Phonon drag thermal Hall effect in metallic strontium titanate

TL;DR

This study demonstrates that phonon drag significantly influences the thermal Hall effect in metallic SrTiO$_3$, with the effect being highly sensitive to stoichiometry and electron-phonon interactions, revealing new insights into thermal transport in quantum paraelectric materials.

Contribution

The paper provides a quantitative explanation of the phonon drag contribution to the thermal Hall effect in metallic SrTiO$_3$, highlighting the role of electron-phonon momentum exchange.

Findings

The thermal Hall effect amplitude varies with stoichiometry and doping.

Enhanced THE in metallic SrTiO$_3$ exceeds electronic and phononic contributions separately.

Momentum exchange between electrons and phonons is crucial for the observed effects.

Abstract

SrTiO$_3$, a quantum paralectric, displays a detectable phonon thermal Hall effect (THE). Here we show that the amplitude of THE is extremely sensitive to stoichiometry. It drastically decreases upon substitution of a tiny fraction of Sr atoms with Ca, which stabilizes the ferroelectric order. It drastically increases by an even lower density of oxygen vacancies, which turn the system to a dilute metal. The enhancement in the metallic state exceeds by far the sum of the electronic and the phononic contributions. We explain this observation as an outcome of three features: i) heat is mostly transported by phonons; ii) the electronic Hall angle is extremely large; and iii) there is substantial momentum exchange between electrons and phonons. Starting from Herring's picture of phonon drag, we arrive to a quantitative account of the enhanced THE. Thus, phonon drag, hitherto detected as an amplifier of thermoelectric coefficients, can generate a purely thermal transverse response in a dilute metal with a large Hall angle. Our results reveal a hitherto unknown consequence of momentum-conserving collisions between electrons and phonons.ely thermal transverse response in a dilute metal with a large Hall angle. Our results reveal a hitherto unknown consequence of momentum-conserving collisions between electrons and phonons.