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

TL;DR

This paper develops a first-principles microscopic theory for long-range nonlinear electron-phonon interactions in solids, extending beyond linear models, and demonstrates its application to specific materials like LiF and KTaO3.

Contribution

It introduces a semi-analytical expression for long-range 1-electron-2-phonon interactions that incorporates full phonon dispersion, advancing first-principles modeling of nonlinear electron-phonon effects.

Findings

Derived a semi-analytical expression for 1-electron-2-phonon matrix elements.

Showed the importance of phonon dispersion in nonlinear interactions.

Calculated spectral functions for LiF and KTaO3 from first principles.

Abstract

Electron-phonon interactions in solids are crucial for understanding many interesting phenomena, such as conventional superconductivity, temperature-dependent band-gap renormalization, and polarons. For harmonic materials, the linear interaction of one electron with one phonon is sufficient to quantitatively describe these properties. However, in anharmonic materials such as quantum paraelectrics, halide perovskites, and high-pressure hydrides, the nonlinear electron-phonon interactions may play an important role. Currently, the only available Hamiltonians for nonlinear electron-phonon interaction are model Hamiltonians, written in terms of phenomenological parameters. Here, we present a microscopic theory for long-range nonlinear electron-phonon interactions, which can be combined with first-principles calculations. We provide a semi-analytical expression for the long-range part of the 1-electron-2-phonon matrix element. We show that in contrast to the long-range 1-electron-1-phonon interaction, the continuum approximation is not sufficient and the entire phonon dispersion must be taken into account. Additionally, we show that the quasiparticle energies can be written in terms of a 1-electron-2-phonon spectral function. To demonstrate the method, we calculate the 1-electron-2-phonon spectral function for LiF and KTaO$_3$ from first principles. Our framework is a step forward toward complete first-principles calculations of nonlinear electron-phonon interactions in solids.