Geometric signatures of topological origin in the particle-hole continuum of Weyl semimetals

We present a full geometric description of the particle-hole continuum in Weyl semimetals, emphasizing distinctive features in the joint density of states for particle-hole excitations across nodal points. These are shown to arise as a geometric consequence of the linear effective Hamiltonian around nodal points, and are thus characteristic of Weyl semimetals. We discuss how such geometric characteristics of the particle-hole continuum of Weyl semimetals can be present in resonant inelastic X-ray scattering (RIXS) spectra. Our work provides signatures of the presence of Weyl nodes in bulk band structures, and indicates that RIXS is a promising tool that can potentially be used to identify and characterize nodal points in materials, especially in settings that are difficult to access with other spectroscopies. The calculation presented here also serves as a first checkpoint for comparison with ongoing RIXS experiments.