Momentum space toroidal moment in a photonic metamaterial

Berry curvature, the counterpart of the magnetic field in the momentum space, plays a vital role in the transport of electrons in condensed matter physics. It also lays the foundation for the emerging field of topological physics. In the three-dimensional systems, much attention has been paid to Weyl points, which serve as sources and drains of Berry curvature. Here, we demonstrate a toroidal moment of Berry curvature with flux approaching to in judiciously engineered metamaterials. The Berry curvature exhibits a vortex-like configuration without any source and drain in the momentum space. Experimentally, the presence of Berry curvature toroid is confirmed by the observation of conical-frustum shaped domain-wall states at the interfaces formed by two metamaterials with opposite toroidal moments. The appearance of toroidal multipolar moments in electrodynamics interrogates the question for their existence in Berry curvature, which can be seen as the "magnetic field" in the momentum space. Here, the authors observe 3D vortex distributions in the Berry curvature within a photonic metamaterial.