Raman scattering is emerging as a surprising probe of electron topology in quantum materials. It has been used recently to detect and characterize a topological phase transition that accompanies the magnetic transition in ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$. Here we present a theory of Raman scattering from nodal electrons with Weyl and quadratic band touching spectra, which has to reach beyond the standard effective mass approximation. After reviewing and providing the details of our previous theory development, we discuss several new results. We show that the light-polarization dependence of Raman scattering is universal in the case of Weyl electrons and given by an analytic expression, while it contains symmetry-protected features in the case of quadratic band-touching nodes. We also analyze modifications of the Raman signal due to the ubiquitous tilting of the Weyl spectrum, and argue that universality is lost only in a finite frequency range that springs out of the threshold frequency for untilted nodes. Finally, we explore the frequency dependence of Raman scattering for the case of Dirac electrons coexisting with a flat band in the same region of the first Brillouin zone, which is inspired by the material ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$.

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• Dirac fermions
• Optical & microwave phenomena
• Topological phases of matter
• Weyl fermions
• Dirac semimetal
• Weyl semimetal
• Diagrammatic methods
• Inelastic light scattering