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

Abstract

The interaction between the electrons and the lattice vibrations in a solid is responsible for various important effects, such as formation of polarons, temperature dependent bandgaps, phonon-limited carrier transport, and conventional superconductivity. Most works assume a linear electron-phonon interaction, where the electron only interacts with one phonon at a time. However, the validity of this assumption has not been verified in polar anharmonic materials, where large ionic displacements may invalidate the assumption of linear interaction. Here, we show that nonlinear electron-phonon interactions contribute significantly to the finite-temperature electron mobility of the inorganic lead halide perovskite CsPbI$_3$. We calculate the electron mobility from first principles using the self-energy relaxation time approximation and the long-range approximation. The effect of nonlinear interaction is taken into account using the recently derived expression for the long-range part of the one-electron-two-phonon matrix element. We show that due to the low phonon frequencies of CsPbI$_3$, the one-electron-two-phonon interaction changes the temperature scaling of the mobility and contributes about 10\% to the mobility at room temperature. The results underscore the importance of including nonlinear electron-phonon interaction in anharmonic halide perovskites.