First-principles theory of nonlinear long-range electron-phonon interaction

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 quantum paraelectrics and 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 microscopic semi-analytical expression for the long-range part of the 1-electron-2-phonon matrix element, which can be interfaced with first principles techniques.

We calculate an expression for the quasiparticle energies and phonon-limited transport, and show that they can be written in terms of a 1-electron-2-phonon spectral function. To demonstrate the method in practice, we calculate the 1-electron-2-phonon spectral function for LiF and CsPbI3 from first principles, and we show that the nonlinear interaction contributes significantly to the electron mobility of CsPbI3. We also show that unlike for the long-range 1-electron-1-phonon interaction, the continuum approximation is not sufficient and that the entire phonon dispersion must be taken into account. The framework in this article bridges the gap between model Hamiltonians and first-principles calculations for the 1-electron-2-phonon interaction.