CM In the literature: open

How do phonons couple to a magnetic field in nonmagnetic insulators?

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 SiO2 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

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.