Footprints of the Kitaev spin liquid in the Fano lineshapes of the Raman active optical phonons*

We develop a  theoretical  description of the Raman spectroscopy in the spin-phonon coupled Kitaev system and  show that it can provide  intriguing observable signatures of fractionalized excitations characteristic of the underlying spin liquid phase. In particular, we obtain the explicit form of the phonon modes and construct the coupling Hamiltonians based on D3d symmetry. We then systematically compute the Raman intensity and  show that the spin-phonon coupling renormalizes phonon propagators and generates the salient Fano linshape. We find that the temperature evolution of the Fano lineshape displays two crossovers, and the low temperature crossover shows pronounced magnetic field dependence. We thus identify the observable effect of the Majorana fermions and the Z2 gauge fluxes encoded in the Fano lineshape. Our results explain  several phonon Raman scattering experiments in the candidate  material alpha-RuCl3.