Majorana spectroscopy of three-dimensional Kitaev spin liquids

We analyze the dynamical response of a range of three-dimensional Kitaev quantum spin liquids, using lattice models chosen to explore the different possible low-energy spectra for gapless Majorana fermions, with either Fermi surfaces, nodal lines, or Weyl points. We find that the behavior of the dynamical structure factor is distinct in all three cases, reflecting the quasiparticle density of states in two fundamentally different ways. First, the low-energy response is either straightforwardly related to the power with which the low-energy density of states vanishes; or for a nonvanishing density of states, to the phase shifts encountered in the corresponding x-ray edge problem, whose phenomenology we extend to the case of Majorana fermions. Second, at higher energies, there is a rich fine structure, determined by microscopic features of the Majorana spectrum. Our theoretical results test the usefulness of inelastic neutron scattering as a probe of these quantum spin liquids: we find that although spin flips fractionalize, the main features of the dynamical spin response nevertheless admit straightforward interpretations in terms of Majorana and flux loop excitations.