Phonon dynamics in two- and three-dimensional Kitaev spin liquids

In recent years, it has been shown that the phonon dynamics may serve as an indirect probe of fractionalization of spin degrees of freedom. Here we propose that the sound attenuation, measurable by the ultrasound experiments, allows for the characterization and identification of the Kitaev quantum spin liquid in both two- and three dimensions. In both cases, the sound attenuation has a characteristic angular and temperature dependences, which reflect the various nodal structures of Majorana fermions possible in the Kitaev spin liquids. We present our resuts for the sound attenuation in honeycomb and hyperhonecomb Kitaev models, since these two models are relevant for Kitaev candidate materials $alpha$-RuCl$_3$ and $eta$-Li$_2$IrO$_3$, respectively.