Thermal Hall effect in undoped cuprates

Recent experiments on thermal Hall conductivity in undoped cuprates observed an unexpectedly large result. Several mechanisms of phonon Hall effect have been proposed to explain this phenomenon. Here by using the Kubo formula with the energy magnetization included we show that a magnetic field acting on phonons in undoped cuprates naturally gives a nonzero intrinsic thermal Hall effect. Temperature-dependent thermal Hall conductivity κ_H is estimated by using phonon dispersions and the Berry connections of both the phonon bands and the electrons, which will be discussed in a model of LCO. The magnetic-field dependence of κ_H will also be shown in the same model.