I will discuss how the presence of topological nodal points in the bulk three-dimensional electronic band structure of a material can be inferred by resolving its particle-hole continuum in energy and momentum. I will first highlight some geometric characteristics of the particle-hole continuum of a noninteracting electron system when nodal points are present in its energy dispersion, either below or above the Fermi level. I will then argue that resonant inelastic x-ray scattering (RIXS) is an appealing tool for directly accessing and studying the features of the particle-hole continuum of topological semimetals, especially in settings that preclude the use of other probes, such as within magnetic fields. Going a step further, I will discuss how polarization-resolved RIXS can be used to visualize the Berry curvature distribution around Weyl nodes and thus determine their topological charge. This indicates the potential for measurement of quantized topological invariants using RIXS. I will conclude with a quick overview of ongoing experimental and theoretical work.
