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

TL;DR

This paper develops a general theoretical framework to calculate phonon drag contributions to Nernst and thermal Hall effects, and successfully applies it to explain experimental observations in dilute SrTiO$_{3-\delta}$ with no adjustable parameters.

Contribution

The authors introduce a linear response theory-based method to compute phonon drag effects on Nernst and thermal Hall conductivities applicable to various systems.

Findings

The theory quantitatively matches experimental data for SrTiO$_{3-\delta}$.

All model parameters are derived from experiments without fitting.

The approach provides a unified framework for phonon drag effects in thermal transport.

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.