Phonon Hall Effect in Four-Terminal Junctions

TL;DR

This paper investigates the phonon Hall effect in four-terminal devices using nonequilibrium Green's functions, revealing lattice-dependent behavior and magnetic field effects on temperature differences in paramagnetic dielectrics.

Contribution

It introduces an exact Green's function approach to study the phonon Hall effect in four-terminal setups and uncovers lattice symmetry as a key factor influencing the effect.

Findings

Square lattice shows no phonon Hall effect.

Honeycomb lattice exhibits phonon Hall effect.

Temperature difference reverses sign at high magnetic fields.

Abstract

Using an exact nonequilibrium Green's function formulism, the phonon Hall effect for paramagnetic dielectrics is studied in a four-terminal device setting. The temperature difference in the transverse direction of the heat current is calculated for two-dimensional models with the magnetic field perpendicular to the plane. We find a surprising result that the square lattice does not have the phonon Hall effect while a honeycomb lattice has. This can be explained by symmetry. The temperature difference changes sign if the magnetic field is sufficiently large.