Stable and metastable states and the formation and destruction of breathers in the discrete nonlinear Schrödinger equation

Statistical mechanics explains many localization phenomena of lattices such as the discrete nonlinear Schrödinger equation. However, numerical simulations show that the complete thermalization is rarely achieved. Instead, one observes metastable statistical states that are robust when excited locally. This paper investigates thermodynamically metastable states where the trajectory is confined to some part of the energy shell. The partition function and the entropy are computed with a perturbation method. This method is applicable to stable and metastable states, and it allows us to give approximative analytic expressions for the entropy in the complete thermodynamic state space.     

On the path length of an excess electron interacted with optical phonons in a molecular chain

We show that in a molecular chain with dispersionless phonons at zero temperature, a “quasistationary” moving soliton state of an excess electron is possible. As the soliton velocity vanishes, the path length of the excess electron exponentially tends to infinity. It is demonstrated that in the presence of dispersion, when the soliton initial velocity exceeds the maximum group velocity of the chain, the soliton slows down until it reaches the maximum group velocity and then moves stationarily at this maximum group velocity. A conclusion is made of the fallacy of some works were the existence of moving polarons in a dispersionless medium is considered infeasible.     

In situ observation of the ultrafast lattice dynamics of graphite under ion irradiation

We develop a pump-probe experiment system, in which vibrational dynamics of a solid sample under ion irradiation can be measured in real time. In situ observation enables us to monitor small changes induced by ion irradiation, without being influenced by the irreproducibility of the sample quality or the experimental configuration. We apply the experimental system to investigate the femtosecond dynamics of the coherent E_2g1 phonon of graphite under 5 keV He⁺ irradiation. A slight decrease in the dephasing rate of the phonon at the initial stage, as well as a downshift followed by an upshift of the phonon frequency, are clearly demonstrated, all of which were ambiguous in the ex situ experiment due to the poor reproducibility of the surface quality. This technique could also be applied to study femtosecond vibrational dynamics in real time during thermal annealing, film deposition with e.g. ablation and sputter, and molecular adsorption on substrates.     

Phonon focussing patterns: Calculation of response of finite area detectors to pulsed ballistic beams of dispersive and dispersionless phonons

The phonon images of crystals are described in the frame of the Boltzmann kinetic equation. Monochromatic heat pulses of the dispersive and dispersionless acoustic phonons are considered. Exact expressions for the energy and quasimomentum carried by a pulsed beam of monochromatic dispersionless acoustic phonons falling onto a detector of the finite area are derived. These formulae provide us with a convenient starting point for numerical calculations of phonon images. For the example of long wave-length acoustic phonons and a point as well as extended sources, an algorithm for numerical calculations of phonon images of anisotropic crystalline media is presented. However, it is quite general and can be easily adapted for dispersive phonons and to quasiparticles with an arbitrary dispersion low.     

Ab initio lattice dynamics and elastic constants of ZrC

Ab initio calculations and a direct method are applied to derive the phonon dispersion relations and phonon density of states for the ZrC crystal. The results are in good agreement with neutron scattering data. The force constants are determined from the Hellmann-Feynman forces induced by atomic displacements in a 222 supercell. The elastic constants are found using the deformation method and successfully compare with experimental data. Received 2 July 1999 and Received in final form 26 November 1999     

Nonlinear lattice dynamics of bismuth as a means of clarifying the nature of coherent phonons

The nonlinear regime of generation of coherent phonons in bismuth single crystals irradiated by ultrashort high-energy laser pulses has been investigated. In this regime, autoecho phenomenon is implemented at a low (helium) crystal temperature, manifesting itself as a collapse and revival of reflection oscillations generated by coherent A _1g phonons. Different mechanisms of the observed phenomena are considered.     

Coupling of electrons and phonons in a doped antiferromagnet

It is well-known that low-energy electronic excitations in high-T _c superconductors have energies of the order of the exchange couplingJ, i.e. of the same order as the phonon energies. Therefore, low-energy electronic excitations and phonons should strongly influence each other. To investigate this problem we consider a coupled electron-phonon system. For the electronic degrees of freedom we start from the three band Hubbard or Emery model. In analogy to the transformation of the three band Hubbard model to thet?J model, studied by Zhang and Rice, we derive an effective electron-phonon interaction. Its electronic degrees of freedom are those of thet?J model which couple to the phonons of the original system. The coupling of electrons and phonons is discussed by means of the phonon Green function for a breathing-like mode.     

Lattice dynamics of LaMnO3: Coupling of the lattice and orbital degrees of freedom

The lattice dynamics of regular LaMnO₃ is calculated within a shell model with pairwise interionic interaction potentials and with a Jahn-Teller (JT) contribution included into the energy and dynamic matrix of the crystal. A correlation is made between Raman spectral lines and lattice vibrations. The positions of some lines in the Raman spectrum are found to depend heavily on the linear JT coupling constant V _e . The effect of the JT coupling on the phonon density of states of LaMnO₃ is investigated.     

Effect of changing incident wavelength on Raman features of optical phonons in SiC nanorods and TaC nanowires

Novel Raman scattering in polar semiconductor SiC and TaC one-dimensional materials have been carried out. With increasing incident laser wavelength from 488 to 633 nm there is a huge difference in Raman intensity enhancement for the LO/IF peaks and the TO peak. This has been interpreted as due to Fröhlich interaction and abundant defects in polar nano-scale semiconductor materials.     

On the extendedness of eigenstates in a hierarchical lattice: A critical view

We take a critical view at the basic definition of extended single particle states in a non-translationally invariant system. For this, we present the case of a hierarchical lattice and incorporate long range interactions that are also distributed in a hierarchical fashion. We show that it is possible to explicitly construct eigenstates with constant amplitudes (normalized to unity) at every lattice point for special values of the electron-energy. However, the end-to-end transmission, corresponding to the above energy of the electron in such a hierarchical system depends strongly on a special correlation between the numerical values of the parameters of the Hamiltonian. Keeping the energy and the distribution of the amplitudes invariant, one can transform the lattice from conducting to insulating simply by tuning the numerical values of the long range interaction. The values of these interactions themselves display a fractal character.     

First-principles calculations on ferroelectricity and lattice dynamics of Type-II multiferroic SmMn2O5

In this work, we report on the structural, electronic, and ferroelectric properties of SmMn₂O₅ by using first-principles density functional theory plus on-site Coulomb interaction (DFT + U) calculations. A thorough analysis was preformed to reveal the competing characteristics of different high-temperature (T) phases and the polarization mechanism in the low-T multiferroic phase. We show that the structural characteristics of the high-T phases have a strong influence on the low-T multiferroicity. In addition to the spin-induced lattice distortion that reduces substantially the purely electronic ferroelectricity, the dominant polarization mechanism in low-T SmMn₂O₅ still originates from the electronic polarization. By performing mode decomposition of the Hellmann–Feynman forces and the lattice distortion induced by the q = (0.5, 0, 0) magnetic order, we find that the Raman-active A_g mode characterized by the Mn⁴⁺O₆ octahedron distortion and synergistic displacement of Mn³⁺ and Sm ions is of primary importance, while the infrared (IR)-active B_2u mode plays a secondary role. These findings provide a theoretical foundation for future studies concerning the enhanced magnetoelectric effects of SmMn₂O₅ due to its pure exchange–striction mechanism.     

Functional group contributions to the auger spectra of methyl cyanide and methyl isocyanide

We have obtained and analyzed the C and N core—valence—valence Auger spectra of methyl cyanide and methyl isocyanide. From both a fingerprint level interpretation, based on nitrogen, acetylene and methane as models, and from detailed spectral assignments, based on one-electron binding energies, we have shown that the spectra can be interpreted as resulting from independent contributions from the methyl group and the cyanide (or isocyanide) group. The contributions from the methyl and cyanide (or isocyanide) groups occur at different energies and exhibit different degrees of hole—hole correlation energy; the latter is shown to be consistent with differing degrees of functional group orbital delocalization. The detailed assignments to experimental spectral features, for the transitions involving the four highest filled molecular orbitais, form a consistent set with only a single exception. Intensity is missing in the region of the C spectrum of methyl cyanide corresponding to transitions involving the cyanide group π and σ orbitals.     

A renormalization scheme for calculating the spectrum of a vibronic system occurring in molecules or impurities in insulators

An iteration scheme which makes use of a numerical renormalization group approach is used to calculate the spectrum of vibronic levels. This spectrum resulted from dynamic effects occurring in certain molecules or impurities in insulators.The Hamiltonian of these systems is expressed in the matrix form, using products of suitable electron-phonon states as a basis. In applying this method to multimode electron-phonon systems, phonon modes are coupled in a chain-like fashion. Then a finite chain calculation in terms of Hubbard X-operators is explored by setting up the vibronic Hamiltonian.Calculations are based on Lanczos algorithm, in which only the nearest neighbor matrix elements along the chain need to be taken into account. The iterative scheme is then applied to a two-level electronic system coupled to phonons. A single-particle Green's function corresponding to a two-level system is applied to calculate the spectral density of states, which, coupled to single mode is carried out. The strength of lines in density of states is affected by the coupling constant as well as the temperature dependence of some measurable quantities.     

Electron correlations and quantum lattice vibrations in strongly coupled electron-phonon systems: A variational slave boson approach

We investigate the ground-state properties of the two-dimensional Hubbard model with an additional Holstein-type electron-phonon coupling on a square lattice. The effects of quantum lattice vibrations on the strongly correlated electronic system are treated by means of a variational squeezed-polaron wave function proposed by Zheng, where the possibility of static (frozen) phonon-staggered ordering is taken into account. Adapting the Kotliar-Ruckenstein slave boson approach to the effective electronic Hamiltonian, which is obtained in the vacuum state of the transformed phonon subsystem, our theory is evaluated within a two-sublattice saddle-point approximation at arbitrary band-filling over a wide range of electron-electron and electron-phonon interaction strengths. We determine the order parameters for long-range charge and/or spin ordered states from the self-consistency conditions for the auxilary boson fields, including an optimization procedure with respect to the variational displacement, polaron and squeezing parameters. In order to characterize the crossover from the adiabatic (=0) to the nonadiabatic (=) regime, the frequency dependencies of these quantities are studied in detail. In the predominant charge (spin) ordered phases the static Peierls dimerization (magnetic order) is strongly reduced with increasing . As the central result we present the slave boson ground-state phase diagram of the Holstein-Hubbard model for finite phonon frequencies.