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.     

Ultra-fast dynamics of coherent lattice and spin excitations at the Gd(0001) surface

The Gd(0001) surface is investigated by pump–probe experiments using femtosecond laser pulses at 740–860 nm wavelength. Employing optical second-harmonic generation, spin and lattice dynamics are separated through the symmetry of optical field contributions that are even and odd with respect to magnetization reversal. A coherent phonon–magnon mode at a frequency of 3 THz that is excited through the exchange-split surface state is observed in the time domain. A magneto-elastic phonon–magnon interaction based on spin–orbit coupling is weak for Gd and a modulation of the exchange interaction mediated by the lattice vibration is proposed as a microscopic interaction mechanism of this coupled mode. In parallel, electron–electron and electron–phonon interactions and their magnetic counterparts lead to incoherent dynamics of the electron, lattice, and spin subsystems. Variation of the optical wavelength shows that for longer wavelengths up to 860 nm the coherent mode dominates, while for shorter ones (≥740 nm) incoherent contributions prevail. This dependence indicates that selective depopulation of the occupied surface state component drives the coherent excitation. However, temperature-dependent studies show that the oscillation amplitude of even and odd contributions scales with the spin polarization of the surface state, suggesting that the spin dependence of the ion potentials contributes as well. Furthermore, the frequency of the coherent mode presents a blue shift with a delay of 0.17 THz/ps that saturates at the static frequency of the respective bulk phonon. This behavior is a consequence of equilibration of the screened ion potential at the surface subsequent to the intense laser excitation. PACS 78.47.+p; 63.22.+m; 63.20.Ls; 75.30.Ds     

Phonon autoecho in bismuth and antimony single crystals

Phonon autoecho is observed upon pumping Bi and Sb semimetals with ultrashort high-energy laser pulses. The autoecho is manifested as a revival of reflection oscillations generated by an A_1g coherent phonon after their complete disappearance. The phenomenon of phonon autoecho offers decisive evidence of the nonclassical character of the state of the crystal lattice that is accomplished in pumping-probing experiments by femtosecond laser pulses.     

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 phonon states in porous silicon films

The dynamics of differential transmission and reflectance spectra of porous silicon films was studied using the femtosecond excitation technique (τ≈50 fs, ?ω_pump=2.34 eV) with supercontinuum probing (?ω_probe=1.6–3.2 eV) and controlled time delay with a step of Δt=7 fs between the pump and probe pulses. A short-lived region of photoinduced bleaching was observed in the differential transmission spectra at wavelengths shorter than the pump wavelength. The excitation of coherent phonon states with a spectrum corresponding to nanocrystalline silicon with an admixture of a disordered phase was observed. The relaxation of electronic excitation was found to slow down in the spectral region where the amplitude of excited coherent vibrations was maximal.     

Coherent phonons in NdBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−<Emphasis Type="Italic">x</Emphasis></Subscript> single crystals: Optical-response anisotropy and hysteretic behavior

Femtosecond pump-probe measurements of reflection from crystallographic planes are performed to investigate lattice relaxation dynamics in the NdBa₂Cu₃O_{7? x} high-temperature superconductor. Ultrafast phonon response is examined over a wide temperature range for various orientations of the pump and probe polarization vectors with respect to particular crystallographic axes. The initial phases of coherent phonons are measured, and hysteretic behavior is revealed in the transition between two temperature regions above T_c for the ac plane.     

Die Bewegung eines Exzitons entlang eines Polymers unter dem Einfluß der Gitterschwingungen

In this paper the influence of lattice vibrations on the migration of electronic excitation energy along a one-dimensional system is treated with the aid of perturbation theory. The lattice is assumed to be in thermodynamic equilibrium, so that it is possible to average over all the lattice coordinates. With this assumption the caseT=0 is solvable exactly; the propagation of energy will be coherent. The caseT>0, however, has to be treated with an approximation that becomes invalid for very low temperatures. It results that atT>0 the exponentially decreasing coherent part of the propagation is accompanied by an incoherent part, which, after a certain critical timet _kr, becomes the more important one;t _kr is a function of the parameters that specify the system.     

Effect of the amplitude of excitation pulses on the shape of photon-echo signals in two-level systems

It is theoretically established that multiple photon-echo signals reflect the oscillatory structure of the primary echo signal, which arises under the conditions of collinear excitation of two-level active centers by laser pulses having the same width but different amplitudes. It is shown that the oscillatory structure of the primary photon echo exists within the intervals (?t ₁, t ₁) and (?2t ₁, 2t ₁), where t ₁ is the pulse width. It is found that, when the pulse width is of the same order of magnitude as the delay between the pulses and the amplitudes of the excitation pulses obey certain relations, the oscillatory structure of the primary photon-echo signal becomes asymmetric. In the mode of quadratic detection of the primary photon-echo signal, the asymmetric oscillatory structure of the primary echo manifests itself as a manifold of isolated signals (multiple photon echoes), with the time intervals between these signals being equal to the pulse width.     

Nonadiabatic effects in the lattice dynamics of compressed rare-gas crystals

Electron-ion contributions to the energy of rare-gas crystals are discussed from first principles in the framework of the Tolpygo model and its variants. The frequencies of phonons in a neon crystal at pressures p ≠ 0 are calculated in terms of models that go beyond the scope of the adiabatic approximation. Analysis of the contributions from different interactions to the lattice dynamics of the crystals demonstrates that the phonon frequencies calculated in the framework of the simplest model (allowing only for the nearest neighbors) and the most complex model (with the inclusion of the nearest neighbors, next-nearest neighbors, nonadiabatic effects, etc.) for small wave vectors are close to each other. The difference between the phonon frequencies calculated within the above models is most pronounced at the Brillouin zone boundary. Under strong compression, the phonon spectrum along the Δ direction is distorted and the longitudinal mode is softened as a result of the electron-phonon interaction. The contribution from terms of higher orders in the overlap integral S at p ≠ 0 to the phonon frequencies is more significant than that obtained in the band-structure calculations of the neon crystal.     

Phonons and electron-phonon interactions in rare-gas crystals at high pressures

The lattice dynamics of compressed rare-gas crystals is theoretically investigated within the ab initio approach in the framework of the Tolpygo model, which explicitly allows for the deformation of electron shells. The deformation of the electron shells is associated with the retardation of the electron response and treated as a nonadiabaticity (the electron-phonon interaction). This approach and the ab initio short-range repulsive potentials are used to construct the dynamic matrix, which makes it possible to calculate the phonon frequencies and the electron-phonon interaction of crystals in the series Ne-Xe at any point of the Brillouin zone. The contributions of the long-range Coulomb and van der Waals forces to the dynamic matrix are the structure sums that depend only on the lattice type. The structure sums for the face-centered cubic lattice are calculated using the Ewald and Emersleben methods, as well as the direct summation over the vectors of the face-centered cubic lattice. The use of 20 spheres in the last case provides an accuracy of no less than four significant figures. An analysis of the role played by the phonon-electron interaction at five points of high symmetry in the Brillouin zone (X, L, U, K, W) at high pressures demonstrates that not only the longitudinal phonon modes (at the points X and L) but also the transverse phonon modes (at the points U, K, and W) are softened. The inclusion of the electron-phonon interaction at the point X improves agreement between the theoretical and experimental phonon frequencies for the argon crystal.     

Structure and lattice dynamics of rare-earth ferroborate crystals: Ab initio calculation

The ab initio calculation of the crystal structure and the phonon spectrum of crystals RFe₃(BO₃)₄ (R = Pr, Nd, Sm) has been performed in the framework of the density functional theory. The ion coordinates in the unit cell, the lattice parameters, the frequencies and the types of fundamental vibrations, and also the intensities of lines in the Raman spectrum and infrared reflection spectra have been found. The elastic constants of the crystals have been calculated. For low-frequency A₂ mode in PrFe₃(BO₃)₄, a “seed” vibration frequency that strongly interacts with the electronic excitation on a praseodymium ion was found. The calculation results satisfactory agree with the experimental data.     

Lifetime of optical phonons in fs-laser excited bismuth

This paper presents experimental and theoretical results on the temperature-dependent optical response of a single crystal of bismuth to excitation by femtosecond laser pulses. We demonstrate that the measured damping rate of the transient reflectivity oscillations relates to the lifetime of optical phonons. The lifetime is the inverse rate of the decay of optical phonons into two acoustic phonons. This lifetime also indicates the approach to the vibration instability (catastrophe) threshold that manifests the beginning of the disordering of a solid crystal and transition to a liquid state. We observe the red shift of phonon frequency, which increases with the rise of the initial lattice temperature. The red shift is different from the previously observed red shift proportional to the electron temperature, and thus to the excitation laser fluence. The coherent phonon excitation process imprinted into the initial change in the reflectivity and the following reflectivity oscillations allowed us to uncover the temporal phonon history preceding the structural transformation of solid Bi.     

Ultrasonic attenuation in insulating crystals

A theory for the dampingΓ of ultrasonic waves due to three-phonon processes is developed by using a Green's function method. The imaginary part of the self-energy of the impressed ultrasound phonons interacting with thermal phonons is calculated. In the limits ofω τ very large and very small the known results are rederived, whereω is the frequency of the ultrasonic wave andτ the thermal phonon relaxation time. The intermediate range ofω τ values is discussed in detail for the case of longitudinal phonon attenuation. It is found, that forω τ>1 a Landau-Rumer type law applies also for longitudinal phonons,Γ～ωT ⁴. But it is shown that dispersion effects and large third-order elastic anisotropy can lead to a stronger temperature dependence thanT ⁴ and a weaker dependence on frequency thanω. These results are compared with recent experiments.     

Vibrational density of states of hen egg white lysozyme

The resonant Raman scattering in GeSi/Si structures with GeSi quantum dots has been analyzed. These structures were formed at various temperatures in the process of molecular-beam epitaxy. It has been shown that Raman scattering spectra recorded near resonances with the E₀ and E₁ electronic transitions exhibit the lines of Ge optical phonons whose frequencies differ significantly from the corresponding values in bulk germanium. In the structures grown at low temperatures (300–400°C), the phonon frequency decreases with increasing excitation energy. This behavior is attributed to Raman scattering, which is sensitive to the size of quantum dots, and shows that quantum dots are inhomogeneous in size. In the structures grown at a higher temperature (500°C), the opposite dependence of the frequency of Ge phonons on excitation energy is observed. This behavior is attributed to the competitive effect of internal mechanical stresses in quantum dots, the localization of optical photons, and the mixing of Ge and Si atoms in structures with a bimodal size distribution of quantum dots.     

Excitation of Autoionization States and Electronic Stopping Powers at Collisions of Slow Ions with a Solid

It has been shown that the excitation of autoionization states at collisions of keV ions with a solid is decisive for inelastic energy loss and, correspondingly, the electronic stopping power dE/dx. It has been proposed to estimate the electronic stopping power dE/dx using the relation of cross sections for the excitation of autoionization states to ionization cross sections. When ionization cross sections are unknown, scaling is used to calculate ionization cross sections at the excitation of the L and M shells. A threshold dependence of the electronic stopping power dE/dx on the energy of bombarding ions has been predicted.     

Theorie vibronischer Spektren in Ionenkristallen

The electronic bands of some foreign ions in a crystal exhibit one or a few intermixed sequences of equidistant lines (vibronic spectra.) Examples are the divalent rare-earth ions in alkali-halide and alkaline-earth-halide crystals. It is shown that such sequences of lines are only possible if a) the disturbed lattice dynamics gives rise to localized or quasi-localized modes and b) the electronic functions of the defect ion (properly symmetrized in the static crystal field) do not overlap the nearest lattice ions. To calculate the single lines of a vibronic band a refined method of moments is developed. Its parameters (oscillator displacement and frequency change) follow from the dynamics of the disturbed lattice. The lattice vibrations are calculated by means of modern scattering theory. To describe the scattering resonance the advantageous concept of metastable (quasi-localized) vibrations is introduced. Then the projection of the cartesian coupling functions of first and second order onto the disturbed lattice eigenvectors can be determined. Their matrix elements <n|U _x |n> and <n|U _xx |n> define the change of the equilibrium positions and frequencies during the transition. Further on general symmetry-selection rules are derived for the electron-lattice coupling. Finally the important case of a pure electrostatic coupling is discussed in more detail. It is evident that the study of vibronic spectra gives important information about the dynamics of the disturbed lattice and the electron-lattice coupling. Especially they constitute a method to investigate localized and quasi-localized modes, even if their dipole moment is too small for direct optical excitation, or if their frequency lies in the absorbing region of the crystal.     

Critical temperature of metallic hydrogen sulfide at 225-GPa pressure

The Eliashberg theory generalized for electron—phonon systems with a nonconstant density of electron states and with allowance made for the frequency behavior of the electron mass and chemical potential renormalizations is used to study T _c in the SH₃ phase of hydrogen sulfide under pressure. The phonon contribution to the anomalous electron Green’s function is considered. The pairing within the total width of the electron band and not only in a narrow layer near the Fermi surface is taken into account. The frequency and temperature dependences of the complex mass renormalization ReZ(ω), the density of states N(ε) renormalized by the electron—phonon interactions, and the electron—phonon spectral function obtained computationally are used to calculate the anomalous electron Green’s function. A generalized Eliashberg equation with a variable density of electron states has been solved. The frequency dependence of the real and imaginary parts of the order parameter in the SH₃ phase has been obtained. The value of T _c ≈ 177 K in the SH₃ phase of hydrogen sulfide at pressure P = 225 GPa has been determined by solving the system of Eliashberg equations.     

Femtosecond mechanisms of electronic excitations in crystalline materials

The lattice dynamics of crystals is investigated in the course of high-power electronic excitation. It is revealed that, at W _e < W _eo , atoms and ions are displaced from their regular sites for 100–300 fs. Subsequent relaxation of the crystal lattice in response to a strong local electric field induced by the collisional displacement of ions occurs for 10–50 ns in an oscillatory manner with a period of 0.5–1.5 ps.     

Theory of space-charge waves in semiconductors with negative differential conductivity

Phenomena that accompany optical excitation of eigenmodes of electron gas oscillation in semiconductors with an N-shaped current-voltage (I-U) characteristic in a strong electric field are investigated theoretically. The dependence of the current flowing through a sample on the oscillation frequency of the interference pattern of light illuminating the sample is analyzed. Nonsteady-state and nonuniform illumination produces an internal electric field, which interacts resonantly with the eigenmodes when the oscillation frequency of the interference pattern coincides with an eigenfrequency of electronic gas oscillation. As the maximum of the I-U curve is approached, the interaction becomes nonlinear in character.