First-principles charge transport including electron-two-phonon scattering processes

Predicting charge transport in materials from first principles is an open challenge. Although much progress has been made recently, nearly all work to date has relied on electron-phonon (e-ph) interactions obtained from lowest-order perturbation theory. However, in materials with polar bonds, the e-ph interactions are long-ranged, so assuming that higher-order e-ph processes are negligible is not justified. We recently investigated electron-two-phonon (e-2ph) scattering processes, and showed that these higher-order contributions are substantial even in a weakly polar material like GaAs [N.-E. Lee et. al., arxiv 1903.08261].
In this talk, we address the question of how the e-2ph processes affect transport. We derive a Boltzmann transport equation (BTE) that incorporates both one-phonon and two-phonon scattering, and solve it both within the relaxation time approximation and with an iterative approach (ITA). We compute the mobility in GaAs at 200-400 K, and show that the BTE-ITA with e-2ph processes gives a mobility in excellent agreement with experiments, resolving the known mobility overestimate in the BTE-ITA with one-phonon processes only. Future extensions to strongly polar materials will also be discussed.