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

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}.

• The paper demonstrates that applying the GW approximation renormalizes the electron-phonon coupling by about 80% for graphene’s A'1 phonon mode compared to LDA and GGA.
• The paper finds that the GW approach nearly doubles the phonon slope at the K point, aligning well with experimental X-ray and Raman spectroscopy data.
• The paper underscores the limitations of conventional DFT methods and highlights the need for advanced computational techniques to accurately model phonon dispersions in materials with strong electron correlations.

Impact of Electron-Electron Correlation on Phonon Dispersions in Graphene and Graphite

The paper "Impact of the electron-electron correlation on phonon dispersions: failure of LDA and GGA functionals in graphene and graphite" offers a detailed investigation into how electron-electron correlations affect the phonon dispersions in materials such as graphene and graphite. Specifically, it highlights the limitations of the Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA) functionals as employed in density functional theory (DFT) for these materials.

Summary of Key Findings

1. Electron-Phonon Coupling (EPC) under GW approximation: The study utilizes the GW approximation, a Green's function method accounting for many-body effects, to evaluate the electron-phonon coupling for selected phonon modes. The findings reveal that the inclusion of non-local exchange-correlation effects leads to a significant renormalization of the square of the EPC for the A$'_1$ phonon mode at the {\bf K} point by approximately 80% compared to LDA and GGA.
2. Phonon Dispersion Discrepancies: Within the GW framework, the phonon slope for the aforementioned mode is almost double that reported by GGA and LDA. Importantly, this finding is consistent with experimental data derived from inelastic x-ray scattering and Raman spectroscopy.
3. Hybrid Functional Calculations: The paper also examines the performance of the hybrid B3LYP functional, noting that it overestimates EPC at the {\bf K} point by roughly 30% in comparison to the experimental reference.
4. Instability in Graphene under Hartree-Fock: The study observes that, within the Hartree-Fock approximation, the graphene structure shows an instability when distorted following the A$'_1$ phonon at the {\bf K} point, emphasizing the critical role of screening in accurately describing phonon-electron interactions.

Implications and Future Directions

The research has significant implications for both theoretical understanding and practical applications. The inadequacy of LDA and GGA in capturing essential physical properties in materials like graphene underscores the need for more accurate methods like the GW approximation when investigating materials with significant electron correlation effects.

From a theoretical perspective, the findings suggest a compelling need to reevaluate the dependence on conventional DFT approaches when studying phonon-mediated properties in materials characterized by strong electron-electron interactions. Practically, this has ramifications for the interpretation of experimental data, particularly in the fields of superconductivity, thermal transport, and electronic property evaluation of two-dimensional materials.

Future Directions:

• Extension to Other Materials: While the study is focused on graphene and graphite, exploring similar effects in other materials could provide a wider context and application of these findings.
• Enhanced Computational Methods: Further advancements in computational methods that incorporate electron-electron correlations could provide more efficient and accurate modeling across a broader range of materials.
• Integration with Experimental Studies: Aligning computational models with experimental studies to refine predictions of phonon-related properties in novel materials remains a promising avenue for refinement and validation.

In conclusion, the paper provides insightful evidence that advanced ab-initio methods like GW are crucial for accurately understanding and predicting the behavior of phonon dispersions in complex materials systems, highlighting the necessity for ongoing improvement of computational techniques in materials science.