Phonon surface mapping of graphite: disentangling quasi--degenerate phonon dispersions

TL;DR

This study provides detailed two-dimensional phonon dispersion maps of graphite near the K point, resolving previous ambiguities and revealing strong trigonal warping and electron-phonon interactions crucial for graphene research.

Contribution

It offers the first detailed phonon surface mapping around the K point, clarifying phonon branch assignments and quantifying electron-phonon coupling in graphite.

Findings

Resolved the assignment of transverse and longitudinal phonon branches at K.

Observed strong trigonal warping of phonon dispersions.

Determined the electron-phonon coupling constant as 166 (eV/Å)^2.

Abstract

The two-dimensional mapping of the phonon dispersions around the $K$ point of graphite by inelastic x-ray scattering is provided. The present work resolves the longstanding issue related to the correct assignment of transverse and longitudinal phonon branches at $K$. We observe an almost degeneracy of the three TO, LA and LO derived phonon branches and a strong phonon trigonal warping. Correlation effects renormalize the Kohn anomaly of the TO mode, which exhibits a trigonal warping effect opposite to that of the electronic band structure. We determined the electron--phonon coupling constant to be 166$\rm(eV/\AA)^2$ in excellent agreement to $GW$ calculations. These results are fundamental for understanding angle-resolved photoemission, double--resonance Raman and transport measurements of graphene based systems.