Long-wavelength Phonons Research Articles

Low-frequency dispersion of phonons in one-dimensional chains

The wave velocity of long-wavelength acoustic phonons is found in one-dimensional crystals with an arbitrary basis by an elementary argument founded upon the equality of kinetic and potential energies in a linear wave. This argument also extends to quasiperiodic crystals such as those based on the Fibonacci sequence. Inspired by recent experiments, these ideas are then applied to an artificial quasicrystalline transmission line made by coupling electromagnetic cavities in a Fibonacci sequence.

Emergence of large nonadiabatic effects induced by the electron-phonon interaction on the complex vibrational quasiparticle spectrum of doped monolayer MoS2

We present a comprehensive first-principles analysis of the nonadiabatic effects due to the electron-phonon interaction on the vibrational spectrum of the electron-doped monolayer ${\mathrm{MoS}}_{2}$. Deep changes in the Fermi surface upon doping cause the linewidth broadening of the normal modes governing the spin-conserving intervalley electronic scattering, which become unstable with the population of all the spin-split conduction valleys. We find that the nonadiabatic spectral effects modify dramatically the adiabatic dispersion of the long-wavelength optical phonon modes, responsible for intravalley scattering, as soon as inequivalent valleys get populated. These results are illustrated by means of a simple analytical model. Finally, we explain the emergence of an intricate dynamical structure for the strongly interacting out-of-plane polarized ${A}_{1}^{\ensuremath{'}}$ optical vibrational mode spectrum by means of a multiple-phonon quasiparticle picture defined in the full complex frequency plane, showing that this intriguing spectral structure originates from the splitting of the original adiabatic branch induced by the electron-phonon coupling.

Quantum oscillations in acoustic phonons in Weyl semimetals

We theoretically study the modification of the energy spectrum of long-wavelength acoustic phonons due to the electron-phonon interaction in a three-dimensional topological Weyl semimetal under the influence of quantizing magnetic fields. We find that the dispersion and attenuation of phonons show striking oscillatory behaviors as varying the magnetic field at low temperatures. These oscillations are distinct when the Fermi energy is in different energy regimes. Moreover, the van Hove singularity of the Weyl spectrum can manifest as a transition between different oscillation patterns when increasing the magnetic field. These phonon behaviors could provide testable fingerprints of the Fermi surface morphology and relativistic feature of the Weyl semimetal.

Interaction of phonons with discrete breathers in one-dimensional chain with tunable type of anharmonicity

In this paper, we consider the interaction of small amplitude waves (phonons) with standing discrete breather (DB) in the one-dimensional chain of harmonically coupled particles interacting with the anharmonic one-site potential, which can be of hard-type or soft-type anharmonicity. The coefficients of phonon reflection and transmission are calculated numerically. It is found that for the case of hard-type anharmonicity (soft-type anharmonicity) DBs are more transparent for short-wavelength (long-wavelength) phonon waves, while they efficiently reflect long-wavelength (short-wavelength) phonons. In thermal equilibrium, when all phonons have equal energy density, it is found that for the same width of the transparency window, DB transmits less energy in the case of the hard-type anharmonicity. This is so because, in this case, DB reflects long-wavelength phonons, which have larger group velocity and hence greater contribution to the net energy flux through the DB. In this sense, DBs more efficiently suppress thermal conductivity in the chain with hard-type anharmonicity. Our results contribute to a better understanding of the role of discrete breathers in the heat flow in nonlinear chains.

Dynamics of relaxation and dressing of a quenched Bose polaron

We study the non-equilibrium dynamics of relaxation and dressing of a mobile impurity suddenly immersed--or quenched-- into a zero temperature homogeneous Bose Einstein condensate (BEC) with velocity $v$. A many body generalization of Weisskopf-Wigner theory is implemented to obtain the impurity fidelity, reduced density matrix and entanglement entropy. The dynamics depend crucially on the Mach number $\beta =v/c$, with $c$ the speed of sound of superfluid phonons and features many different time scales. Quantum Zeno behavior at early time is followed by relaxational and dressing dynamics determined by Cerenkov emission of long-wavelength phonons for $\beta >1$ with a decay rate $\Gamma_p \propto (\beta-1)^3$. The polaron dressing dynamics \emph{slows-down} as $\beta \rightarrow 1$ and is characterized by power laws $t^{-\alpha}$ with different exponents for $\beta \lessgtr 1$. The asymptotic entanglement entropy features a sharp discontinuity and the residue features a cusp at $\beta =1$. These non-equilibrium features suggest \emph{universal} dynamical critical phenomena near $\beta \simeq 1$, and are a direct consequence of the linear dispersion relation of long wavelength superfluid phonons. We conjecture on the emergence of an asymptotic dynamical attractor with $\beta \leq 1$.

Long-wavelength emergent phonons in Bloch skyrmion crystals distorted by exchange anisotropy and tilted magnetic fields

Skyrmion crystals (SkX) are periodic alignment of magnetic skyrmions, i.e., a type of topologically protected spin textures. Compared with ordinary crystals, they can be drastically deformed under anisotropic effects because they are composed of field patterns whose deformation does not cause any bond-breaking. This exotic ductility of SkX bring about great tunability of its collective excitations called emergent phonons, which are vital for magnonics application. The question is how to quantitatively determine the emergent phonons of distorted SkX. Here we systematically study the long wavelength emergent phonons of SkX distorted by (a) a negative exchange anisotropy, and (b) a tilted magnetic field. In both cases, deformation and structural transitions of SkX thoroughly influence the frequency, anisotropy of vibrational pattern and dispersion relation, and coupling between lattice vibration and in-lattice vibration for all modes. Tilted magnetic fields are very effective in tuning the emergent phonons, such that all modes except the Goldstone mode can be excited by AC magnetic fields when a tilted bias field is presented.

Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling.

The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized nor fully understood. Of particular importance is the scaling of the attenuation rate Γ(k) with small wavenumbers k → 0 in the thermodynamic limit of macroscopic glasses. Here, we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber k†, where phonons are no longer quantized into bands. For k < k†, finite-size effects dominate Γ(k), which is quantitatively described by a theory of disordered phonon bands. For k > k†, we find that Γ(k) is affected by the number of quasilocalized nonphononic excitations, a generic signature of glasses that feature a universal density of states. In particular, we show that in a frequency range in which this number is small, Γ(k) follows a Rayleigh scattering scaling ∼k¯d+1 (¯d is the spatial dimension) and that in a frequency range in which this number is sufficiently large, the recently observed generalized-Rayleigh scaling of the form ∼k¯d+1 log(k0/k) emerges (k0 > k† is a characteristic wavenumber). Our results suggest that macroscopic glasses-and, in particular, glasses generated by conventional laboratory quenches that are known to strongly suppress quasilocalized nonphononic excitations-exhibit Rayleigh scaling at the lowest wavenumbers k and a crossover to generalized-Rayleigh scaling at higher k. Some supporting experimental evidence from recent literature is presented.

Enhanced thermoelectric figure of merit in Bi2Te3–CNT–PEDOT nanocomposite by introducing conducting interfaces in Bi2Te3 nanostructures

Bi2Te3–CNT–PEDOT nanocomposites have been synthesized by mixing PEDOT:PSS with hydrothermally synthesized Bi2Te3–CNT nanocomposites. Introducing conducting interfaces by adding PEDOT in Bi2Te3–CNT boosts the charge carrier mobility, resulting in improved electrical conductivity and simultaneously lowering the lattice thermal conductivity by enhancing phonon scattering and thus resulting in two-fold enhancement of the figure of merit. The detailed mechanism behind the enhancement of charge carrier mobility is discussed by considering the role of conducting interfaces and strong coupling of CNTs and PEDOT conducting chains. The formation of a large number of interfaces in Bi2Te3–CNT–PEDOT nanocomposites acts as strong scattering centers and thermal barriers for long-wavelength phonons, which reduces the lattice thermal conductivity. The formation of interfaces between Bi2Te3 nanostructures and CNT–PEDOT conducting channels has been studied by Kelvin probe force microscopy which clearly showed a smaller interface potential barrier for the Bi2Te3–CNT–PEDOT nanocomposite.

Temperature-driven narrowing of the insulating gap as a precursor of the insulator-to-metal transition: Implications for the electronic structure of solids.

We present a microscopic picture rationalizing the surprisingly steep decrease in the bandgap with temperature in insulators, crystalline or otherwise. The gap narrowing largely results from fluctuations of long-wavelength optical phonons-when the latter are present-or their disordered analogs if the material is amorphous. We elaborate on this notion to show that possibly with the exception of weakly bound solids made of closed-shell electronic configurations, the existence of an insulating gap or pseudogap in a periodic solid implies that optical phonons must be present, too. This means that in an insulating solid, the primitive cell must have at least two atoms and/or that a charge density wave is present, with the possible exception of weakly bonded solids such as rare-gas or ferromagnetic Wigner crystals. As a corollary, a (periodic) elemental solid held together by nonclosed shell interactions and whose primitive unit contains only one atom will ordinarily be a metal, consistent with observation. Consequences of the present picture for Wigner solids are discussed. A simple field theory of the metal-insulator transition is constructed that directly ties long-wavelength optical vibrations with fluctuations of an order parameter for the metal-insulator transition. The order parameter is shown to have at least two components, yet no Goldstone mode arises as a result of the transition.

Thermal Properties of a Eutectic InSb + MnSb Composite

We have studied the thermal conductivity κ(T) and thermal diffusivity a(T) of a eutectic InSb + MnSb composite in the range 80–700 K with the heat flux parallel and perpendicular to MnSb inclusions. The phonon thermal conductivity data have been analyzed in terms of the Holland model. The weaker temperature dependence of thermal conductivity in the range 250–450 K is due to resonance transfer of the energy of ionized impurity states. The observed anisotropy in κ(T) in the range 80–250 K is associated with the scattering of long-wavelength phonons by interfaces. The anomalies in κ(T) and a(T) observed in the phase transition region are due to phonon scattering by magnetic order parameter fluctuations.

Phonon spectrum and phonon focusing in coarse-grained atomistic simulations

This work investigates the accuracy, efficiency, and applicability of coarse-grained (CG) atomistic methods in simulation of phonon dynamics. First, we compute and compare phonon dispersion relations in CG models with those in atomically resolved models, using the concurrent atomistic-continuum (CAC). The CG atomistic models using the CAC method are shown to reproduce long-wavelength phonons with great accuracy, while capturing the dynamics of some short-wavelength phonons that are usually inaccessible to CG methods. We then present CG simulation results of the propagation of heat pulses in Si with the interaction between atoms being modelled with the Stillinger-Weber potential; the experimentally observed phonon-focusing patterns in the (1 0 0) and (1 1 1) planes of Si crystals are reproduced. The accuracy and efficiency of the CAC method in CG simulation of acoustic and optical phonon branches are quantified with respect to atomically-resolved molecular dynamics simulations. The applicability and limitations of concurrent multiscale methods in the simulation of phonon transport across atomistic-continuum interface are investigated. Possible ways to overcome the limitations are discussed.

The effects of curvature on the thermal conduction of bent silicon nanowire

Curvature induced by mechanical deformation in nanostructures has been found to significantly affect their stability and reliability during applications. In this work, we investigated the effects of curvature induced by mechanical bending on the thermal properties of silicon nanowire (SiNW) by using molecular dynamics simulations. By examining the relationship between the curved geometry and local temperature/heat flux distribution, we found that there is no temperature gradient/heat flux along the radial direction of the bent SiNW, and the local heat current density along the circumferential direction varies with the radius of curvature. Interestingly, a ∼10% reduction in the thermal conductivity is found in the bent SiNW due to the depression of long-wavelength phonons caused by its inhomogeneous deformation. The present work demonstrates that the curvature induced by mechanical bending can be used to modulate the thermal conductivity of SiNWs.

On the Intracenter Relaxation of Shallow Arsenic Donors in Stressed Germanium. Population Inversion under Optical Excitation

The relaxation rates of lower excited states 1s(T), 2p0, 2s, 3p0, and 2p± of arsenic donors in a germanium crystal are calculated upon the interaction with long-wavelength acoustic phonons depending on the uniaxial stress in the crystallographic direction [111]. The populations of states under optical excitation are estimated for calculated times. It is shown theoretically that optical excitation of the medium forms an inverse population of arsenic donor levels and leads to the possibility of the implementation of a four-level laser scheme with the radiative transition between 2p states and the 1s triplet state at zero strain. The estimated value of the expected gain in the medium under optical excitation conditions by CO2 laser radiation in the medium at a donor concentration of 2 × 1015 cm–3 is ~0.35 cm–1 at a frequency of 1.98 THz if the laser transition is 2p± → 1s(T) and 1.25 THz if the laser transition is 2p0 → 1s(T).

Selective breakdown of phonon quasiparticles across superionic transition in CuCrSe2

Superionic crystals exhibit ionic mobilities comparable to liquids while maintaining a periodic crystalline lattice. The atomic dynamics leading to large ionic mobility have long been debated. A central question is whether phonon quasiparticles—which conduct heat in regular solids—survive in the superionic state, where a large fraction of the system exhibits liquid-like behaviour. Here we present the results of energy- and momentum-resolved scattering studies combined with first-principles calculations and show that in the superionic phase of CuCrSe2, long-wavelength acoustic phonons capable of heat conduction remain largely intact, whereas specific phonon quasiparticles dominated by the Cu ions break down as a result of anharmonicity and disorder. The weak bonding and large anharmonicity of the Cu sublattice are present already in the normal ordered state, resulting in low thermal conductivity even below the superionic transition. These results demonstrate that anharmonic phonon dynamics are at the origin of low thermal conductivity and superionicity in this class of materials. Neutron and X-ray scattering studies combined with first-principles calculations suggest that the large, liquid-like ionic mobility in the canonical superionic crystal CuCrSe2 is due to anharmonic phonon dynamics.

Raman Spectra of Nonpolar Crystalline Nanoparticles: Elasticity Theory-like Approach for Optical Phonons

A simple way to investigate theoretically the Raman spectra (RS) of nonpolar nanoparticles is proposed. For this aim we substitute the original lattice optical phonon eigenproblem by the continuous Klein-Fock-Gordon-like equation with Dirichlet boundary conditions. This approach provides the basis for the continuous description of optical phonons in the same manner how the elasticity theory describes the longwavelength acoustic phonons. Together with continuous reformulation of the bond polarization model it allows to calculate the RS of nanoparticles without referring to their atomistic structure. It ensures the powerful tool for interpreting the experimental data, studying the effects of particle shape and their size distribution. We successfully fit recent experimental data on very small diamond and silicon particles, for which the commonly used phonon confinement model fails. The predictions of our theory are compared with recent results obtained within the dynamical matrix method - bond polarization model (DMM-BPM) approach and an excellent agreement between them is found. The advantages of the present theory are its simplicity and the rapidity of calculations. We analyze how the RS are affected by the nanoparticle faceting and propose a simple power law for Raman peak position dependence on the facets number. The method of powder RS calculations is formulated and the limitations on the accuracy of our analysis are discussed.

Molecular dynamics study on heat conduction in poly(3,4-ethylenedioxythiophene)

The poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) composite has been gaining attention as a potential organic thermoelectric material owing to its superior electrical property and low thermal conductivity. Several experiments have recently demonstrated that introduction of high-boiling-point solvents increases optimal charge carrier concentration and leads to high crystallinity, resulting in noticeable improvement of thermoelectric performance. Therefore, much attention has been paid to electrical properties. Understanding of intrinsic heat conduction in PEDOT is also important since the thermal conductivity of bulk polymers is sensitive to macroscopic alignment and transport properties of individual chains. Moreover, thermoelectric performance inversely scales with thermal conductivity. In this work, by molecular dynamics simulations, we have investigated heat conduction in PEDOT chains and evaluated the impact of adsorbed protonic acid on the thermal conductivity of PEDOT. Owing to the quasi-ballistic nature of heat conduction in PEDOT chains, we found that thermal conductivity has strong size dependence and varies from 1–10 W m−1 K−1. Furthermore, we found that the adsorption on PEDOT of toluene sulfonic acid (TSA); a monomer of PSS; suppresses contribution of the long-wavelength phonons to heat conduction. These results suggest that decreasing the length of PEDOT chains in a composite and increasing the surface density of adsorbed TSA molecules are effective methods of reducing the thermal conductivity of the composite, leading to the enhancement of thermoelectric performance.

Current-density implementation for calculating flexoelectric coefficients

Flexoelectricity, where a voltage is induced in an insulator by a strain gradient, becomes increasingly important as electronic devices shrink to the nanoscale. In order to develop a quantitative understanding of the flexoelectric effect in materials, the authors have developed and implemented a first-principles methodology based on density functional perturbation theory to calculate the flexoelectric response. The strategy of mapping a strain gradient onto a long-wavelength acoustic phonon, and calculating the electrical response via the current density, allows the full flexoelectric tensor to be determined with unprecedented accuracy and efficiency. This paves the way for an improved understanding of the underlying mechanisms responsible for flexoelectric effects, thus promising improved control of these effects in the context of nanoelectronic devices.

Relaxation Dynamics of Carriers in Graphene

We study the damping of anomalous Rabi oscillations in monolayer graphene by means of electron–phonon interaction. Our calculations show that the electron–phonon interaction led to the novel incoherent anomalous Rabi oscillations in graphene. Conventional Rabi oscillations occur near resonance show an energy relaxation discussed elsewhere. Anomalous Rabi oscillations display almost zero energy relaxation in the presence of long-wavelength phonons at the Dirac point in the first Brillouin zone. The role of electron–phonon interaction in dephasing of anomalous Rabi oscillations is prominent far away from the Dirac point. There are huge numbers of anomalous Rabi cycles present near the Dirac point.

Monte-Carlo study of electronic transport in non-σh-symmetric two-dimensional materials: Silicene and germanene

The critical role of silicon and germanium in the semiconductor industry, combined with the need for extremely thin channels for scaled electronic devices, has motivated research towards monolayer silicon (silicene) and monolayer germanium (germanene). The lack of horizontal mirror (σh) symmetry in these two-dimensional crystals results in a very strong coupling—in principle diverging—of electrons to long wavelength flexural branch (ZA) phonons. For semi-metallic Dirac materials lacking σh symmetry, like silicene and germanene, this effect is further exacerbated by strong back-scattering at the Dirac cone. In order to gauge the intrinsic transport limitations of silicene and germanene, we perform low- and high-field transport studies using first-principles Monte-Carlo simulations. We take into account the full band structure and solve the electron-phonon matrix elements to treat correctly the material anisotropy and wavefunction overlap-integral effects. We avoid the divergence of the ZA phonon scattering rate through the introduction of an optimistic (1 nm long wavelength) cutoff for the ZA phonons. Even with this cutoff for long-wavelength ZA phonons, essentially prohibiting intravalley scattering, we observe that intervalley ZA phonon scattering dominates the overall transport properties. We obtain relatively large electron mobilities of 701 cm2 V−1 s−1 for silicene and 2327 cm2 V−1 s−1 for germanene. Our results show that silicene and germanene may exhibit electronic transport properties that could surpass those of many other two-dimensional materials, if intravalley ZA phonon scattering could be suppressed.

The φ4 Model, Chaos, Thermodynamics, and the 2018 SNOOK Prizes in Computational Statistical Mechanics

The one-dimensional $\phi^4$ Model generalizes a harmonic chain with nearest-neighbor Hooke's-Law interactions by adding quartic potentials tethering each particle to its lattice site. In their studies of this model Kenichiro Aoki and Dimitri Kusnezov emphasized its most interesting feature : because the quartic tethers act to scatter long-wavelength phonons, $\phi^4$ chains exhibit Fourier heat conduction. In his recent Snook-Prize work Aoki also showed that the model can exhibit chaos on the three-dimensional energy surface describing the two-body two-spring chain. That surface can include {\it at least two} distinct chaotic seas. Aoki pointed out that the model typically exhibits different kinetic temperatures for the two bodies. Evidently few-body $\phi^4$ problems merit more investigation. Accordingly, the 2018 Prizes honoring Ian Snook (1945-2013) will be awarded to the author(s) of the most interesting work analyzing and discussing few-body $\phi^4$ models from the standpoints of dynamical systems theory and macroscopic thermodynamics, taking into account the model's ability to maintain a steady-state kinetic temperature gradient as well as at least two coexisting chaotic seas in the presence of deterministic chaos.