Phonon dynamics in the generalized Kitaev model with magnetic field*

Applying magnetic field to candidate Kitaev materials is a promising avenue in search of the elusive quantum spin liquid (QSL) state.

For example, experiments on the prime candidate α-RuCl₃ in an in-plane magnetic field reveal an intermediate non-magnetically ordered ground state, whose nature is currently under debate. In this work we probe the effects of magnetic field on the Kitaev spin liquid state through phonon dynamics. Specifically, we study the sound attenuation and the Hall viscosity, with characteristic temperature evolution of the phonons coupled to the fermionic Majrana exctiations. We use a mean-field approach to account for the effect of the magnetic field, through the Zeeman term as well as the perturbative  three-spin interaction term kappa,  in the generalized J-K-Γ model pertinent to candidate materials. We  obtain distinct temperature evolution of the sound attenuation expected for phonons scattering on Majorana fermions. We also find

that the phonon dynamics acquires a non-zero Hall viscosity  both in the pure Kitaev and in the generalized J-K-Γ  model as long as  time reversal symmetry is  broken.