Phonon polariton Hall effect

The phonon Hall effect conventionally describes the generation of a transverse heat current in an applied magnetic field. In this work, we extend the effect to hybrid light-matter excitations and demonstrate theoretically that phonon polaritons, formed by coupling optical phonons with terahertz radiation, support transverse energy flow when coherently driven in an applied magnetic field. Using the example of PbTe, which exhibits strongly coupled phonon polaritons, we show that the magnetic field splits the phonon-polariton branches into left and right-handed circular polarization, obtaining unequal group velocities. We derive the energy current operators for propagating phonon polaritons and show how their mixed phononic-photonic nature enables controllable transverse phonon-polariton transport in the terahertz regime. Our results demonstrate bending of light through a phonon polariton Hall effect, which provides a route towards terahertz polaritonic devices.