The phonon dispersion of graphite revisited

TL;DR

This paper reviews and compares first-principles calculations and empirical models of graphite's phonon dispersion, highlighting the importance of long-range interactions and providing improved parameters for modeling phonons in graphitic nanostructures.

Contribution

It offers a detailed analysis of phonon dispersion calculations in graphite, demonstrating the effectiveness of GGA and refined force-constant models for accurate predictions.

Findings

GGA yields better agreement with experiments than LDA.

Force-constant models with up to 4th-nearest neighbors fit low-frequency modes well.

Including second-nearest neighbor non-diagonal terms improves high-frequency mode accuracy.

Abstract

We review calculations and measurements of the phonon-dispersion relation of graphite. First-principles calculations using density-functional theory are generally in good agreement with the experimental data since the long-range character of the dynamical matrix is properly taken into account. Calculations with a plane-wave basis demonstrate that for the in-plane optical modes, the generalized-gradient approximation (GGA) yields frequencies lower by 2% than the local-density approximation (LDA) and is thus in better agreement with experiment. The long-range character of the dynamical matrix limits the validity of force-constant approaches that take only interaction with few neighboring atoms into account. However, by fitting the force-constants to the ab-initio dispersion relation, we show that the popular 4th-nearest-neighbor force-constant approach yields an excellent fit for the low frequency modes and a moderately good fit (with a maximum deviation of 6%) for the high-frequency modes. If, in addition, the non-diagonal force-constant for the second-nearest neighbor interaction is taken into account, all the qualitative features of the high-frequency dispersion can be reproduced and the maximum deviation reduces to 4%. We present the new parameters as a reliable basis for empirical model calculations of phonons in graphitic nanostructures, in particular carbon nanotubes.