Phonon Drag Effect in Nernst and Thermal Hall Effects: General Theory and Application to Dilute Metal SrTiO$_{3-\delta}$

Abstract

In magnetic fields, thermal gradient-induced effects such as the Nernst and thermal Hall effects are significantly influenced by phonon drag, which works in conjunction with the force on electrons in a magnetic field. We introduce a method to calculate Nernst and thermal Hall conductivities influenced by phonon drag using linear response theory to treat the magnetic field as a first-order perturbation. Our formula is general enough to apply to various systems in which the Green's functions of electrons and phonons are given. We apply the obtained general theory to the recent experiments of dilute metal SrTiO$_{3-\delta}$, known for strong Nernst and thermal Hall effects due to phonon drag. We find good agreement even quantitatively. This is notable as all model parameters are derived from experimental data without adjustable parameters.