Softening Of Frequency Research Articles

Twist Angle-Dependent Phonon Hybridization in WSe2/WSe2 Homobilayer.

The emerging moiré superstructure of twisted transition metal dichalcogenides (TMDs) leads to various correlated electronic and optical properties compared to those of twisted bilayer graphene. In such a versatile architecture, phonons can also be renormalized and evolve due to atomic reconstruction, which, in turn, depends on the twist angle. However, observing this reconstruction and its relationship to phonon behavior with conventional, cost-effective imaging methods remains challenging. Here, we used noninvasive Raman spectroscopy on twisted WSe2/WSe2 (t-WSe2) homobilayers to examine the evolution of phonon modes due to interlayer coupling and atomic reconstruction. Unlike in the natural bilayer (NB), ∼0° as well as ∼60° t-WSe2 samples, the nearly degenerate A1g/E2g mode in the twisted samples (1-7°) split into a doublet in addition to the nondegenerate B2g mode, and the maximum splitting is observed around 2-3°. Our detailed theoretical calculations qualitatively capture the splitting and its dependence as a function of the twist angle and highlight the role of the moiré potential in phonon hybridization. Additionally, we found that around the 2° twist angle, the anharmonic phonon-phonon interaction is higher than the natural bilayer and decreases for larger twist angles. Interestingly, we observed anomalous Raman frequency softening and line-width increase with the decreasing temperature below 50 K, pointing to the combined effect of enhanced electron-phonon coupling and cubic anharmonic interactions in moiré superlattice.

Stringlet excitation model of the boson peak.

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.

Ultralow lattice thermal conductivity and excellent thermoelectric performance of monolayer CdGaInS4: a first-principles investigation.

Monolayer CdGaInS4 is an excellent optoelectronic material, but its thermoelectric properties remain unexplored. Through first-principles studies, we investigate the thermoelectric transport properties of monolayer CdGaInS4. The results show that the degenerate weakly dispersive valence band results in an ultrahigh Seebeck coefficient, and the small parabolic electron pockets lead to good electron mobility and conductivity. The ultralow lattice thermal conductivity is attributed to the complete decoupling and softening of the low frequency out-of-plane mode and the strong bonding anharmonicity, giving rise to significant phonon scattering. These results provide good physical descriptors for the search for and theoretical design of excellent two-dimensional thermoelectric materials, and motivate relative measurements in monolayer CdGaInS4 and its applications as a promising thermoelectric material.

Effect of nano-crystallization and atomic substitution on electronic and heat properties of Bi2Te3

The specific heat of nano-crystalline (NC) Bi2Te3 (20 nm) in the temperature range of 150 K to 300 K is theoretically studied and compared with the specific heat of the bulk Bi2Te3 materials. Carrier concentration and Hall coefficient are also evaluated using free electron model and compared with experimental results. Lattice (phonon) specific heat has been observed with an overlap repulsive potential with the help of Debye model. For Nano Crystalline materials having high interface volume ratio, the Debye temperature and phonon frequencies are reasonably less at the interfaces than at the core of nano-crystal. Such softening of phonon frequencies at interfaces results in enhancement of Specific Heat in nano-structures. Total specific heat would include interface, core and electronic specific heat. The temperature derivative of the internal energy yields the electronic contribution to specific heat. The present analysis based on the softening of phonon frequencies mechanism is sufficient to describe the enhancement in specific heat by nano-crystallization.

A Novel Insight into the Strain Effect of T2g Mode Splitting and Bandgap in Diamond

Herein, a comprehensive analysis of the change in the bandgap and Raman frequency of diamond under the uniaxial strain along the [100], [110] and [111] directions using first‐principles calculation is presented. The results demonstrate that the triple degenerate T2g mode splitting occurs spontaneously, owing to the strain‐induced symmetry breaking. Phonon splitting into two or three different modes demonstrates its anisotropy characteristics. The tensile softening and compressive stiffening of Raman frequencies depend on the bond length, bond angle, and bond strength response to the uniaxial strain. The bandgap decreases with increasing whether the tensile or compressive strain, which is attributed to the strain‐induced change of bond identities. These findings demonstrate that the uniaxial strain engineering has potential application in future diamond electronic devices.

Layer-dependent electronic structure, dynamic stability, and phonon properties of few-layer SnSe

There is still a lack of fundamental understanding of the structural properties and thermal conductivity of few-layer SnSe, although it is the current recording material for thermoelectric conversion efficiency. From first-principles molecular dynamics and lattice dynamics, the electronic structure, structural properties, and lattice vibrational properties of few-layer SnSe are thus investigated in this study. The results show that SnSe exhibits semiconducting characteristics with the optical absorption mainly concentrated in the visible and near-ultraviolet regions. The band gap varies from 0.90 to 1.35 eV as the number of atomic layers decreases from bulk to single layer (1L). Four-layer (4L) SnSe shows typical bulk characteristics in terms of phase stability and electronic and vibrational properties. On further reducing the number of atomic layers, the quantum confinement effect becomes significant. At room temperature, the Pnma structural symmetry of 4L SnSe is dominated by the Jahn-Teller effect, consistent with the bulk phase. The second-order phase transition from Pnma to Cmcm driven by the phonon anharmonic effect occurs in 1L SnSe. A competitive picture of these two effects can be observed in 3L and 2L SnSe. At the enhancement temperature, the distribution peak of the phonon density of states between 3.5 and 4.5 THz shows a significant redshift relative to the harmonic case, exhibiting strong phonon anharmonicity. Correspondingly, the Raman-active normal modes ${B}_{3g}^{1}$ and ${A}_{g}^{2}$, which contribute to the peak, present significant frequency softening, consistent with the experimental observations. The reduction in the number of atomic layers will aggravate the frequency softening of these modes. Due to the strong phonon anharmonicity and dynamic instability of the Pnma phase, the lattice thermal conductivity of few-layer SnSe at room temperature is significantly lower than that of the bulk phase.

Eliashberg theory of the Jahn-Teller-Hubbard model

We study a multiorbital Hubbard model coupled to local Jahn-Teller phonons to investigate the superconducting state realized in fullerides. A weak-coupling approach is employed in combination with a local self-energy approximation. In addition to the normal and anomalous self-energies of the electrons, we consider the phonon self-energy, which allows a self-consistent treatment of the energetics. The frequency dependence of the self-energies and their characteristic coefficients, such as renormalization factors and dampings, are investigated in detail using numerical calculations. It is clarified that the anisotropic phonons play an important role in the stabilization of the superconducting state. By comparing the full results to those without phonon self-energies, we show that the superconductivity is stabilized by the softening of the phonon frequency. The effects of electronic fluctuations are also considered, which leads to the coupling to orbitons, an analog of plasmons in the electron gas. This additional contribution further stabilizes the superconducting state.

Pressure-induced structural transformations on linear carbon chains encapsulated in carbon nanotubes: A potential route for obtaining longer chains and ultra-hard composites

In this paper, we report high-pressure Raman experiments (0 − 28 GPa) in two different systems, i.e., linear carbon chains encapsulated by multi-walled (Cn@MWCNTs) and double-walled (Cn@DWCNTs) carbon nanotubes. By running high-pressure cycles, it is observed basically two changes in the Raman spectra of chains that are the softening and disappearance of Cn modes. We attributed the irreversible redshift of the Cn band to the coalescence between adjacent chains. On the other hand, the disappearance of the Cn band at the onset of the CNT collapse pressure is assigned to the tube-chain cross-linking. This effect appears to be independent of the Cn length and the number of walls of the tubes, depending only on the innermost CNT diameter. We show that the pressure to coalesce longer chains is higher than 10 GPa. Density functional theory and molecular dynamics calculations were performed in order to support the interpretation of experimental data. The calculations show an irreversible pressure-induced softening of frequency of the confined linear carbon chain. Furthermore, molecular dynamics calculations showed that coalescence between the shorter chains occurs in a region of lower pressure than that of the longer chains, thus supporting the experimental observations. Our findings shed new light on the understanding of the Cn@CNT system stability and pave the way for using high-pressure to obtain ultra-long chains (at lower pressures) and ultra-hard composites (at higher pressures).

Химическое сжатие, структурная нестабильность и ИК-активные фононы в ряду редкоземельных аналогов францисита Cu-=SUB=-3-=/SUB=-RE(SeO-=SUB=-3-=/SUB=-)-=SUB=-2-=/SUB=-O-=SUB=-2-=/SUB=-Cl

ATR and transmission spectra of a series of rare-earth francisite-like phases Cu3RE(SeO3)2O2Cl (RE is a rare earth element, RE = Nd, Sm, Eu, Gd, Dy, Ho, Tm, Yb) were studied. The frequencies of the IR-active phonons of the crystals under study were determined. In the dependences of phonon frequencies on the ionic radius in a series of isostructural compounds, two tendencies are observed: a hardening of frequencies due to an increase in chemical pressure and a softening of the vibration frequencies, in which rare-earth ions are involved, due to an increase in the mass of a specific rare-earth ion. In the Cu3Dy(SeO3)2O2Cl crystal, an anomalous softening of low-frequency phonons at low temperatures was observed, which was apparently associated with the structural instability of the compound.

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ATR and transmission spectra of a series of rare-earth francisite-like phases Cu3RE(SeO3)2O2Cl (RE is a rare earth element, RE = Nd, Sm, Eu, Gd, Dy, Ho, Tm, Yb) were studied. The frequencies of the IR-active phonons of the crystals under study were determined. In the dependences of phonon frequencies on the ionic radius in a series of isostructural compounds, two tendencies are observed: a hardening of frequencies due to an increase in chemical pressure and a softening of the vibration frequencies, in which rare-earth ions are involved, due to an increase in the mass of a specific rare-earth ion. In the Cu3Dy(SeO3)2O2Cl crystal, an anomalous softening of low-frequency phonons at low temperatures was observed, which was apparently associated with the structural instability of the compound.

Size effect on optical conductivity of Bi2Te3 nanoparticles due to softening of phonon frequencies

The frequency-dependent optical conductivity σ(w) strongly depends on the particle size in nanostructures. Phonon frequencies are believed to be decrease on a decrease in particle size due to the softening of phonon frequencies around grain boundaries in nanomaterials. The optical conductivity of Bi2Te3 nanoparticles is studied using the two components model: First is the coherent motion of Drude electrons within the Bi2Te3 nanoparticles, and second is the incoherent hopping of charge carriers from one Bi2Te3 nanoparticle to another. The model has the phonon frequency and relaxation rates as the independent free parameters, which depend on nanoparticle size. The relaxation rates that are a function of frequency are incorporated in optical conductivity through memory functions. The coherent motion of Drude carriers exhibited a peak in intensity near zero frequency regime and decreased to a minimum value in the far-infrared region. The incoherent hopping of electrons from one Bi2Te3 nanoparticle to another produces a broad peak in the frequency-dependent optical conductivity at around the mid-infrared region. On decreases in nanoparticle size, softening of phonon frequencies occurs at interfaces due to an increase in interface volume ratio; as a result, the peak in optical conductivity at the mid-infrared region shifts towards lower frequencies.

Nonlinear Coupling of Phononic Resonators Induced by Surface Acoustic Waves

The rising need for hybrid physical platforms has triggered a renewed interest in the development of agile radio-frequency phononic circuits with complex functionalities. The combination of traveling waves with resonant mechanical elements appears as an appealing means of harnessing elastic vibration. In this work, we demonstrate that this combination can be further enriched by the occurrence of traveling surface acoustic waves (SAWs), induced by elastic nonlinearities, interacting with a pair of otherwise linear micron-scale mechanical resonators. Reduction of the resonator-gap distance and an increase in the SAW amplitude results in a frequency softening of the resonator-pair response that lies outside the usual picture of geometrical Duffing nonlinearities. The dynamics of the SAW excitation scheme allows further control of the resonator motion, notably leading to circular-polarization states. These results may pave the way toward versatile high-frequency phononic microelectromechanical-systems--nanoelectromechanical-systems circuits fitting both classical and quantum technologies.

Monitoring of wind effects on a wind-sensitive hybrid structure with single-layer cable-net curtain walls under Typhoon Muifa

As a new type of building structure, the single-layer cable net (SL cable net) is widely used in many large landmark buildings with modern glass curtain walls. As a kind of wind-sensitive structure, the wind effects on the SL cable net is a problem that cannot be ignored. Therefore, a field measurement was carried out at the China Maritime Museum during Typhoon Muifa. The wind field characteristics and the wind-induced dynamic responses of the SL cable net during this typhoon were well studied. The relationship between the wind characteristics and the dynamic characteristics was analyzed. It was found that the vibration intensity of the SL cable net, unlike that of high-rise buildings, is not correlated with the time-varying mean but is positively correlated with the fluctuating wind speed. By using the method SSI and NExT, it was found that the low-order frequencies of the SL cable net are insensitive to the time-varying mean but have a negative correlation with the RMS fluctuating wind speed. The vibration of the SL cable net was proved to be a more direct cause of the phenomenon of frequency softening. Reasons of this phenomenon were discussed in this paper. At last, damping ratios of the SL cable net were studied and found to be insensitive to the structural vibration or wind speed in this paper.

Doping controlled Fano resonance in bilayer 1T'-ReS2: Raman experiments and first-principles theoretical analysis.

In the bilayer ReS2 channel of a field-effect transistor (FET), we demonstrate using Raman spectroscopy that electron doping (n) results in softening of frequency and broadening of linewidth for the in-plane vibrational modes, leaving the out-of-plane vibrational modes unaffected. The largest change is observed for the in-plane Raman mode at ∼151 cm-1, which also shows doping induced Fano resonance with the Fano parameter 1/q = -0.17 at a doping concentration of ∼3.7 × 1013 cm-2. A quantitative understanding of our results is provided by first-principles density functional theory (DFT), showing that the electron-phonon coupling (EPC) of in-plane modes is stronger than that of out-of-plane modes, and its variation with doping is independent of the layer stacking. The origin of large EPC is traced to 1T to 1T' structural phase transition of ReS2 involving in-plane displacement of atoms whose instability is driven by the nested Fermi surface of the 1T structure. Results are compared with those of the isostructural trilayer ReSe2.

Symmetry induced phonon renormalization in few layers of 2H-MoTe2 transistors: Raman and first-principles studies

Understanding of electron–phonon coupling (EPC) in two-dimensional (2D) materials manifesting as phonon renormalization is essential to their possible applications in nanoelectronics. Here we report in situ Raman measurements of electrochemically top-gated 2, 3 and 7 layered 2H-MoTe2 channel based field-effect transistors. While the and B2g phonon modes exhibit frequency softening and linewidth broadening with hole doping concentration (p) up to ∼2.3 × 1013/cm2, A1g shows relatively small frequency hardening and linewidth sharpening. The dependence of frequency renormalization of the mode on the number of layers in these 2D crystals confirms that hole doping occurs primarily in the top two layers, in agreement with recent predictions. We present first-principles density functional theory analysis of bilayer MoTe2 that qualitatively captures our observations, and explain that a relatively stronger coupling of holes with or B2g modes as compared with the A1g mode originates from the in-plane orbital character and symmetry of the states at valence band maximum. The contrast between the manifestation of EPC in monolayer MoS2 and those observed here in a few-layered MoTe2 demonstrates the role of the symmetry of phonons and electronic states in determining the EPC in these isostructural systems.

Possible experimental test of the nonlinear phononics interpretation of light-induced superconductivity

Experimental evidence for a transient enhancement of the superconducting critical temperature of YBa2Cu3O6+x in the presence of an intense THz or infrared pump pulse was ascribed to nonlinear phononics effects. Here, I introduce a simple phenomenological Ginzburg-Landau model of this phenomenon, to explore further consequences and possible experimental tests of this interpretation. This treatment predicts that, upon cooling below Tc in the absence of pumping, (a) an abrupt softening of a Raman-active mode frequency and (b) a spontaneous lattice distortion, growing linearly with (Tc−T) should occur. Numerical estimates for YBa2Cu3O6+x indicate that the frequency softening could likely be observable, whereas the lattice distortion may be too small. A comparison with Raman experiments for the relevant phonon modes in YBa2Cu3O6+x does not lend support to the nonlinear phononics interpretation. On the other hand, however, a very large (up to 18%) phonon frequency softening just below Tc, qualitatively similar to the predictions of the present model for its size and abrupt temperature dependence, was observed over 20 years ago in HgBa2Ca3Cu4O10+x; its explanation in terms of Josephson plasmons has been controversial. Light-induced superconductivity still needs to be investigated in this material and it may be of interest to explore if it is present and possibly connected, via the mechanism discussed here, to the observed anomalous phonon behavior.Received 12 March 2020Revised 20 August 2020Accepted 21 August 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033384Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDynamical phase transitionsSuperconducting phase transitionTransition temperatureCondensed Matter, Materials & Applied Physics

Strain effect on magnetic-exchange-induced phonon splitting in NiO films

NiO thin films with various strains were grown on SrTiO3 (STO) and MgO substrates using a pulsed laser deposition technique. The films were characterized using an x-ray diffraction, atomic force microscopy, and infrared reflectance spectroscopy. The films grown on STO (001) substrate show a compressive in-plane strain which increases as the film thickness is reduced resulting in an increase of the NiO phonon frequency. On the other hand, a tensile strain was detected in the NiO film grown on MgO (001) substrate which induces a softening of the phonon frequency. Overall, the variation of in-plane strain from −0.36% (compressive) to 0.48% (tensile) yields the decrease of the phonon frequency from 409.6 cm−1 to 377.5 cm−1 which occurs due to the ∼1% change of interatomic distances. The magnetic exchange-driven phonon splitting Δω in three different samples, with relaxed (i.e. zero) strain, 0.36% compressive strain and 0.48% tensile strain, was measured as a function of temperature. The Δω increases on cooling in NiO relaxed film as in the previously published work on a bulk crystal. The splitting increases on cooling also in 0.48% tensile strained film, but Δω is systematically 3–4 cm−1 smaller than in relaxed film. Since the phonon splitting is proportional to the non-dominant magnetic exchange interaction J1, the reduction of phonon splitting in tensile-strained film was explained by a diminishing of J1 with lattice expansion. Increase of Δω on cooling can be also explained by rising of J1 with reduced temperature.

Single-Impact Nonlinear Resonant Acoustic Spectroscopy for Monitoring the Progressive Alkali–Silica Reaction in Concrete

Alkali–silica reaction (ASR) is a ubiquitous cause of concrete degradation. The reaction produces an expandable gel that may cause internal over-stressing and cracking. This paper demonstrates the utility of single-impact nonlinear resonant acoustic spectroscopy (SINRAS) for monitoring the progress of ASR over the course of a standard ASR-susceptibility test. In SINRAS, the transient softening and subsequent recovery of resonance frequency due to one strong impact are analyzed. The performance of SINRAS in monitoring ASR is compared to that of multi-impact nonlinear resonant acoustic spectroscopy (MINRAS), where the gradual resonance frequency shifts caused by impacts of increasing intensity is measured. The changes in standard linear expansion and linear resonance frequency are recorded in parallel. Finally, the sensitivity of measured parameters to sample temperature is investigated. Our findings indicate that SINRAS, while being much simpler and faster to conduct, yields results that strongly correlate to those from MINRAS and even gives an additional parameter describing the rate of recovery. The extracted nonlinearity parameters exhibit good sensitivity and clearly differentiate between concrete with reactive and non-reactive aggregates. Further, this study suggests that the influence of sample temperature on the nonlinearity parameters depends on the level of ASR progression and has to be taken account.

Acoustic Anomalies and Phase Transition Behaviors of Lead-Free Piezoelectric (Na1/2Bi1/2)TiO₃-xBaTiO₃ Single Crystals as Revealed by Brillouin Light Scattering.

The elastic properties of unpoled and prepoled (Na1/2Bi1/2)TiO3-xBaTiO3 (NBT-xBT) single crystals near the morphotropic phase boundary were investigated as a function of temperature using Brillouin light scattering. The acoustic mode frequency and the related acoustic damping of unpoled NBT-xBT showed very broad minimum and maximum, respectively, consistent with typical relaxor behaviors. The frequency softening of the longitudinal acoustic mode together with the increase in acoustic damping was largest along the <100> direction, indicating that polarization fluctuations were most substantial along this crystallographic direction. The difference in acoustic behaviors between the unpoled NBT-xBTs with x = 0.05 and 0.08 were negligible, which means that the NBT-xBT system exhibits typical relaxor properties over a certain composition range of at least 5~8%. The obtained relaxation time of polar nanoregions in the paraelectric phase showed a gradual slowing-down character without any critical divergent behavior. The prepoling of NBT-xBT along the <100> direction induced drastic changes in both mode frequency and damping at ~110 °C when the poling field was larger than 1.4 kV/mm, corresponding to the depoling process from macroscopic/mesoscopic ferroelectric order to ergodic relaxor state upon heating. Phase coexistence of ferroelectric and relaxor states was observed at the intermediate poling field of 1.4 kV/mm.

Structural properties of β-metal(II) hydroxides: Combined XAS and Raman spectroscopic studies on lattice stability

Temperature-dependent x-ray absorption (XAS) and high-pressure (HP) Raman spectroscopy results on two prominent β-metal(II) hydroxides, viz. β-Ni(OH)2 and β-Co(OH)2 are presented. Raman data at ambient conditions show the β-Co(OH)2 phonons to be softer than the β-Ni(OH)2 ones. Analysis of the extended x-ray absorption fine structure data at metal K-edge as a function of temperature reveals the Einstein frequencies of the metal-oxygen and the metal-metal bonds to be, respectively, 309 and for β-Co(OH)2 and the same to be 385 and for β-Ni(OH)2. In both the β-metal(II) hydroxides, up to about 10 GPa, HP Raman spectroscopy show a continuous hardening of the phonon modes associated with the metal-oxygen sub-lattices, whereas a systematic frequency softening is displayed by the hydroxyl symmetric stretching mode. These contrasting behaviours imply a gradual development of lattice instability with pressure mainly due to the displacement of H atoms around the metal-oxygen axis. The presented data allow a direct comparison of the local-lattice behaviour by quantifying the strength (XAS) and anharmonicity (RAMAN) of the atomic bonds in the two systems.