Phonon Wave Research Articles

Elongational Rheology and Brillouin Light Scattering of Entangled Telechelic Polybutadiene Based Temporary Networks

This article focuses on the characterization of a series of telechelic polybutadienes with acid end groups (PBd−COOH) neutralized with different alkali metal ions by elongational rheometry. Depending on the ion, the material is found to be strain-hardening or not. While the Li+ ions cause a strain hardening similar to that observed for low density polyethylene, Na+ and K+ essentially do not lead to any strain hardening. Rb+ leads to a different type of strain hardening, like sparsely branched polymers. It is also found that the material behaves brittlely at strain rates ε̇ higher than the crossover frequency ωc. Additionally, an esterified version of the material and the rubidium hydroxide neutralized PBd−COOH is characterized by Brillouin light scattering to assess the local chain dynamics, being essentially noninfluenced by the ion clusters. The dependence of the longitudinal sound velocity cl and hence the longitudinal modulus M from the phonon wave vector q and from the temperature T is compared for two different samples (with and without counterion). It is found that M is insensitive to the presence of the ionic clusters, and therefore, the local chain dynamics are essentially the same for the two model systems and do not play a role in the strain-hardening.

Consistency of the phenomenological theories of wave-type heat transport with the hydrodynamics of a phonon gas

Various phenomenological theories of wave-type heat transport, which can be interpreted as the models of an isotropic rigid heat conductor with an internal vector state variable, have been proposed in the literature with the objective to describe the second sound propagation in dielectric crystals. The aim of this paper is to analyze the relation between these phenomenological approaches and the phonon gas hydrodynamics. The four-moment phonon gas hydrodynamics based on the maximum entropy closure of the moment equations with nonlinear isotropic phonon dispersion relation is considered for this purpose. We reformulate the equations of this hydrodynamics in terms of energy and quasi-momentum as the primitive fields and subsequently demonstrate that, from the macroscopic point of view, they can be understood as describing the reference model of an isotropic rigid heat conductor with quasi-momentum playing the role of the internal vector state variable. This model is determined by the entropy function and the additional scalar potential, but if the finite domain of phonon wave vectors is approximated by the whole space, the additional potential can be expressed in terms of the entropy function and its first derivatives. Then the transformation of primitive fields and the expansion of thermodynamic potentials in powers of the square of quasi-momentum enable us to compare the reference model with the models proposed earlier in the literature. It is shown that the previous models require some subtle modifications in order to achieve full consistency with phonon gas hydrodynamics.

Dynamics of a one-dimensional Holstein polaron with the Davydov ansätze

Following the Dirac-Frenkel time-dependent variational principle, dynamics of a one-dimensional Holstein polaron is probed by employing the Davydov D2 Ansatz with two sets of variational parameters, one for each constituting particle in the exciton-phonon system, and a simplified variant of the Davydov D1 Ansatz, also known as the $\tilde{D}$ Ansatz, with an additional set of phonon displacement parameters. A close examination of variational outputs from the two trial states reveals fine details of the polaron structure and intricacies of dynamic exciton-phonon interactions. Superradiance coherence sizes, speeds of exciton-induced phonon wave packets, linear optical absorption, and polaron energy compositions are also included in the study.

Molecular Dynamics Simulation of Phonon Scattering at Silicon/Germanium Interfaces

Detailed phonon transport at Si/Ge interfaces is studied using the molecular dynamics wave-packet method. Three types of interfaces are investigated: A smooth interface, an interface with random roughness, and an interface with a regularly patterned roughness. The phonon transmissivity for each case is calculated as a function of phonon frequency, roughness characteristic length, and atomic structure. For a smooth interface, the transmissivities predicted by the MD simulations agree well with the acoustic mismatch model based on the continuum assumption. The rough interface simulation results indicate that random roughness is the source of incoherent phonon scattering and decreases the phonon transmission. Periodic structures such as the regularly patterned roughness employed in this paper cause strong phonon wave interference and may restore phonon transmission as the layer thickness increases.

Phonon transport in large scale carbon-based disordered materials: Implementation of an efficient order-Nand real-space Kubo methodology

We have developed an efficient order-$N$ real-space Kubo approach for the calculation of the phonon conductivity which outperforms state-of-the-art alternative implementations based on the Green's function formalism. The method treats efficiently the time-dependent propagation of phonon wave packets in real space, and this dynamics is related to the calculation of the thermal conductance. Without loss of generality, we validate the accuracy of the method by comparing the calculated phonon mean free paths in disordered carbon nanotubes (isotope impurities) with other approaches, and further illustrate its upscalability by exploring the thermal conductance features in large width edge-disordered graphene nanoribbons (up to $\ensuremath{\sim}20\text{ }\text{nm}$), which is out of the reach of more conventional techniques. We show that edge disorder is the most important scattering mechanism for phonons in graphene nanoribbons with realistic sizes and thermal conductance can be reduced by a factor of $\ensuremath{\sim}10$.

Spin-Phonon Coupling Effects in Antiferromagnetic Cr<SUB>2</SUB>O<SUB>3</SUB> Nanoparticles

In the present work we use Raman microscopy to investigate the size effect of spin-phonon coupling in antiferromagnetic Cr2O3 nanoparticles. The peculiarities of the dependency of the phonon wave number on temperature (with a relatively weak peak at 293 cm(-1)) can be attributed to the spin-phonon coupling. The variation with temperature of the spin-phonon mode develops when the antiferromagnetic state is near the ordering temperature of the Cr spins. The observations can be reasonably well interpreted by describing the order parameter. A shift in frequency is caused by a strong spin-phonon interaction in Cr2O3. The obtained s-ph coefficients are found to be consistent with the strain, where raising the strain results in weakening of the s-ph coupling.

Energy exchange between electrons and phonons in quantum dot connected between pyramidal and abrupt transport nanojunctions

Electron–phonon scattering induced intensive heat generation is one of the major bottlenecks for high performance nanoelectronic circuits in miniaturizing their line widths beyond submicron scales. The existence of quantum confinement effects in nanoscaled conduction channels results in which the behaviors of electrons and phonons will become drastically different from those in bulk materials. This is especially true in the junction regions where the nanochannel is linked with the electronic and thermal reservoirs. The present study investigated the structural effect of pyramidal and abrupt junctions in heat exchange between electron and phonon subsystems in the transport through a quantum dot (QD). The numerical results indicated that by confining the electronic and phononic wave functions in the pyramidal junctions, a higher saturation heat exchange would be reached at a lower bias, compared to that of the abrupt junction. The pyramidal junction also becomes more subjected to size effects, where the saturation heat exchange decreases as the size of the junction increases. Such an effect is less significant in the abrupt junctions. Surface reconstruction induced bond stiffening in the pyramidal junctions plays a dominant role in modulating the junction heat exchange by blockading the phonon transportation between the reservoirs through the QD, which effectively reducing the amount of heat being generated. The results may provide new insights on the fundamental science and relationship between contact atomic structures and thermal dissipations in nanoelectronics.

Phonon wave-packet interference and phonon tunneling based energy transport across nanostructured thin films

The molecular dynamics based phonon wave-packet technique is used to study phonon transport across mass-mismatched fcc thin films. Transport behavior of normally incident longitudinal acoustic phonon wave packets with wave vectors ranging in magnitude from 2% to 50% of the ⟨100⟩ first Brillouin zone boundary is examined as a function of thin film thickness when the phonon mean free path exceeds film thickness. The results indicate that for thin film to bulk solid mass ratios up to a factor of 6, the transmission of energy through the thin film can be well described by treating the thin film as a bulk solid.

Optical phonons in colloidal CdSe nanorods

AbstractIn this work the vibrational properties of colloidal CdSe nanorods (NRs) and CdSe‐ZnS core–shell NRs are investigated via Raman spectroscopy. The longitudinal optical (LO) phonons in NRs are confined to the NR volume. The confinement of the phonon wave function leads to a relaxation of the q = 0 rule and the phonon frequency is found to depend on the NR diameter. The coupling strength between LO phonons and excitons also depends on the NR diameter. The total coupling strength is much lower than in bulk material due to a decrease of the influence of the Coulomb interaction in nanoparticles. However, the coupling strength is found to rise for decreasing diameters. This is due to the increasing contributions of higher frequency phonons for smaller nanoparticle sizes. A radial breathing mode with a diameter dependent frequency is deduced from ab initio calculations and its existence in NRs is verified experimentally. The diameter‐dependence of the modes' frequency can be used to estimate the NR diameter from a Raman measurement. In core–shell structures, the lattice mismatch between core and shell leads to a compressive strain of the core lattice. The exciton wave function changes with the modified boundary. This is reflected in an altered exciton–phonon coupling strength.

Mechanical and electronic properties of ferromagneticGa1−xMnxAsusing ultrafast coherent acoustic phonons

Ultrafast two-color pump-probe measurements, involving coherent acoustic phonon waves, have provided information simultaneously on the mechanical properties and on the electronic structure of ferromagnetic ${\text{Ga}}_{1\ensuremath{-}x}{\text{Mn}}_{x}\text{As}$. The elastic constants ${C}_{11}$ of ${\text{Ga}}_{1\ensuremath{-}x}{\text{Mn}}_{x}\text{As}$ $(0.03\ensuremath{\le}x\ensuremath{\le}0.07)$ are observed to be systematically smaller than those of GaAs. Both ${C}_{11}$ and ${V}_{\text{s}}$ measured in ${\text{Ga}}_{1\ensuremath{-}x}{\text{Mn}}_{x}\text{As}$ are found to increase with temperature $(78\text{ }\text{K}\ensuremath{\le}T\ensuremath{\le}295\text{ }\text{K})$, again in contrast to the opposite behavior in GaAs. In addition, our experimental results indicate a small blueshifting of the fundamental band gap of ${\text{Ga}}_{1\ensuremath{-}x}{\text{Mn}}_{x}\text{As}$ as Mn concentration increases.

Switchable phononic wave filtering, guiding, harvesting, and actuating in polarization-patterned piezoelectric solids

We demonstrate the ability to manipulate the propagation of phononic (elastic, acoustic) waves in two-dimensional piezoelectric solids by spatially patterning the polarization distribution. We simulate the wave fields by the finite element method and demonstrate the ability to dynamically alter the wave propagation by switching (on/off) the piezoelectric behavior by operating the electrodes in a closed or open circuit configuration. The piezoelectric polarization patterns are nonintuitive and are determined by topology optimization. We illustrate the interesting response of optimally patterned phononic devices with four examples: a filter, a waveguide, an energy harvester, and a wave actuator.

Detecting strain wave propagation through quantum dots by pump-probe spectroscopy: A theoretical analysis

The influence of strain waves traveling across a quantum dot structure on its optical response is studied for two different situations: First, a strain wave is created by the optical excitation of a single quantum dot near a surface which, after reflection at the surface, reenters the dot; second, a phonon wave packet is emitted by the excitation of a nearby second dot and then travels across the quantum dot. Pump-probe type excitations are simulated for quantum dots in the strong confinement limit. We show that the optical signals allow us to monitor crossing strain waves for both structures in the real-time response as well as in the corresponding pump-probe spectra. In the time-derivative of the phase of the polarization a distinct trace reflects the instantaneous shifts of the transition energy during the passage while in the spectra pronounced oscillations reveal the passage of the strain waves.

Optical phonon mixing in bilayer graphene with a broken inversion symmetry

Pristine bilayer graphene is a centrosymmetric material in which parity is a conserved quantity. The high sensitivity of this atomic scale structure to external perturbations that break the inversion symmetry enables significant potentials for device applications. Raman spectroscopy is used here to probe the breakdown of parity conservation in a direct and quantitative manner via a phonon mixing phenomenon. The striking broken-symmetry effects display anticrossing coupling between two opposite parity long-wavelength optical phonons. The spectral intensity transfer between the two observed Raman peaks offers quantitative measurements of the evolution of the phonon wave function and demonstrates a manifestation of broken inversion symmetry in graphene layers.

Phonons in doped and undopedBaFe2As2investigated by inelastic x-ray scattering

We measured phonon frequencies and linewidths in doped and undoped ${\text{BaFe}}_{2}{\text{As}}_{2}$ single crystals by inelastic x-ray scattering and compared our results with density functional theory calculations. In agreement with previous work, the calculated frequencies of some phonons depended on whether the ground state was magnetic or not and, in the former case, whether phonon wave vector was parallel or perpendicular to the magnetic ordering wave vector. The experimental results agreed better with the magnetic calculation than with zero Fe moment calculations, except the peak splitting expected due to magnetic domain twinning was not observed. Furthermore, phonon frequencies were unaffected by the breakdown of the magnetic ground state due to either doping or increased temperature. Based on these results we propose that phonons strongly couple not to the static order, but to high frequency magnetic fluctuations.

Nanoscale mechanical contacts probed with ultrashort acoustic and thermal waves

Using an ultrafast optical technique we measure coherent phonon-pulse reflection from---and heat flow across---a mechanical contact of nanoscale thickness between a thin metal film and a spherical dielectric indenter. Picosecond phonon wave packets at $\ensuremath{\sim}50\text{ }\text{GHz}$ returning from this interface probe the pressure distribution, the contact area, and the indentation profile to subnanometer resolution, revealing the film deformation in situ. These measurements and simultaneous thermal-wave imaging at $\ensuremath{\gtrsim}1\text{ }\text{MHz}$ are consistent with significant enhancement of phonon transport across the near-contact nanogap.

The structural, electronic, elastic, phonon, and thermodynamical properties of the SmX (X=P, Sb, Bi) compounds

Abstract A detailed theoretical study of structural, electronic, elastic, phonon, and thermodynamical properties of SmX (X = P, Sb, Bi) compounds is presented by performing ab-initio calculations based on density-functional theory using the Vienna ab-initio simulation package (VASP). For describing the interaction between electrons and ions, the projector-augmented wave (PAW) method is used. The generalized-gradient approximation (GGA) is chosen for the exchange–correlation functional. The calculated structural parameters, such as the lattice constant with and without spin-polarization (SP), bulk modulus, cohesive energy, second-order elastic constants, the electronic band structures and the related total density of states with and without SP and spin–orbit coupling (SOC) are presented. The high-pressure phase of all compounds is investigated and phase transition pressure from NaCl (B1) to high-pressure phase is determined. For B1 structure, the calculated values of lattice constants are compared with the available experimental and other theoretical data and bulk modulus values are compared with available other theoretical results. In order to gain further information, we have calculated Zener anisotropy factor ( A ), Poisson’s ratio ( ν ), Young’s modulus ( E ), shear modulus ( C ′), elastic wave velocities, Debye temperature, phonon frequencies and one-phonon density of states for B1 structure of these three compounds. The temperature dependent behavior of heat capacity and entropy for these compounds in B1 phase is also presented.

Phonon localization and thermal rectification in asymmetric harmonic chains using a nonequilibrium Green’s function formalism

Thermal transport across one-dimensional atomic chains is studied using a harmonic nonequilibrium Green's function formalism in the ballistic phonon transport regime. Introducing a mass impurity in the chain and mass loading in the thermal contacts leads to interference of phonon waves, which can be manipulated by varying the magnitude of the loading. This shows that thermal rectification is tunable in a completely harmonic system.

Temperature dependent physical effects of ultrasonic wave in beryllium chalcogenides

Temperature dependent physical effects of ultrasonic wave viz. ultrasonic attenuation due to interaction of sound wave and thermal phonons, thermoelastic loss and dislocation damping have been studied in beryllium chalcogenides (BeX, X = S, Se and Te) in the temperature range 50–500 K, along three crystallographic directions of propagation viz. [1 0 0], [1 1 0] and [1 1 1] for longitudinal and shear modes of propagation. Second and third order elastic moduli have been obtained using electrostatic and Born repulsive potentials and taking hardness parameter and nearest neighbour distance as input data. Gruneisen numbers, acoustic coupling constants and drag coefficients have been evaluated for longitudinal and shear waves along different directions of propagation and polarization. The results have been discussed and compared with the available data. It has been found that the temperature dependence of ultrasonic attenuation follows the temperature variation of diffusion coefficient and is mainly dominated by phonon–phonon interaction.

Extracting phonon thermal conductance across atomic junctions: Nonequilibrium Green’s function approach compared to semiclassical methods

The thermal conductance of nanoscale phonon modes is typically calculated using the Boltzmann transport equation. A particular implementation of this method is the acoustic mismatch model (AMM) that compares impedance ratios at a mathematically abrupt transition between two equilibrium regions. The shortcomings of this model can be rectified by starting from a microscopic physics based equation describing the propagation of phonon waves across an extended junction, with carefully computed thermal boundary conditions on either side. The resulting nonequilibrium Green’s function (NEGF) formalism provides an accurate yet physically transparent machinery to calculate energy transfer, especially in nanosystems where the concept of thermal equilibrium breaks down readily. The purpose of this paper is to establish the NEGF formalism of thermal conductivity with a few simple examples and illustrate its particular strengths compared to the AMM.

Universality in electron–modulated-acoustic-phonon interactions in a free-standing semiconductor nanowire

Modulated acoustic phonons and their interactions with electrons in a free-standing cylindrical semiconductor nanowire are investigated theoretically. It is shown that the form factor is a key quantity in discussing the impact of acoustic phonons on electron transport. The form factor calculated using modulated acoustic phonons is identical to that calculated using bulk phonons for a large phonon wave vector along the wire, whereas it is larger for a small phonon wave vector. This increase directly leads to an increase in the electron scattering rate and a reduction in mobility. In addition, the form factor increase has a universality independent of the wire material and radius.