Berry Curvature and Phonon Hall Effect

Abstract

We establish the general phonon dynamics of magnetic solids by incorporating the Mead-Truhlar correction in the Born-Oppenheimer approximation. The effective magnetic-field acting on the phonons naturally emerges, giving rise to the phonon Hall effect. A general formula of the intrinsic phonon Hall conductivity is obtained by using the corrected Kubo formula with the energy magnetization contribution incorporated properly. The resulting phonon Hall conductivity is fully determined by the phonon Berry curvature and the dispersions. Based on the formula, the topological phonon system could be rigorously defined. In the low temperature regime, we predict that the phonon Hall conductivity is proportional to $T^3$ for the ordinary phonon systems, while that for the topological phonon systems has the linear $T$ dependence with the quantized temperature coefficient.

11 pages, derivations added, published version

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• Topological Nature of the Phonon Hall Effect
• Energy Magnetization and Thermal Hall Effect
• Anomalous Hall effect for the phonon heat conductivity in paramagnetic dielectric
• Anomalous Hall Effect in Disordered Multiband Metals
• Phonon Hall thermal conductivity from Green-Kubo formula
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Cited by in corpus (114)

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