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

TL;DR

This paper explores how spin-phonon interactions contribute to the thermal Hall effect in the Kitaev model at higher temperatures, providing a theoretical explanation consistent with experimental observations.

Contribution

It introduces a novel extrinsic phonon mechanism for the thermal Hall effect in the Kitaev model, emphasizing spin-phonon coupling beyond the low-temperature regime.

Findings

Identification of scalar spin chirality from fluctuating spins

Estimation of field strength affecting chiral phonons

Semi-quantitative agreement with experimental thermal Hall conductivity

Abstract

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.