Spin-phonon coupling and thermal Hall effect in the Kitaev model

The Kitaev model, which involves bond-direction-dependent spin interactions on a honeycomb lattice, has attracted significant interest due to its exact solvability and potential uses in quantum computing. A key feature of this model is the half-quantized thermal Hall conductivity (HQTHC) under a magnetic field perpendicular to the lattice; however, HQTHC only appears at low temperatures. Here, in the higher temperature range beyond the HQTHC regime, we theoretically suggest an extrinsic phonon contribution to the thermal Hall effect in the Kitaev model through skew-scattering of chiral phonons by scalar spin chirality, previously examined in Mott insulators. We demonstrate the emergence of scalar spin chirality from fluctuating spins, estimate the resulting field strength and its symmetric form applied to chiral phonons, and obtain the associated thermal Hall conductivity in semi-quantitative agreement with existing experiments. This work offers a fundamental understanding of how spin-phonon interactions influence strongly correlated systems.