How do phonons couple to a magnetic field in nonmagnetic insulators?
This text mentions work from 2024 on. Those parts were partly written without a live literature search and have not been checked by an editor yet.
In plain words
Crystals such as quartz, which have no magnetic atoms, still show sideways phonon heat flow in a field, while glassy silica with the same chemistry shows none.
Precise statement
Crystalline quartz shows a phonon thermal Hall signal, larger in cleaner crystals, while amorphous $\mathrm{SiO_2}$ does not (Ling, Fauque and Behnia, SciPost Physics 21, 036, 2026), and estimates based on the Lorentz force on ionic Born charges have not been shown to account for the magnitude. Derive the magnitude of $\kappa_{xy}$ in a diamagnetic crystal from a microscopic coupling (Born effective charges, molecular Berry phases, or the lattice Aharonov-Bohm phase of Behnia, SciPost Physics Core 8, 061, 2025) and explain its absence in the glass.
What would settle it
A first-principles calculation of $\kappa_{xy}$ for quartz that matches experiment in magnitude and sign and gives near-zero $\kappa_{xy}$ for silica glass.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
A lattice Aharonov-Bohm mechanism was proposed (Behnia, SciPost Physics Core, 2025), and a phonon thermal Hall effect in nonmagnetic crystals including Si, Ge and quartz was reported in 2024 (arXiv 2404.02863); no quantitative microscopic theory exists.
Parent problems
- Special case of Why do phonons in many insulators show a thermal Hall effect? · open · from revision 1 The parent was revised since revision 1: it now states another question.
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