Reverse phonon thermal flux from an applied electric field
In the phenomenon known as electron drag, a phonon thermal flux is established in a conducting crystal by an electric field applied under isothermal conditions through directed transfer of quasimomentum from the electronic charge current to the phonon subsystem. Prior understanding of this phenomenon involves a thermal current composed of low-frequency acoustic phonons that is in the same direction as the charge current. This results in an increase of the Peltier thermopower. Here, we show that it is also possible to establish a phonon thermal current that is in the opposite direction to the charge current, which we refer to as a reverse phonon thermal flux. We demonstrate this behavior both through a simple qualitative model and through first-principles calculations performed for three materials: p-type 𝜃-TaN, n-type BAs, and n-type Si. The reverse phonon flux is shown to arise through intervalley electron-phonon scattering processes involving high-frequency acoustic phonons. Unlike n-BAs and n-Si, the combined features in the band structure and phonon dispersions of p-type 𝜃-TaN promote a particularly large reverse phonon thermal flux comparable in magnitude to the oppositely directed thermal flux from low-frequency phonons. Finally, this work highlights a previously unrecognized behavior in the coupled electron-phonon system and advances our understanding of the rich physics of transport in solids.