ϕ4-kink: Its dynamics in a perturbing force field and defective degenerate mode

Two new aspects of a perturbed ?⁴ equation are introduced: kink plus phonon, and a kink interacting with a phonon wave packet. The ?⁴-kink in the presence of perturbing forces follows newtonian dynamics unambiguously. The non-newtonian behaviour is due to an improper use of the latter idea, the kink-phonon-wave-packet interaction. The origin and role of the recently discovered defective degenerate mode are also stressed.     

Isotopic fingerprint of electron-phonon coupling in high-Tc cuprates

Angle-resolved photoemission spectroscopy with low-energy tunable photons along the nodal direction of oxygen isotope substituted Bi(2)Sr(2)CaCu(2)O(8+delta) reveals a distinct oxygen isotope shift near the electron-boson coupling "kink" in the electronic dispersion. The magnitude (a few meV) and direction of the kink shift are as expected due to the measured isotopic shift of phonon frequency, and are also in agreement with theoretical expectations. This demonstrates the participation of the phonons as dominant players, as well as pinpointing the most relevant of the phonon branches.     

Isotope shifts for the P,Q, R lines in indium-doped silicon

We have measured the isotope shift of the P and R luminescence lines in Si doped with In and diffused with isotopically enriched Fe. We find no measurable shift in the R line. Similar experiments on the luminescence lines attributed to an isolated Fe complex show no shift in the previously identified “phonon replicas.” Theoretical calculations of defect phonon resonances near 9 meV for interstitial and substitutional Fe predict an isotope shift of 0.17 meV for ⁵⁶Fe and ⁵⁴Fe. This value is in disagreement with the observed lack of a shift.     

Soliton trapping and repulsion due to a co-group in trans-polyacetylene

For a chain of trans-polyacetylene with one CO substitution the equations of motion of the couples electron phonon system are integrated within the Su-Schrieffer-Heeger model. The calculations for the time-evolution of an end generated kink show that a -C(=O)- unit presents a trap for both a neutral and a negatively charged kink and a repulsive barrier for a positively charged kink. The limitations of the soliton model are discussed.     

Phonon spectrum of a naphthalene crystal at a high pressure: Influence of shortened distances on the lattice and intramolecular vibrations

The Raman spectra of a naphthalene crystal have been measured at room temperature in the pressure range up to 20 GPa. The pressure shift and Grüneisen parameters for intermolecular and intramolecular phonons have been determined. The maximum rate of the pressure shift for intermolecular phonons is 44 cm^?1/GPa, and the rate of the pressure shift for intramolecular phonons lies in the range from 1 to 11 cm^?1/GPa for different modes. The pressure dependence of the phonon frequencies for direct and inverse pressure variations has a hysteresis in the pressure range from 2.5 to 16.5 GPa. It has been shown that the linear dependence of the intermolecular phonon frequency on the crystal density has a peculiarity, which indicates a possible phase transition at a pressure of 3.5 GPa. The pressure dependence of intramolecular phonons related to the stretching vibrations of hydrogen atoms exhibits features that are characteristic of intermolecular phonons, which is associated with the influence of shortened distances between the hydrogen atoms of the neighboring molecules on the intermolecular interaction potential.     

Initial non-uniform motion of the driven and dampedΦ 4 kink and dynamics of its linear modes

The dynamics of the driven and damped ⁴ kink exhibits a non-uniform onset of the center-of-kink motion and consequently a corresponding generalized relaxation of its linear modes. The usual uniformly driven regime and linear exponential regimes of the damped oscillations or relaxation of its linear modes set in asymptotically for large times. The related characteristics of the initial regime is the expansion of the kink to the constant width of the asymptotic uniformly driven and damped kink.     

Soliton patterns and breakup thresholds in hydrogen-bonded chains

The dynamics of protons in hydrogen-bonded quasi one-dimensional networks are studied using a diatomic lattice model of protons and heavy ions including a φ⁴ on-site substrate potential. It is shows that the model with linear and nonlinear coupling of the quartic type between lattice sites for the protons admits a richer dynamics that cannot be produced with linear couplings alone. Depending on two types of physical boundary conditions, namely of the drop or condensate type, and on conditions requiring the presence of linear and nonlinear dispersion terms, soliton patterns of compact support, whether with a peak, drop, bell, cusp, shock, kink, bubble or loop structure, are obtained within a continuum approximation. Phase trajectories as well as analytical studies provide information on the disintegration of soliton patterns upon reaching some critical values of the lattice parameters. The total energies of soliton patterns are computed exactly in the continuum limit. We also show that when anharmonic interactions of the phonon are taken into account, the width and energy of soliton patterns are in qualitative agreement with experimental data.     

Interaction of optical phonons with anisotropic imperfections

Inelastic (Raman) light scattering by phonons interacting with anisotropic imperfections is investigated. Three different kind of disorder-induced defects (point, linear and planar) have been considered. The optical phonon width and line shape are found to depend importantly on the dimension of the imperfections. There is a close correspondence between the scale of the imperfection and the phonon line shape observed in the Raman scattering experiments. The dependence of the phonon frequency shift and width on the defect concentrations is calculated, and the critical concentrations at which the optical phonon can no longer be observed are determined. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 12, 817–822 (25 December 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Properties of IR-active lattice vibrations in the vicinity of kinks in the Frenkel-Kontorova model

The properties of infrared lattice vibrations in the presence of kinks in the Frenkel-Kontorova model are analyzed. Our results show that the vibration of particles involved in kink formation is very similar to that in a gap mode around a force-constant defect. We found that the IR phonon mode intensity possesses a universal dependence on a certain combination of system parameters and kink concentration. On the basis of these results a criterion is proposed for separating the regime of weakly interacting kinks in the system from the regime of a kink lattice. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 10, 750–754 (25 May 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Raman spectroscopy to probe residual stress in ZnO nanowire

Raman spectroscopic studies are performed to probe the stress along the length of a bent ZnO nanowire. The zone‐centre E₂^high optical phonon shows a systematic red shift as the junction point of the two arms of the nanowire is approached. The mechanism of the red shift is discussed on the basis of the tensile strain. From the red shift of the phonon peak position, the strain at different regions on the nanowire is estimated. Stress in the bent nanowire is also investigated using photoluminescence (PL) spectroscopy. Results of both Raman and PL study confirm that the bent nanowire is under tensile strain. Copyright © 2011 John Wiley & Sons, Ltd.     

Surface optical Raman modes in GaN nanoribbons

Raman scattering studies were performed in GaN nanoribbons grown along [1 0 0]. These samples were prepared inside Na‐4 mica nanochannels by the ion‐exchange technique and subsequent annealing in NH₃ ambient. Detailed morphological and structural studies including the crystalline orientation were performed by analyzing the vibrational properties in these GaN nanoribbons. Pressure in the embedded structure was calculated from the blue shift of the E₂(high) phonon mode of GaN. Possible red shift of optical phonon modes due to the quantum confinement is also discussed. In addition to the optical phonons allowed by symmetry, two additional Raman peaks were also observed at ∼633 and 678 cm⁻¹ for these nanoribbons. Calculations for the wavenumbers of the surface optical (SO) phonon modes in GaN in Na‐4 mica yielded values close to those of the new Raman modes. The SO phonon modes were calculated in the slab (applicable to belt‐like nanoribbon) mode, as the wavenumber and intensity of these modes depend on the size and the shape of the nanostructures. The effect of surface‐modulation‐assisted electron–SO phonon scattering is suggested to be responsible for the pronounced appearance of SO phonon modes. A scaling factor is also estimated for the interacting surface potential influencing the observed SO Raman scattering intensities. Copyright © 2010 John Wiley & Sons, Ltd.     

Phonon spectrum and interaction between nanotubes in single-walled carbon nanotube bundles at high pressures and temperatures

The Raman spectra of single-walled carbon nanotubes at temperatures up to 730 K and pressures up to 7 GPa have been measured. The behavior of phonon modes and the interaction between nanotubes in bundles have been studied. It has been found that the temperature shift of the vibrational G mode is completely reversible, whereas the temperature shift of radial breathing modes is partially irreversible and the softening of the modes and narrowing of phonon bands are observed. The temperature shift and softening of radial breathing modes are also observed when samples are irradiated by laser radiation with a power density of 6.5 kW/mm². The dependence of the relative frequency Ω/Ω₀ for G ⁺ and G ^? phonon modes on the relative change A ₀/A in the triangular lattice constant of bundles of nanotubes calculated using the thermal expansion coefficient and compressibility coefficient of nanotube bundles shows that the temperature shift of the G mode is determined by the softening of the C-C bond in nanotubes. An increase in the equilibrium distances between nanotubes at the breaking of random covalent C-C bonds between nanotubes in bundles of nanotubes is in my opinion the main reason for the softening of the radial breathing modes.     

Size‐dependent evolution of phonon confinement in colloidal Si nanoparticles

A size‐dependent evolution of phonon confinement is revealed in Si nanoparticles (NPs) via Raman spectroscopy. By introducing a variable confinement factor, α, into a well‐known phenomenological phonon confinement model (PCM) developed by Richter et al., acceptable fits are achieved to downshifted and asymmetrically broadened Raman spectra of Si NPs with different diameters, d, from 2.4 nm to 6.3 nm. A comparative study using Raman spectra of colloidal Si NPs, for the first time, shows an apparent positive linear correlation between α and the Si NP size. Based on the PCM, the amplitude of the atomic vibration (phonon) at the real physical boundary of NPs is proportional to e^−α/2, which indicates that the amplitude of the first order optical phonon is relatively larger at the edges for smaller Si nanostructures despite of their stronger phonon confinement weighed by α/d². Copyright © 2015 John Wiley & Sons, Ltd.     

Temperature‐depending Raman line‐shift of silicon carbide

Silicon carbide (SiC) is often used for electronic devices operating at elevated temperatures. Spectroscopic temperature measurements are of high interest for device monitoring because confocal Raman microscopy provides a very high spatial resolution. To this end, calibration data are needed that relate Raman line‐shift and temperature. The shift of the phonon wavenumbers of single crystal SiC was investigated by Raman spectroscopy in the temperature range from 3 to 112°C. Spectra were obtained in undoped 6H SiC as well as in undoped and nitrogen‐doped 4H SiC. All spectra were acquired with the incident laser beam oriented parallel as well as perpendicular to the c‐axis to account for the anisotropy of the phonon dispersion. Nearly all individual peak centers were shifting linearly towards smaller wavenumbers with increasing temperature. Only the peak of the longitudinal optical phonon A₁(LO) in nitrogen‐doped 4H SiC was shifting to larger wavenumbers. For all phonons, a linear dependence of the Raman peaks on both parameters, temperature and phonon frequency, was found in the given temperature range. The linearity of the temperature shift allows for precise spectroscopic temperature measurements. Temperature correction of Raman line‐shifts also provides the ability to separate thermal shifts from mechanically induced ones. Copyright © 2009 John Wiley & Sons, Ltd.     

Bond stretching phonon softening and kinks in the angle-resolved photoemission spectra of optimally doped Bi2Sr1.6La0.4Cu2O6+delta superconductors

We report the first measurement of the Cu-O bond stretching phonon dispersion in optimally doped Bi2Sr1.6La0.4Cu2O6+delta using inelastic x-ray scattering. We found a softening of this phonon at q=( approximately 0.25,0,0) from 76 to 60 meV, similar to the one reported in other cuprates. A comparison with angle-resolved photoemission data on the same sample revealed an excellent agreement in terms of energy and momentum between the angle-resolved photoemission nodal kink and the soft part of the bond stretching phonon. Indeed, we find that the momentum space where a 63+/-5 meV kink is observed can be connected with a vector q=(xi,0,0) with xi > or =0.22, corresponding exactly to the soft part of the bond stretching phonon.     

Temperature effects on the phonon spectrum in YBa2Cu3O7 single crystals and thin films

We have performed detailed investigations on the temperature dependence of the 335 cm^–1 phonon in single crystals and thin films of the YBa₂Cu₃O₇ superconductor. The frequency of this phonon exhibits a downshift of about 5 cm^–1 on passing the superconducting transition from above. The shift of the phonon in thin epitaxial films on MgO or SrTiO₃ substrates is only about 2.5 cm^–1. The width of the asymmetric phonon line displays a slight increase belowT _c due to the electron-phonon interaction in these systems.     

Intermolecular repulsive-dispersive potentials explain properties of impurity spectra in soft solids

Behavior of optical impurity spectra in van der Waals glasses is rationalized with the aid of a two-particle Lennard-Jones model of intermolecular interactions. Simple mathematical manipulations with the 6-12 potential yield inhomogeneous distribution functions (IDFs) of zero phonon lines (ZPLs) at different compressions, and the expressions for wavelength dependent pressure shift coefficients of ZPLs (or holes), local phonon frequencies, and linear and quadratic coupling constants. Experimentally, the ZPL to phonon wing intensity ratios (Huang-Rhys or Debye-Waller factors) are measured for bacteriochlorophyll a in glass-forming triethylamine 5 K. Enhancement of coupling strength with increasing transition wavelength is observed, in qualitative agreement with the model.     

Size‐dependent Raman and infrared studies of PbSe nanoparticles

Micro‐probe Raman and far‐infrared absorption spectroscopies were used to prove the existence of optical phonon modes of PbSe nanoparticles prepared by colloidal chemistry and preliminarily characterized by transmission electron microscopy. To the best of our knowledge, this is the first time that evidence of the surface phonon (SP) mode by Raman spectroscopy has been experimentally observed. The wavenumber of the SP mode is consistent with its prediction by a dielectric continuum model. While for different PbSe nanoparticle sizes the observed SP mode does not show any obvious change in its position, there is a clear shift by approximately 4 cm⁻¹ toward higher wavenumber in the appearance of the LO(Γ) in the Raman spectra from the 3 nm to the 7 nm PbSe nanoparticles. Far‐infrared measurements demonstrate the presence of the transverse optical TO(Γ) and of the coupled phonon modes. Copyright © 2008 John Wiley & Sons, Ltd.     

Impurity spectroscopy in glasses and disordered crystals: Inhomogeneous broadening and electron phonon coupling

Parameters of optical impurity spectra in disordered solids were calculated using the potential energy distribution of the ground state and the guest-host interaction potentials of the lower and upper states. The model can yield inhomogeneous band shapes, pressure shift coefficients of zero phonon lines, (pseudo)local phonon frequencies, and linear and quadratic coupling constants to phonons. Results are compared to properties of Shpol'skii multiplets and zero phonon holes burned over the broad spectra in glasses. Crystal spectra contain discrete lines, but the overall width of multiplets and the bands in weakly polar solvent glasses is similar, and so are the pressure shift coefficients. A decrease of zero phonon transition probability (Debye-Waller factor) with increasing (negative) solvent shift was predicted and confirmed for crystal spectra. In general, no correlation exists between the strength of the first- and second-order couplings, and the vibrational modes involved can be different. Moreover, no relationship was established between the line shift and broadening in a temperature interval from 5 to 100 K.     

Optical phonons in nanosize GaAs and AlAs clusters in an InAs matrix

A Raman scattering method is used to investigate structures containing nanosize GaAs and AlAs clusters, which were grown by molecular-beam epitaxy on InAs substrates by the mechanism of self-organized growth under mechanical stress. A large shift of the phonon lines of GaAs and AlAs clusters with respect to the phonon frequencies in the bulk materials (36 and 24 cm⁻¹ for GaAs LO and TO phonons and 55 and 28 cm⁻¹ for AlAs LO and TO phonons, respectively) is observed in the spectra. This fact is explained by the presence of strong mechanical stresses in the GaAs and AlAs clusters. A comparison of the experimental data with the computed strain dependences of the phonon frequencies shows that the GaAs and AlAs clusters are pseudomorphic, i.e., they do not contain dislocations, which lead to relaxation of the mechanical stresses. In the interval between the InAs TO and LO phonon frequencies, the Raman scattering spectra contain features associated with interfacial phonons. The position of these features also attests to the formation of three-dimensional GaAs and AlAs islands and are described well by a continuum dielectric model. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 7, 463–467 (10 October 1999)