Phonon thermal Hall as a lattice Aharonov-Bohm effect

Abstract

In a growing list of insulators, experiments find that magnetic field induces a misalignment between the heat flux and the thermal gradient vectors. This phenomenon, known as the phonon thermal Hall effect, implies energy flow without entropy production along the orientation perpendicular to the temperature gradient. The experimentally-measured thermal Hall angle in various insulators does not exceed a bound and becomes maximal at the temperature of peak longitudinal thermal conductivity. The present paper aims to propose a scenario providing and explanation for these two experimental facts. It begins by noticing that at this temperature, $T_{max}$, Normal phonon-phonon collisions become most frequent in comparison with Umklapp and boundary scattering events. Furthermore, the Born-Oppenheimer approximated molecular wave functions are known to acquire a phase in the presence of a magnetic field. In an anharmonic crystal, in which tensile and compressive strain do not cancel out, this field-induced atomic phase gives rise to a phonon Berry phase and generates phonon-phonon interference. The rough amplitude of the thermal Hall angle expected in this picture is set by the phonon wavelength, ${\lambda }_{ph}$, and the crest atomic displacement, $\delta u_m$ at $T_{max}$. The derived expression is surprisingly close to what has been experimentally found in black phosphorus, germanium and silicon.

23 pages, 6 figures, 2 tables

References in corpus (9)

• Topological Nature of the Phonon Hall Effect
• Orbital magnetic moments of phonons
• Exact microscopic analysis of a thermal Brownian motor
• Anomalous Hall effect for the phonon heat conductivity in paramagnetic dielectric
• Lindemann melting criterion in two dimensions
• The phonon thermal Hall angle in black phosphorus
• Phonon hydrodynamics in crystalline materials
• Phonon thermal Hall effect in charge-compensated topological insulators
• Discovery of universal phonon thermal Hall effect in crystals

Cited by in corpus (3)

• Thermal Hall conductivity of semimetallic graphite dominated by ambipolar phonon drag
• Extrinsic contribution to bosonic thermal Hall transport
• Phonon Thermal Hall Effect: The Roles of Disorder, Annealing, and Metallic Contacts