Phonon dispersion in two-dimensional solids from atomic probability distributions
arXiv:2001.00776 · doi:10.1063/1.5132419
Abstract
We propose a harmonic linear response (HLR) method to calculate the phonon dispersion relations of two-dimensional (2D) layers from equilibrium simulations at finite temperature. This HLR approach is based on the linear response of the system, as derived from the analysis of its centroid density in equilibrium path integral simulations. In the classical limit, this approach is closely related to those methods that study vibrational properties by the diagonalization of the covariance matrix of atomic fluctuations. The validity of the method is tested in the calculation of the phonon dispersion relations of a graphene monolayer, a graphene bilayer, and graphane. Anharmonic effects in the phonon dispersion relations of graphene are demonstrated by the calculation of the temperature dependence of the following observables: the kinetic energy of the carbon atoms, the vibrational frequency of the optical mode, and the elastic moduli of the layer.
13 pages, 10 figures
References in corpus (25)
- Electric Field Effect in Atomically Thin Carbon Films
- Two Dimensional Atomic Crystals
- Raman spectroscopy as a versatile tool for studying the properties of graphene
- Intrinsic ripples in graphene
- Elastic properties of hydrogenated graphene
- The Shear Mode of Multi-Layer Graphene
- Phonon anharmonicities in graphite and graphene
- Phonon dispersions and vibrational properties of monolayer, bilayer, and trilayer graphene
- Scaling Properties of Flexible Membranes from Atomistic Simulations: Application to Graphene
- Theory of 2D crystals: graphene and beyond
- Atomistic simulations of structural and thermodynamic properties of bilayer graphene
- Vibrational modes and low-temperature thermal properties of graphene and carbon nanotubes: A minimal force-constant model
- Suppression of anharmonicities in crystalline membranes by external strain
- Vibrational properties of graphene fluoride and graphane
- A path-integral molecular dynamics simulation of diamond
- The Schrödinger formulation of the Feynman path centroid density
- Kinetic energy of protons in ice Ih and water: a path integral study
- Thermodynamics of quantum crystalline membranes
- Quantum effects in graphene monolayers: Path-integral simulations
- Anharmonic effects in the optical and acoustic bending modes of graphene
- Quantum and classical ripples in graphene
- Hydrogen and muonium in diamond: A path-integral molecular dynamics simulation
- Elastic properties and mechanical tension of graphene
- Thermal properties of graphene from path-integral simulations
- Molecular hydrogen in graphite: A path-integral simulation
Cited by in corpus (8)
- Anharmonicity of the acoustic modes of graphene
- Quantum effects in two-dimensional silicon carbide
- Nuclear quantum effects in graphane
- Elastic properties and mechanical stability of bilayer graphene: Molecular dynamics simulations
- Isotopic effects in structural properties of graphene
- Hydrogen dynamics on defective monolayer graphene
- Isotopic effects in chair graphane
- Quantum nuclear motion in silicene: Assessing structural and vibrational properties through path-integral simulations