Transverse Optical Mode Frequency Research Articles

Anisotropic superconductivity mediated by ferroelectric fluctuations in cubic systems with spin-orbit coupling

Motivated by the experimental observation that superconductivity in bulk doped SrTiO$_{3}$ is enhanced as a putative ferroelectric quantum critical point (FE-QCP) is approached, we study the pairing instability of a cubic system in which electrons exchange low-energy ferroelectric fluctuations. Instead of the gradient coupling to the lattice distortion associated with ferroelectricity, we consider a direct coupling between the electrons and the bosonic ferroelectric field that appears in the presence of spin-orbit coupling. Working in the weak-coupling regime, we find that the pairing interaction is dominated by the soft transverse optical (TO) mode, resulting in a $T_{c}$ enhancement upon approaching the FE-QCP. Focusing on even-parity states, we find that although the $s$-wave state always wins, states with higher Cooper-pair angular momentum become close competitors as the TO mode softens. We show that the cubic anisotropy of the FE fluctuations mixes the $s$-wave and $g$-wave states, resulting in a characteristic anisotropy of the gap function. The gap anisotropy behaves non-monotonically as the FE-QCP is approached: upon decreasing the TO mode frequency, the gap anisotropy first changes sign and then increases in magnitude. We discuss the possible applications of our results to the superconducting state of SrTiO$_{3}$.

Phonon characteristics of Si‐doped InAs grown by gas‐source molecular beam epitaxy

AbstractUsing Raman scattering spectroscopy with 514‐ and 633‐nm light sources, we have studied the phonon characteristics of Si‐doped InAs films grown on (100) n‐type InAs by gas‐source molecular beam epitaxy having charge carrier concentration (n) between 2.26 × 1018 and 1.68 × 1020 cm−3. The unscreened longitudinal optical (LO) phonon is observed near ~238 cm−1 along with two plasmon‐LO‐phonon (PLP) coupled L± modes. With increasing n, the L− mode is downshifted from the LO phonon towards the transverse optical mode frequency. This abnormal behavior is ascribed to the large scattering vector and heavy Landau damping. The L+ mode close to the plasma frequency ωP is also detected in samples with n > 1019 cm−3. The observed unscreened LO mode in the forbidden configuration is attributed to the resonance enhanced scattering induced by surface space charge. Reliable values of charge carrier density and mobility are estimated from the simulated shifts of PLP modes in the low Si‐doped InAs films. At higher doping level, a full‐line shape analysis is desired for assessing accurate values of the transport parameters. In Si‐doped InAs, we appraised the existing experimental data of localized vibrational modes (LVMs) from Raman and Fourier transform infrared spectroscopy by exploiting a sophisticated Green's function theory and incorporating lattice relaxation effects around SiIn and SiAs defects for constructing accurate perturbation models. The simulated results of LVMs for several isolated (Td) defects, nearest neighbor pair (C3v), and next‐nearest neighbor complex centers (Cs) are compared, contrasted, and discussed with the experimental data.

Study of vibrational modes in (Ga2S3)x−(Ga2Se3)1-x mixed crystals by Raman and infrared reflection measurements

Raman and infrared (IR) reflection characteristics were investigated in the frequency region of 100–450 cm−1 for (Ga2S3)x − (Ga2Se3)1-x mixed crystals for compositions of x increasing from 0.0 to 1.0 by intervals of 0.25 obtained by Bridgman crystal growth technique. In the Raman spectra of these crystals four dominant peak features were observed while two bands were detected in the IR spectra of interest samples. Kramers-Kronig dispersion relations applied to IR spectra presented the frequencies of transverse optical modes. The compositional dependencies of revealed Raman- and IR-active mode frequencies on (Ga2S3)x − (Ga2Se3)1-x crystals were established. One-mode behavior was displayed from indicated dependencies.

Preventing transient parametric instabilities in high power gravitational wave detectors using thermal transient compensation

Laser interferometer gravitational wave detectors such as Advanced LIGO use large fused silica test masses in which temperature perturbations take many hours to reach dynamic equilibrium. When environmental disturbances cause the optical cavities to lose optical power there is a sudden thermal transient which causes the mirror profile to change significantly over time. This causes time dependent tuning of transverse optical mode frequencies, some of which cause parametric instability. These transient parametric instabilities greatly increase the complexity of active control of parametric instability. Here we report on modeling and testing of a system in which a low power laser is designed to maintain a constant heat flux when cavity power is lost, thereby enabling thermal transients to be minimized and cavity locking to be re-established. We demonstrate a reduction in the thermal transient in the optical mode spacing to <3 of the transient without compensation. For advanced LIGO this would reduce the complexity of control systems for controlling parametric instabilities.

Synchrotron radiation infrared microscopic study of non-bridging oxygen modes associated with laser-induced breakdown of fused silica

Nanosecond pulse laser-driven optical breakdown at SiO2 surfaces as probed by synchrotron-based Fourier transform infrared (SRFTIR) and photoluminescence (PL) microscopies is presented. SRFTIR mapping of laser damage identified localized non-bridging Si-O vibrational modes at ∼950 cm−1 which became stiffer as 355 nm laser pulse lengths were increased from 5 to 20 ns. The bridging Si-O-Si transverse optic mode frequency varied significantly across damaged regions indicating a wide range of average bond angles, softening slightly with increasing pulse length. 355 nm-excited PL images of laser modified regions could be directly correlated with the structural modifications identified through SRFTIR.

Raman spectra of beryllium to 23 GPa

Raman spectra of Be were studied at room temperature at pressures up to23 GPa. The transverse-optical (TO) zone-centre phonon mode of hcp Be could beobserved to maximum pressure. Neither new modes nor anomalies in the pressureshift were observed in the pressure range of 8.6-14.5 GPa where a phasetransition has been reported. The TO mode frequency and its pressuredependence are discussed in terms of the elastic properties of Be.

Structure and dynamics of ammonium halides under high pressure

The structures of ammonium halides ND 4I and ND 4Br have been studied by means of neutron diffraction at pressures up to 9 GPa. We found that the high-pressure phase V of ammonium halides has the same structure as the low-temperature phase III-tetragonal one with antiparallel ordering of ammonium ions. Vibrational spectra of NH 4I have been studied at pressures up to 5 GPa. Libration and transverse optical mode frequencies as functions of pressure were obtained.

Thickness-deconvolved structural properties of thermally grown silicon dioxide films

We have studied structural and optical properties of thermally grown silicon dioxide films. These properties were examined by incrementally etching back the oxide films and performing infrared reflection absorption spectroscopy measurement at each thickness. We have divided the oxide into incremental layers and calculated the dielectric function of each of the layers. This study shows that the incremental layer, whose structure differs from that of bulk oxide, with thickness below 1 nm exists at the silicon and silicon dioxide interface. In addition, farther from the interface, the transverse optical mode frequency shifts slightly in wave number to a higher value.

Raman study of confined TO phonons in GaAs/AlAs superlattices grown on GaAs (311)A and B surfaces

The use of Raman scattering in different polarization geometries makes it possible to observe the splitting of transverse optical (TO) phonon modes confined in GaAs/AlAs superlattices grown on faceted GaAs (311)A surfaces. The frequencies of TO modes with atomic displacements in the direction along the facets were observed to be higher than in the transverse one. Increased splitting, up to 3.5 cm−1, was observed for (311)A superlattices when the average thickness of the GaAs layers was 6 monolayers or less. The splitting was absent in superlattices grown on (311)B surfaces under the same conditions. The effect of splitting is reputed to be caused by corrugation of GaAs/AlAs (311)A interfaces and formation of lateral superlattices or arrays of quantum wires, depending on the GaAs layer thickness.

In situ characterization of cubic boron nitride film growth in the IR spectral region

Cubic boron nitride (c-BN) layers were deposited by a plasma activated process in a hollow cathode arc deposition device. The deposition process is analyzed by in situ polarized infrared reflection spectroscopy. The s-polarized infrared reflectance spectra of a growing BN film show the structure of the in-plane vibration of sp 2 bonded BN at 1370 cm −1 for film thicknesses greater than 20 nm. At thicknesses greater than 50 nm, the out of plane vibration at 780 cm −1 can be observed also. The signature of the cubic phase can be detected at a thickness of 95 nm. By simulation of the spectra, the damping constant of the c-BN oscillator was estimated to be 170 cm −1, nearly independent of the thickness. The transverse optical mode frequency of the c-BN phonon starts at 1090 cm −1, decreases to a minimum of 1070 cm −1 at a film thickness of 300 nm and increases at higher thicknesses. Up to a film thickness of 300 nm the oscillator strength increases from 5×10 5 cm −2 to 22×10 5 cm −2 and remains constant during further growth. The c-BN layer growth was investigated in situ during the variation of the DC bias voltage. At a bias voltage of −275 V a reflectance feature can be observed at 1360 cm −1 corresponding to the in-plane vibration of sp 2 bonded material.

A study of phonon anharmonicity in BaF2thin films using the infrared emission technique

Thermal emission spectra of metal-backed thin films of BaF2 are observed at the emission angle of 25 degrees . Changes in the spectra are observed for the films prepared under different conditions. The spectra observed at elevated temperatures are analysed by using a response function based on the virtual-mode theory for an ionic film to estimate the temperature dependence of lattice dynamical quantities such as effective phonon frequency and damping. The damping around the longitudinal optical (LO) mode frequency is approximately proportional to temperature, while that around the transverse optical (TO) mode frequency varies non-linearly. The TO mode frequency decreases with temperature and the LO mode frequency is nearly the same for all temperatures. The experimental results are consistent with the existing theory of lattice anharmonicity. The frequency-dependent self-energy caused by the anharmonicity is significant for the temperature dependence of the phonon frequency and damping.

Effect of temperature and antiferromagnetic ordering on the dielectric constants of MnO and MnF2

Temperature dependence (4.2-300K) of the static dielectric constant epsilon is reported for two antiferromagnets namely MnF2 (TN approximately=67.3K) and MnO (Tn approximately=118K) for the electric field E parallel and perpendicular to the spin easy axis. Comparison with the temperature variation of epsilon in the diamagnets ZnF2 and MgO shows that the phonon contribution in all four materials follows the equation epsilon (T)= epsilon (0)+A/(exp(h nu T/kBT)-1), nu T being the transverse optical-mode frequency. The magnetic contributions, epsilon /sub ///m and epsilon perpendicular to m for E parallel and perpendicular to the easy axes respectively, have the following characteristics: (i) in both MnF2 and MnO, epsilon perpendicular to m is negative and considerably larger than epsilon /sub ///m; (ii) in MnF2, epsilon /sub ///m is positive and varies nearly as sigma 2 ( sigma =order parameter) whereas in MnO, epsilon /sub ///m is negligible; and (iii) in MnF2, where accurate data on the magnetic energy um is available, epsilon perpendicular to m(T)/ epsilon perpendicular to m(0) varies as um(T)/um(0) both above and below TN (somewhat similar variation is observed in MnO). Despite several common features in these results for MnO and MnF2, the signs and magnitudes of epsilon /sub ///m and epsilon perpendicular to m cannot yet be explained.

Dielectric properties of alkali halides using mott-littleton polarization theory

Some new relations between the electronic and static dielectric constants and the transverse optical mode frequency are obtained using the Mott-Littleton expressions for effective polarization fields. The usefulness of these relations is demonstrated, in explaining the dielectric behaviour of alkali halide crystals under the effect of pressure, by calculating the volume derivatives of dielectric constant and transverse optical mode Grüneisen parameter.

Rydberg potential in diatomic ionic crystals

AbstractThe short‐range Rydberg potential function is used to calculate the transverse optical mode frequency (ωto), transverse optical mode Grüneisen parameter (γto), and Grüneisen parameter (γ) for rock salt and caesium chloride structure ionic solids. The pressure derivative of bulk modulus (dB/dP) and Debye characteristic temperature (θD) are also evaluated using this short‐range interaction. The results obtained using Rydberg potential are found in good agreement with recent experimental data.

Lattice dynamics of mixed alkali halides. I. Negative-ion substitution

Phonon frequencies of one-mode behavior of mixed alkali-halide crystals with negative-ion substitution have been calculated as a function of wave-vector and molar-mixing ratio. The mixed-crystal model utilizes a pseudo-unit-cell as a basic repetitive unit incorporated into the breathing-shell model of lattice dynamics. The fundamental repetitive unit cell for the mixed crystal $A{B}_{1\ensuremath{-}x}{C}_{x}$ consists of $A$ ions at their normal lattice site and with nearest neighbors consisting of a fractional amount of $B$ and $C$ ions proportional to their mixing molar ratio. The model parameters are deduced from physical observables such as the elastic constants, long-wavelength transverse-optical mode frequency, and the high- and low-frequency dielectric constants of the parent compounds. Room-temperature calculations of one- and two-phonon densities of states and dispersion relations of $\mathrm{K}{\mathrm{Cl}}_{1\ensuremath{-}x}{\mathrm{Br}}_{x}$, $\mathrm{K}{\mathrm{Cl}}_{1\ensuremath{-}x}{\mathrm{I}}_{x}$, and $\mathrm{K}{\mathrm{Br}}_{1\ensuremath{-}x}{\mathrm{I}}_{x}$ are found to agree with the available Raman scattering, infrared reflection, and absorption data.

The pressure dependence of alkali halide to mode frequencies

The hydrostatic pressure dependencies of the transverse optic mode frequency of 12 different alkali halides have been measured at 77 and 295 K. Combining this with existing values for the isothermal compressibilities yields mode Grüneisen parameters and their temperature and pressure dependences. The data favours the hypothesis that the frequencies vary linearly with ‘compression’ (fractional change in volume), rather than with pressure. This means that the mode Grüneisen parameters are decreasing slowly with increasing pressure. It is shown that this is theoretically more reasonable than the increasing γ conclusion that would result from a linear frequency vs pressure relationship.

Analysis of the dielectric behaviour of transition metal oxides

We present an analysis of the dielectric behaviour of MnO, CoO and NiO on the basis of the shell model of Dick and Overhauser. The electronic polarizability, ionic polarizability, the effective charge parameter and transverse optic mode frequency have been calculated for the crystals under study. A comparison of the results with experimental data reveals the necessity of considering the effect of exchange charge polarization in the theory of the shell model.

Growth and optical properties of CuGaTe2 thin films

CuGaTe 2 thin films with thicknesses in the range of 1000–2000 Å have been prepared by flash evaporation of pre-reacted material onto glass and silicon substrates. The films were single phase, polycrystalline and stoichiometric within 1%, as shown by transmission electron diffraction measurements and ion backscattering spectrometry. Four characteristic energy gaps of 1.227, 1.280, 1.97 and 2.67 eV were obtained from an analysis of the optical transmission spectra in the photon energy range from 1 to about 3 eV. A model is proposed for the band structure of CuGaTe 2 near the point Γ of the Brillouin zone. Transmission measurements in the far infrared yielded three transverse optical mode frequencies of 166.4 cm −1 , 201.4 cm −1 and 209.2 cm −1 .

Temperature and pressure dependence of the transverse-optic modes of ionic crystals and their associated anharmonic self-energies

The temperature dependence (2-300 K) and hydrostatic pressure dependence (0-7 kbar) of the $q\ensuremath{\approx}0$ transverse-optic mode frequency ${\ensuremath{\omega}}_{t}$ and its associated damping $2\ensuremath{\Gamma}(0,t,{\ensuremath{\omega}}_{t})$ are reported for the alkali, silver, and thallium halides. These results are analyzed to yield the temperature dependence of the thermal strain ${\ensuremath{\Delta}}^{E}(0,t)$ and far-infrared anharmonic self-energies ${\ensuremath{\Delta}}_{T}^{A}(0,t,{\ensuremath{\omega}}_{t})$ associated with the mode at ${\ensuremath{\omega}}_{t}$. In addition, calculations of ${\ensuremath{\Delta}}^{E}(0,t)$, ${\ensuremath{\Delta}}_{T}^{A}(0,t,\ensuremath{\Omega})$ at $\ensuremath{\Omega}=0$ and $\ensuremath{\Omega}={\ensuremath{\omega}}_{t}$, and $\ensuremath{\Gamma}(0,t,{\ensuremath{\omega}}_{t})$ are presented for the alkali halides crystallizing in the NaCl structure using current many-body thermodynamic Green's-function anharmonic theories, and these are compared with the experimental results.

Dielectric susceptibility of a paraelectric material

Abstract An expression is obtained for the dielectric susceptibility of a paraelectric material from a Hamiltonian propounded by Silverman and Joseph using the double-time Green function technique. Using the temperature dependence of the low-lying transverse optic mode frequency, it is shown that the static dielectric susceptibility obeys a Curie-Weiss law.