Phonon Thermal Hall Effect in quartz and its absence in silica

TL;DR

This study compares phonon thermal Hall effects in crystalline quartz and amorphous silica, finding the effect in quartz but not in silica, and proposes a model involving lattice drift and Berry forces to explain the phenomenon.

Contribution

It demonstrates the presence of a phonon thermal Hall effect in quartz and its absence in silica, highlighting the role of lattice order and proposing a theoretical explanation involving Berry forces.

Findings

Finite thermal Hall signal in quartz, none in silica.

Cleaner quartz exhibits larger thermal Hall conductivity.

Thermal Hall response linked to differences in entropy production and magnetic coupling.

Abstract

The observation of a misalignment between the applied heat flux and the measured temperature gradient in insulating solids induced by magnetic field has become a subject of experimental investigation, theoretical speculation, and unsettled controversy. To identify the origin of this phonon thermal Hall effect, we performed a comparative study of longitudinal and transverse heat transport in crystalline (quartz) and vitreous (silica) SiO$_2$ using identical experimental set-ups and thermometers. A finite signal was detected in the crystalline samples and none in the amorphous sample, within our resolution. The cleaner crystal exhibited a larger thermal Hall conductivity than the dirtier one, ruling out disorder as the driver of the effect. On the other hand, the amplitude of the transverse thermal resistivity is almost identical in the two crystalline samples (W$_{\perp}$/B$\approx 10^{-6}$ m.K.W$^{-1}$.T$^{-1}$). We show that in a phonon gas, as in a molecular gas displaying the Senftleben-Beenakker effect, heat is conducted through two channels, and argue that a thermal Hall response is unavoidable whenever these channels differ both in entropy production and in their coupling to the magnetic field. Under such conditions, the conserved energy current and the non-conserved entropy current cease to be parallel. Finally, the magnitude of the transverse thermal resistivity can be accounted for by a surprisingly simple picture. The heat flux induces a tiny drift velocity of the lattice nuclei, the magnetic field exerts a transverse Berry force on this drift, and this force is balanced by an entropic restoring force.