2 + 1 Flavors QCD Equation of State in NJL Model with Proper Time Regularization

Totally symmetric A_1g phonons are studied for the equilibrium and coherent states of a Bi₂Te₃ lattice. Equilibrium phonons were investigated in the frequency domain by the method of spontaneous Raman scattering, whereas coherent phonons were studied by the method of active femtosecond spectroscopy in the time domain. In the latter case, femtosecond laser pulses were used both for generating and detecting coherent A_1g phonons having a well-defined phase allowing the selective optical control of the lattice dynamics. A comparison of the results obtained in the frequency and time domains suggests that diagonal and nondiagonal elements of the density matrix of lattice excitations relax with the same characteristic time to the equilibrium and zero values, respectively.     

Observation of coherent optical phonons excited by femtosecond laser radiation in Sb films by ultrafast electron diffraction method

The generation of coherent optical phonons in a polycrystalline antimony film sample has been investigated using femtosecond electron diffraction method. Phonon vibrations have been induced in the Sb sample by the main harmonic of a femtosecond Ti:Sa laser (λ = 800 nm) and probed by a pulsed ultrashort photoelectron beam synchronized with the pump laser. The diffraction patterns recorded at different times relative to the pump laser pulse display oscillations of electron diffraction intensity corresponding to the frequencies of vibrations of optical phonons: totally symmetric (A _1g ) and twofold degenerate (E _g ) phonon modes. The frequencies that correspond to combinations of these phonon modes in the Sb sample have also been experimentally observed.     

Raman active modes of NiSi crystal

Raman scattering intensities of the NiSi Raman-active modes have been calculated with three Raman measurement configurations, which can be used for the symmetry assignment of the NiSi Raman peaks. Raman-active vibrations of the NiSi crystal have also been theoretically studied. Results show that the lattices with A_g and B_2g modes vibrate only in the plane normal to the NiSi[0 1 0] direction while the lattices with B_1g and B_3g modes vibrate only along the NiSi[0 1 0] axis. Based on such study, the relationship between the anisotropic strain distribution in the NiSi thin film and the Raman peak shifts has been briefly discussed.     

Lattice dynamics and praphase in N-bensylanyline crystals

N-benzylanyline single crystals are grown, and X-ray diffraction probing of their structure allows their symmetry to be attributed to the C_2h.⁵ phase. Polarized Raman studies of these crystals allow the frequencies of lattice phonons to be estimated and their symmetry to be established. The abnormal behavior of the two lowest-frequency A_g symmetry soft modes, the condensation of which is not detected below the melting point (36–38°C), is noted. The possibility of a high-temperature virtual phase transition and praphase is discussed. Theory group consideration of the praphase allows determination of its symmetry and the symmetry of phonons related to the virtual phase transition.     

Softening of charge density wave excitations at the superstructure transition in 2H-TaSe2

Raman scattering measurements performed between 5 K and 300 K on 2H-TaSe₂ reveal new modes which are assigned to the modes of the charge density wave, observed in light scattering due to the Fermi surface induced distortion. The mode at 49 cm^?1 of E_2g symmetry softens (with concurrent line-width broadening) towards 122 K, the transition temperature from the incommensurate distorted to the undistorted phase. The mode at 82 cm^?1 of A_1g symmetry appears to be connected with the transition at 90 K from the commensurate to the incommensurate superstructure. The mode at 24.5 cm^?1 of E_2g shows no temperature dependence and is clearly due to the rigid-layer vibration.     

Lattice vibrations in the orthorhombic commensurate charge density wave phase of 2H-TaSe2

Lattice vibrations in 2H-TaSe₂ have been reinvestigated by Raman scattering in view of the recent orthorhombic structure of the commensurate charge density wave (CCDW) phase. The renormalization of six charge density waves on two layers gives four A_g modes and two B_1g modes in the orthorhombic CCDW phase, in place of two A_1g modes and two E_2g modes in the hexagonal CCDW phase which had been believed. The splitting of the E_2g modes to the A_g and B_1g modes in the orthorhombic symmetry depends on the interlayer interaction. The observed small splitting less than 3 cm^-1 shows the weak interlayer interaction. The energies of the four A_g modes and the two B_1g modes are presented as a function of temperature.     

Raman scattering from β-GaS

The energies and symmetries of the six first order Raman active phonon modes of the layer semiconductor β-GaS (D⁴_6h are: 22.0(E_2g), 74.2(E_1g), 188.0(A_1g), 291.4(E_1g), 295.2(E_2g) and 359.9(A_1g) cm^?1. Several additional weak Raman modes are observed with energies closely corresponding to the phonon modes found in optical absorption. These transitions involve mostly band edge phonons and can become allowed by a slight disordering of the structure or from the presence of impurities or stoichiometric defects. The disordering appears to explain the observation of optical second harmonic generation from these crystals which are predominantly centrosymmetric.     

Characterization of the Suzuki phase in doped alkali halides by Raman spectroscopy

The symmetries and frequencies of the Raman active modes of the Suzuki phase in the systems 6NaCl:CdCl₂; and 6NaCl:MnCl₂, have been calculated. Three of the four peaks allowed by symmetry (A_1g and 2F_g) agree to within 25% in position with the experimental values presented here and with other experimental results. The fourth peak (E_g) seems to be associated with a very soft mode, which explains why this peak has not been observed. The features of the Raman spectrum depend mainly upon the chlorine ions.     

Raman polarization analysis of highly crystalline polyethylene fiber

The complex orientation dependence in space of Raman active vibrations in the orthorhombic structure of polyethylene (PE) is discussed in terms of Raman tensor elements as intrinsic physical parameters of the lattice. Building upon the symmetry assignment of these vibrational modes, we systematically studied, from both theoretical and experimental viewpoints, the changes of polarized intensity for the A_g and the B_2g + B_3g vibrational modes with respect to PE molecular orientation. After explicitly expanding the Raman selection rules associated with the A_g and the B_2g + B_3g modes, introducing them into general expressions of the orientation distribution function, and validating them by means of a least‐square fitting procedure on experimental data, we compare here two mesostructural models for a highly crystallized and self‐aligned PE fiber structure. Stereological arguments are shown concerning the arrangement of orthorhombic fibrils in such a sample that unfold the correct values of five independent Raman tensor elements for orthorhombic PE. Copyright © 2010 John Wiley & Sons, Ltd.     

Fano line shape and anti-crossing of Raman active E2g peaks in the charge density wave state of NbSe2

Low energy Raman scattering from the ab-plane of the 2H polytype single crystal NbSe₂ has been investigated in the normal (N), incommensurate charge density wave (ICDW) and superconducting (SC) phases. The temperature dependence of the polarization resolved Raman response has been obtained for the excitation wavelength of 647 nm and fitted to phenomenological models for the E_2g and A_1g symmetry channels. The A_1g response can be fitted by a simple damped oscillator peak superimposed on continuous background. The E_2g response displays an anti-resonance interference pattern between the inter-layer phonon and the CDW-induced mode such that a hybridized configuration (Fano line shape [1]) is required for modelling. The polarization specific peak maxima positions and line widths as a function of temperature, deduced in this manner, are presented. Partial suppression of the electronic continuum scattering in the Raman shift range up to 110 cm⁻¹ in the A_1g symmetry channel and beyond 300 cm⁻¹ in the E_2g symmetry channel is indicative of high energy electronic states far away from the Fermi surface participating in the ICDW formation.     

On the nature of coherent phonons generated by ultrashort laser pulses in single-crystal antimony

Reflectivity oscillations generated by A_1g coherent phonons in an antimony single crystal have been studied by a method involving pumping and probing by femtosecond laser pulses, which was complemented by spectral filtration of the signal. An analysis of the spectrally resolved signal showed that not only the integrated intensity but also the spectrum of the probe pulse are functions of the delay time between the pumping and probing and oscillate between the Stokes and anti-Stokes components at the optical-phonon frequency. A comparison of the integrated lattice excitation relaxation dynamics with the spectrally resolved lattice excitation relaxation dynamics revealed new facets in the nature and generation mechanism of coherent phonons.     

Phase transitions in RbCaF3. I: Optical studies

Phase transitions in RbCaF₃ have been investigated by optical birefringence measurements and Raman scattering experiments. A near discontinuity in the onset of spontaneous birefringence at 196 K shows that the cubic to tetragonal phase change is “slightly” first order. The Raman spectra of the tetragonal phase support a D¹⁸_4h structure in which two phonons of A_1g and E_g symmetry soften as the 196 K transition is approached from lower temperatures. A very slow transition to a lower symmetry structure was observed at about 42 K in the Raman measurements.     

Pump pulse duration dependence of coherent phonon amplitudes in antimony

Coherent optical phonons of A_1k and E_k symmetry in antimony have been studied using the femtosecond pump–probe technique. By varying the pump-pulse duration and keeping the probe duration constant, it was shown that the amplitude of coherent phonons of both symmetries exponentially decreases with increasing pulse width. It was found that the amplitude decay rate for the fully symmetric phonons with larger frequency is greater than that of the doubly degenerate phonons, whereas the frequency and lifetime for coherent phonons of both symmetries do not depend on the pump-pulse duration. Based on this data, the possibility of separation between dynamic and kinematic contributions to the generation mechanism of coherent phonons is discussed.     

Coherent control of the lattice dynamics of bismuth near the lindemann stability limit

The relative contributions of the anharmonicity of the lattice potential and the nonequilibrium concentration of charge carriers to the time dependence of the coherent A _1g phonon frequency in bismuth excited by high-energy ultrashort laser pulses are studied by the coherent control method. The contributions are separated by the pump-probe method in which excitation is performed by two pulses with a controlled time delay. It is shown that, depending on the relative delay between the pump pulses, both correlation and anticorrelation between the amplitude and the initial frequency of oscillations are observed while the chirp and the initial frequency of the coherent phonon are anticorrelated. In addition, it has been found that the contributions of the lattice and the electronic subsystem are always anticorrelated. Therefore, a certain phase can be assigned to an electronic excitation and it may be suggested that the time dependence of the phonon frequency is determined not only by instantaneous values of the lattice and electronic response but also by the phase relations between them.     

Pressure induced lattice anomalies in pnictides

Hydrostatic pressure Raman and synchrotron XRD measurements at room temperature have been carried out on a series of NdFeAsO_1−xF_y (Nd1111) oxypnictides in order to investigate pressure-induced lattice modifications. The synchrotron XRD data indicate that there is an increased deviation of the lattice constants from smooth pressure dependence in the superconducting compound, in close agreement with the results from SmFeAsO_1−xF_x (Sm1111), although the effect is less pronounced in Nd1111. As in Sm1111 the hydrostatic pressure Raman measurements show that the A_1g mode of the rare earth atom deviates from the linear pressure dependence. Anomalous pressure dependence and a hysteresis is observed in the phonon width of the phonon modes. The calculated Grüneisen parameter for the Nd phonon is very similar to the corresponding value for SmFeAsO_1−xF_x compound and it does not vary with substitution. For the As mode it has a lower value indicating a stiffer phonon with the increased ion size. In connection with the XRD measurements the Raman data show a sudden increase of the pressure-induced lattice anomalies close to doping where the compounds become superconducting.     

CDW evidence in one-dimensional K0.3MoO3 by means of Raman scattering

Raman scattering measurements on the one-dimensional (1-D) blue bronze K_0.3MoO₃ are reported as function of temperature. At about 50 cm^-1 a Raman line of A_g(A) symmetry was found with an anomalous temperature dependence. The line symmetry, the softening of the eigenfrequency and the apparent disappearing of the coupling constant at the critical temperature, allow us to assign this line to the amplitude mode of the CDW, predicted by the theory of the Peierls transition. A Peierls precursor at room temperature was also observed and is discussed.     

Polarized Raman scattering and lattice eigenmodes of antiferromagnetic NdFeO3

The first‐ and second‐order Raman‐active phonons in the orthorhombic Pbnm NdFeO₃ single crystals were studied by means of polarized Raman scattering and lattice dynamics computations (LDC). The zone‐center phonons of A_g symmetry were distinguished from the B_1g eigenmodes by performing polarized Raman scattering experiments using two parallel polarization configurations, X′(ZZ)X′ and Z(X′X′)Z. With the help of LDC, we were able to assign most of the observed Raman‐active modes, including phonons of B_2g and B_3g symmetry. The LDC results indicated that among the 16 force constants employed, the one corresponding to the stretching vibration between the central Fe cation and the axial oxygen atom in a FeO₆ octahedron unit had the largest value. This suggests that the B‐site Fe cation is more tightly bound to the axial O1 ion than the other two equatorial O2 ions. It was further shown that at higher wavenumbers, the displacement of oxygen atoms contributed dominantly to the zone‐center vibrations. Copyright © 2008 John Wiley & Sons, Ltd.     

Raman scattering and interaction and interference of optical vibrations in a γ-Li<Subscript>3</Subscript>PO<Subscript>4</Subscript> superionic crystal

Polarized Raman spectra of γ-Li₃PO₄ single crystal are investigated at temperatures approximately up to 700 K. It is shown that vibrations of PO₄ tetrahedrons and cations of the lithium sublattice can be separated in the spectra. It is found that an increase in temperature leads to interference of one-phonon optical modes of symmetry B_2g and A _g , which is accompanied by antiresonance in a frequency range near 190 cm^?1. Numerical analysis of the spectrum in the region of interaction of optical modes reveals a strong temperature dependence of the interaction constant, which is determined by anharmonic coupling of optical and acoustic modes.     

Resonant Raman scattering from FeS2 (pyrite)

We have observed resonant Raman scattering from the A_g mode of FeS₂ (pyrite) for incident laser energies between 2.41 and 2.73 eV, these energies being well above the fundamental gap at 0.9 eV. In contrast to the behavior of the A_g mode intensity, the E_g and T_g modes do not show resonant behavior. A simple two band model which predicts the Raman cross section proportional to |?χ/?ω|² is found to be inadequate to describe the observed intensity variation with the incident laser energy.