VCE and QVHE, we demonstrate a robust bulk-boundary principle, which could be the foundation of a new wave of applications of topological metamaterials.