Relation between Photon Thermal Hall Effect and Persistent Heat Current in Nonreciprocal Radiative Heat Transfer

We study the photon thermal Hall effect and the persistent heat current in radiative heat transfer. We show that the photon thermal Hall effect is not a uniquely nonreciprocal effect; it can arise in some reciprocal systems with broken mirror symmetry. This is in contrast with the persistent heat current, which is a uniquely non-reciprocal effect that can not exist in any reciprocal system. Nevertheless, for a specific class of systems with $C_4$ rotational symmetry, we note that the photon thermal Hall effect is uniquely nonreciprocal, and moreover there is a direct connection between the persistent heat current and the photon thermal Hall effect. In the near-equilibrium regime, the magnitude of the photon thermal Hall effect is proportional to the temperature derivative of the persistent heat current in such systems. Therefore, the persistent heat current as predicted for the equilibrium situation can be probed by the photon thermal Hall effect away from equilibrium.