Boltzmann Transport Calculations in Systems with Electron-phonon Coupling

Recent experimental and theoretical calculations point to a complex interplay between the electron and phonon baths in a wide variety of materials [1,2]. We propose a method of coupling the Boltzmann equations for the electron and phonon baths within the relaxation time approximation to describe the changes in the electron and phonon distributions and thus calculate the thermoelectric transport coefficients. Our model for the coupled system will include tight-binding and ${\bf k \cdot p}$ Hamiltonians for both the electron and phonon energies and analytic calculations for the electron and phonon relaxation mechanisms. From these calculations we hope to better understand the role and interplay of electron-phonon and phonon-phonon interactions on the thermoelectric transport coefficients.
[1] - Phys. Rev. Lett. ${\bf 114}$, 115901 (2015). [2] - PNAS ${\bf 112}$, 14777-14782 (2015).