The bulk-edge correspondence predicts topologically protected edge-states immune to disorder and material defects at the interface of inequivalent media. These modes propagate within a common frequency band gap when one of the materials possesses a topological invariant, such as the gap Chern number, that is non-trivial. Three-dimensional (3D) systems can also host gapless topological phases, such as the semi-metal phase, characterized by linear crossings between topologically inequivalent bands, otherwise known as Weyl points. These are monopoles of Berry curvature in momentum space and may arise in pairs by breaking parity (P) symmetry, time-reversal (T) symmetry or both, hence being robust against perturbations.
In this contribution, a first principles method is used to compute the Weyl point’s chirality and to topologically characterize a dispersive Hermitian continuous system, specifically, a magnetized plasma. The method does not require calculating the eigenfunctions of the full band structure, since it quantifies the flux of the Berry curvature using an equivalent definition by means of the photonic Green’s function. A connection between the gap Chern number and the Weyl point’s chirality will be highlighted when considering the flux of the Berry curvature through surfaces defined in two and three-dimensional momentum space. Three different models will be analysed for this purpose: a local framework and two frameworks including spatial dispersion which are the hydrodynamic and the full spatial cut-off models. We extend this formalism to non-Hermitian systems, where the Weyl point evolves into a continuous ring of exceptional points. This transformation may significantly impact wave propagation, leading to novel behaviours such as non-reciprocal transport with enhanced sensitivity to perturbations, which are characteristic of these topological features.