Resonant thermal Hall effect of phonons coupled to dynamical defects

We present computations of the thermal Hall coefficient of phonons scattering off a defect with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon-defect coupling is proportional to the phonon lifetime, and has a `side-jump' interpretation. Consequently, the thermal Hall angle is independent of the phonon lifetime. The contribution to the thermal Hall coefficient is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for three different defect models, which apply to different correlated electron materials. For the pseudogap regime of the cuprates, we propose a model of phonons coupled to an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field, and without spin-orbit interaction.