Coupled Boltzmann Equation Solver: Effects of the Electron-Phonon Interaction on the Transport Coefficients

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 which we use to calculate the thermoelectric transport coefficients. Our model for the coupled Boltzmann Equation solver includes analytic models, including ${\bf k \cdot p}$ Hamiltonians and tight-binding Hamiltonians, for both the electron and phonon energies and analytic models 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).