Importance of nonlinear long-range electron-phonon interaction for the carrier mobility of anharmonic halide perovskites
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$_3$. 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 calculate the electron mobility from first principles within the self-energy relaxation-time approximation, treating the electron-phonon coupling in the long-range approximation. Despite these approximations, the calculated mobilities are in good agreement with the available experimental data, while enabling us to isolate and quantify the contribution of nonlinear electron-phonon interactions relative to the conventional linear coupling. We find that the one-electron-two-phonon interaction modifies the temperature dependence of the mobility in CsPbI$_3$ and reduces its room-temperature value by about 10\%. This sizeable contribution results from the combined effects of strong lattice anharmonicity and large thermal phonon populations, the latter being enhanced by the low phonon frequencies associated with the heavy constituent atoms. These results show when nonlinear electron-phonon interactions become relevant, and indicate they should be considered for finite-temperature properties of halide perovskites.