Anisotropic attenuation of transverse ultrasound in cubic crystals of Ge,Si, and diamond with various isotopic compositions

The attenuation of transverse ultrasound in germanium, silicon, and diamond crystals is considered with allowance for competing isotopic and anharmonic scattering processes. The dependence of the attenuation of transverse ultrasound on the direction of the wave vector of quasi-transverse phonons is analyzed within an anisotropic continuum model. The Landau—Rumer mechanism is considered for anharmonic scattering processes. Given the second-and third-order elastic moduli, the parameters are found determining ultrasonic absorption in the above crystals with various degrees of isotopic disorder. The attenuation coefficients of transverse ultrasound associated with isotopic and anharmonic scattering processes are shown to have qualitatively different angular dependences. Therefore, from studying the anisotropic attenuation of ultrasound in cubic crystals, one can determine the dominant mechanism of ultrasonic absorption in isotopically modified crystals.     

Isotopic phonon effects in β-rhombohedral boron--non-statistical isotope distribution

On the basis of the spectra of IR- and Raman-active phonons, the isotopic phonon effects in β-rhombohedral boron are analysed for polycrystalline (10)B- and (11)B-enriched samples of different origin and high-purity (nat)B single crystals. Intra- and inter-icosahedral B-B vibrations are harmonic, hence meeting the virtual crystal approximation (VCA) requirements. Deviations from the phonon shift expected according to the VCA are attributed to the anharmonic share of the lattice vibrations. In the case of icosahedral vibrations, the agreement with calculations on α-rhombohedral boron by Shirai and Katayama-Yoshida is quite satisfactory. Phonon shifts due to isotopic disorder in (nat)B are separated and determined. Some phonon frequencies are sensitive to impurities. The isotopic phonon effects yield valuable specific information on the nature of the different phonon modes. The occupation of regular boron sites by isotopes deviates significantly from the random distribution.     

Tunable detection of high-frequency phonons in LaF3

Tunable detection of high-frequency phonons in LaF₃ is reported. Phonons generated by a heat-pulse technique are detected by phonon-induced fluorescence from magnetically split energy levels of Er³⁺ impurity ions. Evidence for a strongly frequency-dependent lifetime of acoustic phonons at frequencies above 600 GHz is found. The lifetime is attributed to spontaneous anharmonic phonon decay.     

Generation of high-frequency phonons by defect-induced one-phonon absorption

By defect-induced one-phonon absorption of pulsed infrared radiation, we excited in diamond phonons at 28 THz. Their anharmonic decay leads to nonthermal frequency distributions of acoustic phonons which we investigated in a frequency range between 0.5 THz and 6 THz by use of vibronic sideband spectroscopy.     

Anharmonic renormalization and non-Markovian decay of coherent optical phonons in polar semiconductors

The influence of anharmonic renormalization effects on the decay dynamics of coherent longitudinal optical phonons is investigated from a microscopic point of view. Time-resolved coherent anti-Stokes Raman signals are calculated for GaP on the basis of a full phonon dispersion calculation, and the relevant decay channels are identified and compared. Anharmonic renormalization effects are found to induce non-Markovian behaviour of the decay dynamics and lead to a decrease of the decay time. The renormalization effects only depend on the special properties of the phonon dispersion of the given material. This underlines the intrinsic nature of the non-Markovian decay dynamics of phonons for any material. Non-Markovian dynamics of the decay of coherent LO-phonons is calculated for GaP and result in a 30% faster decay signal than the corresponding Markovian dynamics.     

Direct measurement of the lifetime of optical phonons in single-walled carbon nanotubes

Time-resolved anti-Stokes Raman spectroscopy has been applied to probe the dynamics of optical phonons created in single-walled carbon nanotubes by femtosecond laser excitation. From measurement of the decay of the anti-Stokes Raman signal in semiconducting nanotubes of (6,5) chiral index, a room-temperature lifetime for G-mode phonons of 1.1+/-0.2 ps has been determined. This lifetime, which reflects the anharmonic coupling of the G-mode phonons to lower-frequency phonons, is important in assessing the role of nonequilibrium phonon populations in high-field transport phenomena.     

Anharmonic processes of scattering and relaxation of slow quasi-transverse phonons in cubic crystals

Relaxation of slow quasi-transverse phonons in anharmonic processes of scattering in cubic crystals with positive (Ge, Si, diamond) and negative (KCl, NaCl) anisotropies of the second-order elastic moduli has been considered. The dependences of the relaxation rates on the direction of the wave vector of phonons in scattering processes with the participation of three quasi-transverse phonons (the TTT relaxation mechanisms) are analyzed within the anisotropic continuum model. It is shown that the TTT relaxation mechanisms in crystals are associated with their cubic anisotropy, which is responsible for the interaction between noncollinear phonons. The dominant contribution to the phonon relaxation comes from large-angle scattering. For crystals with significant anisotropy of the elastic energy (Ge, Si, KCl, NaCl), the total contribution of the TTT relaxation mechanisms to the total relaxation rate exceeds the contribution of the Landau-Rumer mechanism either by several factors or by one to two orders of magnitude depending on the direction. The dominant role of the TTT relaxation mechanisms as compared to the Landau-Rumer mechanism is governed, to a considerable extent, by the second-order elastic moduli. The total relaxation rates of slow quasi-transverse phonons are determined. It is demonstrated that, when the anharmonic processes of scattering play the dominant role, the inclusion of one of the relaxation mechanisms (the Landau-Rumer mechanism or the mechanisms of relaxation of the slow quasi-transverse mode by two slow or two fast modes) is insufficient for describing the anisotropy of the total relaxation rates in cubic crystals.     

Evolution of phonon nonequilibrium in single-crystal ZnSe at liquid-helium temperatures

The photoluminescence and nonequilibrium heat transfer observed in ZnSe single crystals grown by the free growth method on an oriented single-crystal ZnSe substrate in a hydrogen atmosphere were investigated. The nonequilibrium heat transfer (or propagation of nonequilibrium phonons) was studied by the heat pulse method. A region of local thermal equilibrium or “a hot phonon spot” was found to form in the material, and the threshold of its formation was determined. The constant of spontaneous anharmonic phonon decay in ZnSe was estimated from an analysis of the propagation of nonequilibrium phonons via comparison of the experimental responses with those calculated by the Monte Carlo method.     

Raman scattering in impurity-induced anharmonic crystals

The theory of first-, second-, and third-order Raman scattering is investigated for isotopically disordered anharmonic crystals. The theory of time-dependent thermodynamic Zubarev Green's functions is adopted to obtain the Raman tensor, intensity of Raman lines, and differential cross sections of various orders of scatterings. It is observed that each class of scattering can be separated into diagonal and nondiagonal parts. The first-order and nondiagonal parts are absent in the case of chemically pure crystals. The diagonal parts are separated into anharmonic and interference terms. The interference terms arise due to the interactions of anharmonic phonons with the local phonons. The temperature and defect dependencies are discussed in detail along with the nature of continuous and line spectra. It is proposed that very high-power laser sources will reveal the third-order spectra, and that the resulting structure can be explained with the help of temperature-dependent one-, two-, and three-phonon density of states.     

A microscopic,anharmonic quasiparticle-phonon coupling theory for vibrational nuclei

A microscopic method of describing quasiparticle-phonon coupling, based upon an equation-of-motion technique for the pairing plus quadrupole Hamiltonian, retaining anharmonic terms, is used to calculate the spectra of both even and odd isotopes of paladium and cadmium. The spurious states in the odd nucleus calculation are removed before diagonalization. The basis is up to three phonons for even nuclei and up to two phonons plus a quasiparticle for odd nuclei.     

Effect of dispersion and damping of thermal phonon states on the longitudinal ultrasonic absorption in germanium crystals

A method has been proposed for approximating a phonon spectrum of cubic crystals, which has been obtained from data on inelastic neutron scattering for symmetric directions, over the entire Brillouin zone in the form appropriate for studying relaxation characteristics of phonon systems. The effect of dispersion and damping of thermal phonon states on the longitudinal ultrasonic absorption in anharmonic processes of scattering with the participation of three longitudinal phonons has been investigated for germanium crystals. It has been shown that the inclusion of the dispersion leads to a decrease in the anisotropy of ultrasonic absorption in the LLL relaxation mechanism and makes it possible to fit the results obtained from calculations of the ultrasonic absorption coefficients to the experimental data in the low-temperature range. The temperature dependence and anisotropy of the relaxation rate of longitudinal thermal phonons in germanium crystals have been determined from experimental data on ultrasonic absorption. The performed analysis has refined values of the relaxation parameters obtained from the interpretation of the data on thermal conductivity of germanium crystals with different isotopic compositions in the isotropic-medium model.     

Resonant interaction between localized and extended vibrational modes in Si: 18O under pressure

The interaction between localized and extended vibrational modes in solids is of central importance in understanding how local vibrational modes decay into phonons. Interstitial oxygen (O(i)) in silicon is a model system for studying such interactions. Using hydrostatic pressure, we have brought the antisymmetric stretch mode of (18)O(i) in silicon into resonance with the second harmonic of the (18)O(i) resonant mode. Infrared spectroscopy was used to observe an anticrossing between these two vibrational modes at pressures near 4 GPa. A model of the interaction between these modes produced excellent agreement with the experimentally observed frequencies and linewidths.     

Role of disorder and anharmonicity in the thermal conductivity of silicon-germanium alloys: a first-principles study

The thermal conductivity of disordered silicon-germanium alloys is computed from density-functional perturbation theory and with relaxation times that include both harmonic and anharmonic scattering terms. We show that this approach yields an excellent agreement at all compositions with experimental results and provides clear design rules for the engineering of nanostructured thermoelectrics. For Si(x)Ge(1-x), more than 50% of the heat is carried at room temperature by phonons of mean free path greater than 1 μm, and an addition of as little as 12% Ge is sufficient to reduce the thermal conductivity to the minimum value achievable through alloying. Intriguingly, mass disorder is found to increase the anharmonic scattering of phonons through a modification of their vibration eigenmodes, resulting in an increase of 15% in thermal resistivity.     

Acoustic phonon damping in cubic metals

Electron-phonon-induced linewidths of phonons are discussed in terms of near neighbor tight-binding parameters. Predictions are made of the anisotropy of the linewidth, and some selection rules are given for long-wavelength acoustic phonons.     

Multiphonon decay of strong mode in quantum lattice

A nonperturbative theory of multiphonon anharmonic decay of strongly excited local mode is developed whereby the mode is considered classically and phonons, quantum mechanically. The decay rate of the mode is expressed via the negative frequency parts of the phonon pair correlation functions. In the case of two-phonon decay the later satisfy the linear integral equations while in the case of two- and more-phonon decay they satisfy the nonlinear integral equations. As a result, the processes mentioned differently depend on the mode amplitude A: two-phonon processes smoothly deminish if A → ∞ while three- and more-phonon processes are fully switched-off at large amplitudes and they abruptly switch-on if the amplitude approaches the critical value. At that the decay rate gets rather high value (of the order of the mode quantum per period). The final stage of the relaxation is well described by the perturbation theory.     

Selective optical generation of coherent acoustic nanocavity modes

Femtosecond pump-probe experiments on a Ga0.85In0.15As nanocavity enclosed by two Ga(0.85)In(0.15)As/AlAs phonon Bragg mirrors reveal selective generation of terahertz confined acoustic modes and regular folded phonons. Selective generation of the confined modes alone is achievable for laser excitation at certain energies below the mirror absorption edges, corresponding to electronic transitions within the cavity layer only. Calculations based on the photoelastic effect explain the experimental results. Decay times of cavity and regular modes evidence longer decay times and anharmonic effects for the cavity mode.     

Anharmonic excitations in the FPU and FK models

The properties of vibrational localized (breathers) and traveling (anharmonic phonons) waves are discussed in an infinite, one-dimensional, monoatomic crystal for the Fermi-Pasta-Ulam and Frenkel-Kontorova models. The shooting and finite difference schemes have been implemented to reckon the displacement fields of breathers and anharmonic phonons, respectively. These tools provide localized and traveling waves proving to be indefinitely stable in simulations carried out by solving the equations of motion. The emphasis is laid on the role of the cubic and quartic terms of the anharmonic potential which turn out to oppose and to shore up the restoring force, respectively. The case of vibrational modes arising in an anharmonic crystal subject to a soft phonon induced instability is also addressed. Received 7 November 2001 and Received in final form 5 February 2002 Published online 6 June 2002     

Transparency due to dipole–dipole interaction in photonic crystals doped with nanoparticles

In this paper, we have studied the two-photon absorption process in photonic crystals doped with four-level nanoparticles. It is considered that all the levels of the particles are interacting with the photonic crystal. The decay linewidths of all the four levels are included in the calculations of two-photon absorption process. The effect of the dipole–dipole interaction has also been included in the formulation. Numerical simulations have been performed for the two-photon absorption spectrum on an isotropic photonic crystal. It is found that the system switches between the transparent and the nontransparent states due to the dipole–dipole interaction. The phenomenon of switching depends on the linewidths of these states.     

Spectral Energy Density of Phonons in Metals with Cubic Lattice

Russian Physics Journal - An expression is given for the spectral energy density of acoustic phonons. The basic properties of anharmonic phonons are introduced, and an expression is written for...     

Coherent optical phonon generation in Bi3Ge4O12

Time-domain spectroscopy of coherent optical phonons in bismuth germinate (Bi4Ge3O12) is presented. Utilizing both impulsive stimulated Raman scattering and time-domain terahertz spectroscopy, more than 12 unique vibrational states ranging in frequency from 2 to 11 THz are identified, each with coherent lifetimes ranging from 1 to 20 ps. These modes are highly sensitive to crystal orientation and demonstrate frequency shifts on picosecond timescales consistent with an anharmonic lattice potential.