Importance of nonlinear long-range electron-phonon interaction on the carrier mobility of anharmonic halide perovskites

Electron-phonon interactions in a solid are crucial for understanding many interesting material properties, such as transport properties and the temperature dependence of the electronic band gap. For harmonic materials, the linear interaction process where one electron interacts with one phonon is sufficient to quantitatively describe these properties. However, this is no longer true in anharmonic materials with significant electron-phonon interaction, such as halide perovskites. Currently, the only available models for nonlinear electron-phonon interaction are model Hamiltonians, written in terms of phenomenological parameters. Here, we provide a postprocessing Python code for the treatment of the long-range part of the 1-electron-2-phonon interaction. We show in the associated manuscripts that it is sufficient to know the phonon frequencies and eigenvectors calculated at a finite electric field, which we provide alongside this software for three selected materials: LiF, KTaO3, and CsPbI3. We calculate the 1-electron-2-phonon spectral functions for these materials, and use the one for CsPbI3 to calculate the contribution of the 1-electron-2-phonon interaction to the electron mobility. We show that the nonlinear interaction contributes significantly to the temperature scaling of the mobility in CsPbI3, due to its low phonon frequencies. For LiF, a very harmonic material with high phonon frequencies, the effect is negligible as expected. In KTaO3 the effect of nonlinear interaction is also negligible, despite the fact that it is an anharmonic material: this is due to the fact that it also has high phonon frequencies.