Resonant thermal Hall effect of phonons coupled to dynamical defects

We present computations of the thermal Hall coefficient of phonons scattering off defects 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. This contribution is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for different defect models, and include a model of an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field which we propose applies to the cuprate pseudogap regime.Comment: 5 pages, 3 figure