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

TL;DR

This paper develops a phenomenological force-constant model to accurately describe phonon dispersion in graphene and carbon nanotubes, enabling analysis of their low-temperature thermal properties and quantum size effects.

Contribution

It introduces a new parameter set for phonon calculations in graphene and nanotubes, improving the understanding of their vibrational and thermal behaviors.

Findings

Phonon spectra of nanotubes show one-dimensional behavior.

Quantization of phonon subbands at low temperatures.

Thermal conductance quantized according to Landauer theory.

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.