First-principles study of topological invariants of Weyl points in continuous media

In recent years there has been a great interest in topological photonics and protected edge states. Here, we present a first-principles method to compute topological invariants of three-dimensional gapless phases. The approach enables the calculation of the topological charges of Weyl points through the use of the photonic Green's function of the system. We take two different approaches, and show that they are consistent. In the first one, we rely on the computation of Chern numbers in two-dimensional cross-sectional planes away from the Weyl point. The second approach is based on direct calculation of the Berry curvature around the Weyl point. We particularize the framework to the Weyl points that emerge in a magnetized plasma due to the breaking of time-reversal symmetry. We discuss the relevance of modeling nonlocality when considering the topological properties of continuous media such as the magnetized plasma. Our theory may be extended to other threedimensional topological phases or to Floquet systems.