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Extrinsic Contribution to Bosonic Thermal Hall Transport

Léo Mangeolle1,2 and Johannes Knolle1,2,3

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Phys. Rev. X 16, 011048 – Published 5 March, 2026

DOI: https://doi.org/10.1103/grzx-v6sj

Abstract

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 intrinsic 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 extrinsic 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 α−RuCl3, and provide a ready-to-use formula for comparison to experimental data.

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Popular Summary

Understanding the origin of thermal Hall conductivity in insulating quantum materials remains a significant experimental and theoretical challenge, often complicated by the assumption that extrinsic effects from disorder can be neglected in favor of intrinsic quantum mechanisms. We counter this assumption by computing the disorder-induced side-jump effect in generality for heat carried by bosonic excitations like phonons and magnons. We rigorously derive the semiclassical kinetic equation and show that upon scattering, a particle does not only change velocity but also jumps to a new position, yielding a contribution to the thermal Hall effect comparable in amplitude to the intrinsic part. Our work provides a basic formula incorporating material-specific properties, and explicitly shows that extrinsic disorder effects are crucial for a full quantitative theory of thermal Hall transport.

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Phys. Rev. X 16, 011048– Published 5 March, 2026
  • Received 26 May 2025
  • Revised 14 November 2025
  • Accepted 12 December 2025
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