We develop a theoretical description of the Raman spectroscopy in the spin-phonon-coupled Kitaev system and show that it can provide 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 Hamiltonian based on the D3d symmetry. We then systematically compute the Raman intensity and show that the spin-phonon coupling renormalizes phonon propagators and generates the salient Fano lineshape. 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 are consistent with the phonon Raman scattering experiments in the candidate material α-RuCl3.
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The authors are thankful to Ken Burch, Jia-Wei Mei, Joji Nasu, Kenya Ohgushi, Thuc T Mai, Luke Sandilands, Yiping Wang, Yang Yang, Mengxing Ye, Shuo Zhang, and especially Dirk Wulferding for valuable discussions. The work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences under Award No. DE-SC0018056. N.B.P. acknowledges the hospitality of the Aspen Center of Physics.
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