Phonon dispersions and vibrational properties of monolayer, bilayer, and trilayer graphene

TL;DR

This study uses density-functional perturbation theory to analyze phonon dispersions and vibrational properties of monolayer, bilayer, and trilayer graphene, revealing mode splitting and shifts due to interlayer coupling.

Contribution

It provides detailed insights into how phonon modes evolve with layer number in graphene, highlighting mode splitting and sensitivity to measurement techniques.

Findings

Optical phonon mode splitting increases with layer number.

Interlayer coupling estimated at about 2 cm$^{-1}$.

Optical modes at K point shift significantly with layer number.

Abstract

The phonon dispersions of monolayer and few-layer graphene (AB bilayer, ABA and ABC trilayers) are investigated using the density-functional perturbation theory (DFPT). Compared with the monolayer, the optical phonon $E_{2g}$ mode at $\Gamma$ splits into two and three doubly degenerate branches for bilayer and trilayer graphene, respectively, due to the weak interlayer coupling. These modes are of various symmetry and exhibit different sensitivity to either Raman or infrared (IR) measurements (or both). The splitting is found to be 5 cm$^{-1}$ for bilayer and 2 to 5 cm$^{-1}$ for trilayer graphene. The interlayer coupling is estimated to be about 2 cm$^{-1}$. We found that the highest optical modes at K move up by about 12 cm$^{-1}$ for bilayer and 18 cm$^{-1}$ for trilayer relative to monolayer graphene. The atomic displacements of these optical eigenmodes are analyzed.