Impact of the electron-electron correlation on phonon dispersions: failure of LDA and GGA functionals in graphene and graphite

TL;DR

This study reveals that non-local exchange-correlation effects significantly influence phonon dispersions in graphene and graphite, showing that common DFT functionals like LDA and GGA fail to accurately predict EPC and phonon slopes, while GW provides better agreement with experiments.

Contribution

The paper demonstrates the importance of GW calculations over LDA and GGA for accurately modeling electron-phonon interactions in graphene and graphite.

Findings

GW strongly renormalizes EPC compared to LDA/GGA

GW phonon slopes align with experimental data

Hartree-Fock predicts structural instability

Abstract

We compute electron-phonon coupling (EPC) of selected phonon modes in graphene and graphite using various ab-initio methods. The inclusion of non-local exchange-correlation effects within the GW approach strongly renormalizes the square EPC of the A$'_1$ {\bf K} mode by almost 80$%$ with respect to density functional theory in the LDA and GGA approximations. Within GW, the phonon slope of the A$'_1$ {\bf K} mode is almost two times larger than in GGA and LDA, in agreement with phonon dispersions from inelastic x-ray scattering and Raman spectroscopy. The hybrid B3LYP functional overestimates the EPC at {\bf K} by about 30%. Within the Hartree-Fock approximation, the graphene structure displays an instability under a distortion following the A$'_1$ phonon at {\bf K}.