Phonon Hall Effect in Four-Terminal Junctions

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.