Continuum approach for long-wavelength acoustic phonons in quasi-2D structures

Abstract

As an alternative to atomistic calculations of long-wavelength acoustic modes of atomically thin layers, which are known to converge very slowly, we propose a quantitatively predictive and physically intuitive approach based on continuum elasticity theory. We describe a layer, independent of its thickness, by a membrane, characterize its elastic behavior by a $(3\times 3)$ elastic matrix as well as the flexural rigidity. We present simple quantitative expressions for frequencies of long-wavelength acoustic modes, which we determine using 2D elastic constants calculated by {\em ab initio} Density Functional Theory. The calculated spectra accurately reproduce observed and calculated long-wavelength phonon spectra of graphene and phosphorene, the monolayer of black phosphorus. Our approach also correctly describes the observed dependence of the radial breathing mode frequency on the diameter of carbon fullerenes and nanotubes.

arXiv commentAccepted by Physical Review B (2016)

References in corpus (7)

• The electronic properties of graphene
• Semiconducting layered blue phosphorus: A computational study
• Finite temperature lattice properties of graphene beyond the quasiharmonic approximation
• Electronic, optical, and thermodynamic properties of borophene from first-principle calculations
• The phonon dispersion of graphite revisited
• Atomically thin binary V-V compound semiconductor: a first-principles study
• High stability of faceted nanotubes and fullerenes of multi-phase layered phosphorus: A computational study

Cited by in corpus (17)

• Unusually low thermal conductivity of atomically thin 2D tellurium
• Thermoelectric Penta-Silicene with a High Room-Temperature Figure of Merit
• Ultralow thermal conductivity in two-dimensional MoO${}_3$
• Is Twisted Bilayer Graphene Stable under Shear?
• Unusually stable helical coil allotrope of phosphorus
• Electron-phonon properties and superconductivity of doped antimonene
• Effect of Net Charge on the Relative Stability of 2D Boron Allotropes
• Microscopic Mechanism of the Helix-to-Layer Transformation in Elemental Group VI Solids
• The Electron-Phonon Coupling Constant for Single-Layer Graphene on Metal Substrates Determined from He Atom Scattering
• Towards Topological Quasi-Freestanding Stanene via Substrate Engineering
• Directional Design of Materials Based on the Multi-Objective Optimization: A Case Study of Two-Dimensional Thermoelectric SnSe
• Long-wavelength deformations and vibrational modes in empty and liquid-filled microtubules and nanotubes: A theoretical study
• Kirigami-Inspired Thermal Regulator
• Low-symmetry two-dimensional BNP${}_2$ and C${}_2$SiS structures with high and anisotropic carrier mobilities
• Discovery of an ultrastable antiferromagnetic two-dimensional CrF3 phase with anisotropic quasi-one-dimensional mechanical, electronic, and thermal properties
• In-Plane Breathing and Shear Modes in Low-Dimensional Nanostructures
• Large Contribution of Quasi-Acoustic Shear Phonon Modes to Thermal Conductivity in Novel Monolayer Ga2O3