Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"

Abstract

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega )$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega )/{\omega }^2$ as a precursor of the instability. We argue that this peak is the analogon of the "boson peak", observed in structural glasses. By means of the level distance statistics we show that the peak is not associated with localized states.

References in corpus (1)

• Anharmonic Decay of Vibrational States in Amorphous Silicon

Cited by in corpus (121)

• Static and Dynamic Properties of a Viscous Silica Melt Molecular Dynamics Computer Simulations
• Vibrations and diverging length scales near the unjamming transition
• Anharmonicity, vibrational instability and Boson peak in glasses
• On the Rigidity of Amorphous Solids
• Local elasticity map and plasticity in a model Lennard-Jones glass
• Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations
• Computer Simulations of Supercooled Liquids and Glasses
• The evolution of vibrational excitations in glassy systems
• Universal Spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution
• Broadband Dielectric Spectroscopy on Glass-Forming Propylene Carbonate
• Vibrational instability, two-level systems and Boson peak in glasses
• Universal origin of boson peak vibrational anomalies in ordered crystals and in amorphous materials
• Local inversion-symmetry breaking controls the boson peak in glasses and crystals
• Anomalous properties of the acoustic excitations in glasses on the mesoscopic length-scale
• The Ioffe-Regel criterion and diffusion of vibrations in random lattices
• Excess Vibrational Modes and the Boson Peak in Model Glasses
• Electromagnetic-radiation absorption of water
• Scaling of phononic transport with connectivity in amorphous solids
• The Boson Peak and its Relation with Acoustic Attenuation in Glasses
• Modern computational studies of the glass transition
• Vibrations of amorphous, nanometric structures: When does continuum theory apply?
• Unveiling Dimensionality Dependence of Glassy Dynamics: 2D Infinite Fluctuation Eclipses Inherent Structural Relaxation
• Boson peak and Ioffe-Regel criterion in amorphous silicon-like materials: the effect of bond directionality
• Heat transport in model jammed solids
• Low-energy quasilocalized excitations in structural glasses
• Vibrational spectrum of topologically disordered systems
• Absence of Marginal Stability in a Structural Glass
• Elastic heterogeneity, vibrational states, and thermal conductivity across an amorphisation transition
• From Crystals to Disordered Crystals: A Hidden Order-Disorder Transition
• Low temperature heat capacity of severely deformed metallic glass
• Vibrational excitations in systems with correlated disorder
• Pressure dependence of the Boson peak in glasses
• Excess Modes in the Vibrational Spectrum of Disordered Systems and the Boson Peak
• Boson peak dynamics of glassy glucose studied by integrated terahertz-band spectroscopy
• Low-energy excess of vibrational states in v-SiO2: the role of transverse dynamics
• On the analysis of the vibrational Boson peak and low-energy excitations in glasses
• Gaussian excitations model for glass-former dynamics and thermodynamics
• Vibrations and Relaxations in a Soft Sphere Glass: Boson Peak and Structure Factors
• Structural origins of the boson peak in metals: From high-entropy alloys to metallic glasses
• From metallic glasses to nanocrystals: Molecular dynamics simulations on the crossover from glass-like to grain-boundary-mediated deformation behaviour
• Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: Configuration changes and vibration modes
• Vibrations in glasses and Euclidean Random Matrix theory
• Propagative and diffusive regimes of acoustic damping in bulk amorphous material
• Theory of harmonic dissipation in disordered solids
• Mean-field model for the density of states of jammed soft spheres
• Disentangling boson peaks and Van Hove singularities in a model glass
• Relation of vibrational excitations and thermal conductivity to elastic heterogeneities in disordered solids
• Voronoi-Delaunay analysis of normal modes in a simple model glass
• The dynamical structure factor in topologically disordered systems
• Lattice instability and enhancement of superconductivity in YB${}_6$
• Brillouin and Boson peaks in Glasses from vector Euclidean Random Matrix Theory
• Emergent percolation length and localization in random elastic networks
• Unifying description of the vibrational anomalies of amorphous materials
• Phonons in Random Elastic Media and the Boson Peak
• The dynamical structure factor in disordered systems
• $q$-independent slow-dynamics in atomic and molecular systems
• Finitely coordinated models for low-temperature phases of amorphous systems
• Frustration and sound attenuation in structural glasses
• Anderson universality in a model of disordered phonons
• Investigation of nonlinear effects in glassy matter using dielectric methods
• Microscopic dynamics of molecular liquids and glasses: Role of orientations and translation-rotation coupling
• Jamming transition of randomly pinned systems
• Vibrational properties of the one-component $\sigma$ phase
• Vibrational spectrum derived from the local mechanical response in disordered solids
• Vector vibrations and the Ioffe-Regel crossover in disordered lattices
• Universality in Glassy Low-Temperature Physics
• Inelastic light, neutron, and X-ray scatterings related to the heterogeneous elasticity of glasses
• Terahertz Dynamics in the Glycerol-Water System
• The nature of non-phononic excitations in disordered systems
• Low-energy optical phonons induce glassy-like vibrational and thermal anomalies in ordered crystals
• Phonon localization in binary alloys with diagonal and off-diagonal disorder: A cluster Green's function approach
• Boson Peak decouples from elasticity in glasses with low connectivity
• Role of disorder in determining the vibrational properties of mass-spring networks
• Density of states in random lattices with translational invariance
• Universal sound absorption in low-temperature glasses
• Probing the role of mobility in the collective motion of non-equilibrium systems
• Localization-delocalization transition for disordered cubic harmonic lattices
• Boson peak in overdoped manganites La_{1-x}Ca_{x}MnO_{3}
• Nature of vibrational eigenmodes in topologically disordered solids
• Fragility and Boson Peak formation in a Supercooled Liquid
• Randomness-Induced Redistribution of Vibrational Frequencies in Amorphous Solids
• Disorder-induced vibrational anomalies from crystalline to amorphous solids
• Near-field localization of the boson peak on tantalum films for superconducting quantum devices
• Elastic constant dishomogeneity and $Q^2$ dependence of the broadening of the dynamical structure factor in disordered systems
• Elastic anomalies in glasses: the string theory understanding in the case of Glycerol and Silica
• Force heterogeneities in particle assemblies: From order to disorder
• Analysis of vibrational normal modes for Coulomb clusters
• Does the boson peak survive in an ultrathin oxide glass?
• Normal modes, and acoustic properties, of an elastic solid with line defects
• Memory vs. irreversibility in thermal densification of amorphous glasses
• Vibrational behaviour of a realistic amorphous-silicon model
• Structural dynamics in thermal-treatment of amorphous indium-oxide films
• Glass-like features of crystalline solids in the quantum critical regime
• An atomic mechanism for the boson peak in metallic glasses
• Theory of heterogeneous viscoelasticity
• Impact of severe plastic deformation on the relaxation of glassy and supercooled liquid states of amorphous Pd${}_{40}$Ni${}_{40}$P${}_{20}$
• High-frequency vibrational density of states of a disordered solid
• Level statistics and Anderson delocalization in two-dimensional granular materials
• Properties of stable ensembles of Euclidean random matrices
• Spectral statistics of the quenched normal modes of a network-forming molecular liquid
• Signature of a polyamorphic transition in the THz spectrum of vitreous GeO2
• Displacement correlations in disordered athermal networks
• Specific heat of the quantum Bragg Glass
• Vibrational dynamics and boson peak in a supercooled polydisperse liquid
• Microstructure and the Boson-peak in thermally-treated In_{x}O films
• Athermal fluctuations in three dimensional disordered crystals
• Nonresonant holeburning in the Terahertz range: Brownian oscillator model
• Study of the localization-delocalization transition for phonons via transfer matrix method techniques
• Universality in the vibrational spectra of weakly-disordered two-dimensional clusters
• Vibrational density of states of amorphous solids with long-ranged power-law correlated disorder in elasticity
• On the origin of the Boson peak in globular proteins
• The scaling behaviour of localised and extended states in one-dimensional tight-binding models with disorder
• Further testing the validity of generalized heterogeneous-elasticity theory for low-frequency excitations in structural glasses
• Open and anisotropic soft regions in a model polymer glass
• Structural Origin of Boson Peak in Glasses
• Localization of vibrational modes in high-entropy oxides
• Disordered statistical physics in low dimensions: extremes, glass transition, and localization
• Sound attenuation derived from quenched disorder in solids
• On the relation between disorder and homogeneity in an amorphous metal
• 'Boson peak' and high-frequency excitations in glassy crystals
• Quantum structure of glasses and the boson peak: a theory of vibrations