Nonlinear phonon Hall effects in ferroelectrics: Existence and nonvolatile electrical control

Nonlinear Hall effects have been previously investigated in noncentrosymmetric systems for electronic systems. However, they only exist in metallic systems and are not compatible with ferroelectrics since these latter are insulators, hence limiting their applications. On the other hand, ferroelectrics naturally break inversion symmetry and can induce a nonzero Berry curvature. Here, we show that a nonvolatile electric-field control of heat current can be realized in ferroelectrics through the nonlinear phonon Hall effects. More precisely, based on the Boltzmann equation under the relaxation-time approximation, we derive the equation for nonlinear phonon Hall effects, and further show that the behaviors of nonlinear Hall effects for phonons (that are bosons) are very different from nonlinear Hall effects for electrons (that are fermions). Our work therefore provides a route for electric-field control of thermal Hall current in ferroelectrics.