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

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.

8 pages, 10 figures

References in corpus (9)

• The Raman Fingerprint of Graphene
• Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics
• Electric Field Effect Tuning of Electron-Phonon Coupling in Graphene
• Epitaxial graphene
• Non-adiabatic Kohn-anomaly in a doped graphene monolayer
• Optical Phonons in Carbon Nanotubes: Kohn Anomalies, Peierls Distortions and Dynamic Effects
• The phonon dispersion of graphite by inelastic x-ray scattering
• Electron Transport and Hot Phonons in Carbon Nanotubes
• The structural properties of the multi-layer graphene/4H-SiC(000-1) system as determined by Surface X-ray Diffraction

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• Chlorine Adsorption on Graphene: Chlorographene
• Electron-Phonon Interactions for Optical Phonon Modes in Few-Layer Graphene
• Imaging Stacking Order in Few-Layer Graphene
• Polaronic signatures and spectral properties of graphene antidot lattices
• Two-phonon Raman bands of bilayer graphene: revisited
• Optical Phonon Anomaly in Bilayer Graphene with Ultrahigh Carrier Densities
• Thermal Transport in Graphene and Graphene Multilayers