Photon Thermal Hall Effect

Abstract

A near-field thermal Hall effect (i.e.Righi-Leduc effect) in networks of magneto-optical particles placed in a constant magnetic field is predicted. This many-body effect is related to a symmetry breaking in the system induced by the magnetic field which gives rise to preferential channels for the heat-transport by near-field interaction thanks to the particles anisotropy tuning.PACS numbers: 44.40.+a, 03.50.De, The Righi-Leduc effect [1] is the thermal analog of classical Hall effect [2]. It consists in the appearance of a heat flux transversally to a heat current induced by a temperature gradient inside a solid under the presence of a magnetic field. Like the Hall effect, it is due to the curvature of carriers trajectories through the magnetic field. At macroscopic scale this effect is related to a symmetry breaking in the transport equations due to the presence of an external magnetic field. At microscale numerous mechanisms can be responsible for this effect. In semiconductors, metals or high-Tc superconductors it is the Lorentz force acting on the free electrons which is responsible for a transversal heat current. In ferromagnetic materials, magnons (spin waves) [3][4][5] currents have been shown to be the source of thermal Hall effect. Recently, a phonon mediated themal Hall effect [6,7] has been highlighted in neutral objects of zero electrical charge. But, so far, no magnetotransverse effect have been predicted for the photon contribution of the thermal conductivity. In this Letter, we investigate the near-field heat exchanges in a four-terminal system composed by magneto-optical particles under the action of a constant magnetic field and we demonstrate the existence of a Hall flux in the direction perpendicular to the primary temperature gradient which is due to a breakdown of the symmetry in the near-field interactions.To start, we consider the system sketched in Fig. 1. It consists in four identical spherical particles made with a magneto-optical material which are arranged in a fourterminal junction. Those particles can exchange electromagnetic energy between them and with the surrounding medium which can be assimilated to a bosonic field at ambiant temperature T a . By connecting the two particles along the x-axis to two heat baths at two different temperatures, a heat flux flows through the system between these two particles. Without external magnetic field all particles are isotropic, so that the two others unthermostated particles have, for symmetry reasons, the same equilibrium temperatures and therefore they do not exchange heat flux through the network. On the contrary, when a magnetic field is applied orthogonally to the particles network, the particles become anisotropic so that the symmetry of system is broken (Fig. 1). As If a magnetic field is applied in the z direction, the particles become biaxial breaking the system symmetry (the optical axis are two complex valued vectors V1 = (i, 1) and V2 = (−i, 1), the eigenvectors of permittivity tensor) a temperature gradient is generated in the ...

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