3D continuum phonon model for group-IV 2D materials

Morten Willatzen, Lok C. Lew Yan Voon, Appala Naidu Gandi, Udo Schwingenschlogl

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A general three-dimensional continuum model of phonons in two-dimensional materials is developed. Our first-principles derivation includes full consideration of the lattice anisotropy and flexural modes perpendicular to the layers and can thus be applied to any two-dimensional material. In this paper, we use the model to not only compare the phonon spectra among the group-IV materials but also to study whether these phonons differ from those of a compound material such as molybdenum disulfide. The origin of quadratic modes is clarified. Mode coupling for both graphene and silicene is obtained, contrary to previous works. Our model allows us to predict the existence of confined optical phonon modes for the group-IV materials but not for molybdenum disulfide. A comparison of the long-wavelength modes to density-functional results is included.
Original languageEnglish
JournalBeilstein Journal of Nanotechnology
Issue number1
Pages (from-to)1345-1356
Publication statusPublished - 2017


  • Molybdenum and Alloys
  • Nanotechnology
  • Chemical Products Generally
  • Mechanics
  • Graphene
  • Molybdenum disulfide
  • Phonon
  • Silicene
  • Two-dimensional materials
  • Continuum mechanics
  • Molybdenum
  • Sulfur compounds
  • Continuum Modeling
  • Density functionals
  • First-principles derivations
  • Lattice anisotropy
  • Optical phonon modes
  • Phonons


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