Low-frequency phonons of few-layer graphene within a tight-binding model

TL;DR

This paper develops a tight-binding model with two sets of matrix elements derived from ab-initio data to accurately describe low-frequency phonons in few-layer graphene, accounting for both covalent and van der Waals interactions.

Contribution

It introduces a novel approach using separate matrix elements for covalent and van der Waals interactions in a tight-binding model, validated against experimental phonon dispersion data.

Findings

Accurately reproduces phonon dispersion in graphite and few-layer graphene.

Validates the model's applicability to other layered carbon structures.

Provides a basis for studying dynamic properties of layered materials.

Abstract

Few-layer graphene is a layered carbon material with covalent bonding in the layers and weak van der Waals interactions between the layers. The interlayer energy is more than two orders of magnitude smaller than the intralayer one, which hinders the description of the static and dynamic properties within parameter-free electron band structure models. We overcome this difficulty by introducing two sets of matrix elements - one set for the covalent bonds in the graphene layers and another one for the van der Waals interactions between adjacent graphene layers in a tight-binding model of the band structure. Both sets of matrix elements are derived from an ab-initio study on carbon dimers. The matrix elements are then applied in the calculation of the phonon dispersion of graphite and few-layer graphene with AB and ABC layer stacking. The results for AB stacking agree well with the available experimental data, which justifies the application of the matrix elements to other layered carbon structures with van der Waals interactions such as few-layer graphene nanoribbons, multiwall carbon nanotubes, and carbon onions.