2024/12/12 by Matthew Houtput, Luigi Ranalli, Houtput, Matthew +11
Engineering · #Thermography and Photoacoustic Techniques #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.2412.09470
Describing electron-phonon interactions in a solid requires knowledge of the electron-phonon matrix elements in the Hamiltonian. State-of-the-art first-principles calculations for the electron-phonon interaction are limited to the 1-electron-1-phonon matrix element, which is suitable for harmonic materials. However, there is no first-principles theory for 1-electron-2-phonon interactions, which occur in anharmonic materials with significant electron-phonon interaction such as halide perovskites and quantum paraelectrics. Here, we derive an analytical expression for the long-range part of the 1-electron-2-phonon matrix element, written in terms of microscopic quantities that can be calculated from first principles. We show that the long-range 1-electron-2-phonon interaction is described by the derivative of the phonon dynamical matrix with respect to an external electric field. We calculate the quasiparticle energy of a large polaron including 1-electron-2-phonon interaction, and show that it can be written in terms of a 1-electron-2-phonon spectral function Tαβ(ω). We demonstrate how to calculate this spectral function and its temperature dependence for the benchmark materials LiF and KTaO3, where it turns out that the effect is very small. The first-principles framework developed in this article is general, paving the way for future calculations of 1-electron-2-phonon interactions in materials where the effect may be larger.