Microscopic theory of phonon polaritons and long wavelength dielectric response

TL;DR

This paper introduces a first-principles quantum approach to calculate phonon-polariton dispersion, capturing complex interactions and anisotropic effects, and demonstrates its effectiveness on various materials.

Contribution

It develops a comprehensive first-principles method for phonon-polariton dispersion that includes retardation, anisotropy, and anharmonic effects, improving upon traditional models.

Findings

Accurately predicts phonon-polariton dispersion in various materials.

Shows anharmonic effects significantly influence dielectric response.

Resolves non-analytical behavior at Brillouin zone center.

Abstract

We present a first-principles approach for calculating phonon-polariton dispersion relations. In this approach, phonon-photon interaction is described by quantization of a Hamiltonian that describes harmonic lattice vibrations coupled with the electromagnetic field inside the material. All Hamiltonian parameters are obtained from first-principles calculations, with diagonalization leading to non-interacting polariton quasiparticles. This method naturally includes retardation effects and resolves non-analytical behavior and ambiguities in phonon frequencies at the Brillouin zone center, especially in non-cubic and optically anisotropic materials. Furthermore, by incorporating higher-order terms in the Hamiltonian, we also account for quasiparticle interactions and spectral broadening. Specifically, we show how anharmonic effects in phonon polaritons lead to a dielectric response that challenges traditional models. The accuracy and consequences of the approach are demonstrated on GaP and GaN as harmonic test systems and PbTe and $\beta$-Ga$_2$O$_3$ as anharmonic test systems.