Extrinsic Contribution to Bosonic Thermal Hall Transport

Bosonic excitations like phonons and magnons dominate the low-temperature transport of magnetic insulators. Similar to electronic Hall responses, the thermal Hall effect (THE) of charge-neutral bosons has been proposed as a powerful tool for probing topological properties of their wave functions. For example, the contribution of the THE of a perfectly clean system is directly governed by the distribution of Berry curvature, and many experiments on topological magnon and phonon insulators have been interpreted in this way. However, disorder is inevitably present in any material, and its contribution to the THE has remained poorly understood. Here, we develop a rigorous kinetic theory of the side-jump contribution to the THE of bosons. We show that the extrinsic THE is always relevant for bosonic systems and can be of the same order as the intrinsic one but sensitively depends on the type of local imperfection. We study different types of impurities and show that a THE can even arise as a pure impurity-induced effect in a system with a vanishing intrinsic contribution. As a side product, we also generalize existing results for the electronic anomalous Hall effect to general types of impurities beyond the standard assumption of local potential scattering. We discuss the importance of our results for the correct interpretation of THE measurements, for example, in the Kitaev magnet <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>α</a:mi> <a:mtext>−</a:mtext> <a:msub> <a:mi>RuCl</a:mi> <a:mn>3</a:mn> </a:msub> </a:math> , and provide a ready-to-use formula for comparison to experimental data.