Vibrational modes and low-temperature thermal properties of graphene and carbon nanotubes: A minimal force-constant model

Abstract

We present a phenomenological force-constant model developed for the description of lattice dynamics of sp2 hybridized carbon networks. Within this model approach, we introduce a new set of parameters to calculate the phonon dispersion of graphene by fitting the ab initio dispersion. Vibrational modes of carbon nanotubes are obtained by folding the 2D dispersion of graphene and applying special corrections for the low-frequency modes. Particular attention is paid to the exact dispersion law of the acoustic modes, which determine the low-frequency thermal properties and reveal quantum size effects in carbon nanotubes. On the basis of the resulting phonon spectra, we calculate the specific heat and the thermal conductance for several achiral nanotubes of different diameter. Through the temperature dependence of the specific heat we demonstrate that phonon spectra of carbon nanotubes show one-dimensional behavior and that the phonon subbands are quantized at low temperatures. Consequently, we prove the quantization of the phonon thermal conductance by means of an analysis based on the Landauer theory of heat transport.

14 pages, 12 figures

References in corpus (8)

• The Raman Fingerprint of Graphene
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• Electrical generation and absorption of phonons in carbon nanotubes
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Cited by in corpus (12)

• Ballistic to diffusive crossover of heat flow in graphene ribbons
• Phonon transport in large scale carbon-based disordered materials: Implementation of an efficient order-N and real-space Kubo methodology
• Anharmonic interatomic force constants and thermal conductivity from Grüneisen parameters: an application to graphene
• Phonon-phonon interactions and phonon damping in carbon nanotubes
• Polaronic signatures and spectral properties of graphene antidot lattices
• Thermodynamic properties of graphene bilayers
• Anharmonicity of the acoustic modes of graphene
• Phonon dispersion in two-dimensional solids from atomic probability distributions
• Vibrational heat capacity of carbon nanotubes in low and ultra-low temperature regions
• Anomalous phonon behavior of carbon nanotubes: First-order influence of external load
• Vibrational properties of nanographene
• Dimensional crossover and enhanced thermoelectric efficiency due to broken symmetry in graphene antidot lattices