Increasing Wave Vector Research Articles

Sodium ion self-diffusion in molten NaBr probed over different length scales.

The single-particle dynamics of sodium ions in molten sodium bromide has been investigated with quasielastic neutron scattering. A detailed and rather extensive data analysis procedure allowed determination of the pure sodium ion dynamics with increasing wave vector. Two different evaluation procedures agree perfectly on the resulting diffusion coefficient of sodium ions on long distances. A simple kinetic theory based on binary collisions of hard spheres is not able to reproduce the sodium diffusion coefficient. The derived reduced linewidth from modeling with a Lorentzian spectral function decreases with increasing wave vector towards the first structure factor maximum. That deviation from the hydrodynamic behavior signals the hindrance of the microscopic diffusion process due to the so-called cage effect when microscopic length scales are probed in a dense fluid. The observed quadratic wave-number-dependent decrease might be evidence for a coupling to density fluctuations as the source of the changes in the diffusion process. The results indicate that in the molten salt NaBr near the melting point the self-diffusion process might be governed by similar processes as already observed in dense metallic liquids.

Bulk and surface plasmons in graphene finite superlattices

In recent years, graphene plasmonics, has attracted significant interest motivated by graphene's unique high carrier mobility, electrically or chemically tunable carrier density, long-lived and strong plasmon excitation confinement. In the context of optoelectronics and nanophotonics, graphene is considered as promising plasmonic material working in the mid-infrared and terahertz spectral windows. However, in a single layer graphene, the electromagnetic energy has a limited capability to plasmon excitations. To obtain a more powerful capacity of excite plasmon resonance, one can employ multilayer graphene structures as possible solution. In this work, we find an analytical expression for the dielectric function of the N-layer graphene structure solving a recurrence relation between the electric potential at different graphene layers. We also find that the highest energy of the plasmon oscillations supported by the multilayer graphene stacks at long wavelength correspond to electrons in each plane oscillating in phase. In addition, a surface plasmon mode emerges at certain finite wave vector outside the bulk plasmon band and it is Landau damping in the continuous interband single particle excitation with increasing wave vector.

Wave vector dependent damping of THz collective modes in a liquid metal

Well-defined damped collective modes have been observed in liquid metals over a wide range of wave vectors. Hydrodynamics predicts that viscosity and thermal conductivity are the cause for the damping of the collective modes. Here we present experimental data from neutron spectroscopy on the damping of collective modes of liquid rubidium over a wide range of wave vectors. We propose a phenomenological model derived from generalized hydrodynamics to describe the damping of the modes and the evolution with increasing wave vector based on the viscoelastic picture of liquid response. As necessary ingredients a wave vector dependent high frequency shear modulus and shear relaxation time appear. We obtain a remarkable good agreement on a quantitative basis between experiment and calculation over a wide range of wave vectors. The emergent picture is that the lifetime of the collective modes in the THz regime is mainly limited through the diffusion of momentum. The proposed methodology might be applicable to a wide range of liquids.

Electric-field influence on the neutron diffuse scattering near the ferroelectric transition of Sr0.61Ba0.39Nb2O6

ABSTRACTUniaxial relaxor ferroelectric Sr0.61Ba0.39Nb2O6 single crystal has been investigated in the vicinity of its phase transition using neutron scattering and dielectric spectroscopy. A global-type thermal hysteresis is evidenced by both techniques in the ferroelectric phase and up to about 15 K above Tc. In addition, a part of the transverse neutron diffuse scattering in the 001 Brillouin zone, presumably related to static nanodomain structure, can be suppressed by prior poling the crystal in electric field of 3 kV/cm. The remaining part of the transverse neutron diffuse scattering and the real part of permittivity show a similar temperature dependence. The temperature position of the maximal scattering intensity Tmax depends significantly on the scattering wave vector. Tmax shifts monotonically to higher temperature with the increasing wave vector in all investigated cooling and heating regimes. It is concluded that the critical fluctuations have space correlations which depend on frequency and wave vector.

Pentacene and poly-pentacene as graphene nanoribbons

The development of electronic devices based on the unique electronic properties of graphene requires the large scale synthesis of graphene nanoribbons which remains a significant challenge. A possible way around this is to seek existing molecules that can be readily chemically synthesized and have the structure of graphene nano-ribbons. One such molecule is pentacene, C22H14, a two dimensional chain of 5 benzene rings.Density functional theory (DFT) is used to examine the electronic and vibrational properties of pentacene, poly-pentacene and its boron nitride analogs. The results show that pentacene and poly-pentacene have similar unique electronic properties to graphene nanoribbons. The HOMO–LUMO energy gap decreases with the length of the chain and the band gap increases with increasing wave vector. In contrast the energy gap for the BN ribbons is relatively independent of the chain length and the wave vector.

Effective-medium theory of elastic waves in random networks of rods

We formulate an effective medium (mean field) theory of a material consisting of randomly distributed nodes connected by straight slender rods, hinged at the nodes. Defining wavelength-dependent effective elastic moduli, we calculate both the static moduli and the dispersion relations of ultrasonic longitudinal and transverse elastic waves. At finite wave vector k the waves are dispersive, with phase and group velocities decreasing with increasing wave vector. These results are directly applicable to networks with empty pore space. They also describe the solid matrix in two-component (Biot) theories of fluid-filled porous media. We suggest the possibility of low density materials with higher ratios of stiffness and strength to density than those of foams, aerogels, or trabecular bone.

Theory of elastic and piezoelectric effects in two-dimensional hexagonal boron nitride

Starting from an empirical force constant model of valence interactions and calculating by Ewald's method the ion-ion force constants, we derive the dynamical matrix for a monolayer crystal of hexagonal boron nitride (h-BN). The phonon dispersion relations are calculated. The interplay between valence and Coulomb forces is discussed. It is shown by analytical methods that the longitudinal and the transverse optical (LO and TO) phonon branches for in-plane motion are degenerate at the $\ensuremath{\Gamma}$ point of the Brillouin zone. Away from $\ensuremath{\Gamma}$, the LO branch exhibits pronounced overbending. It is found that the nonanalytic Coulomb contribution to the dynamical matrix causes a linear increase of the LO branch with increasing wave vector starting at $\ensuremath{\Gamma}$. This effect is general for two-dimensional (2D) ionic crystals. Performing a long-wavelength expansion of the dynamical matrix, we use Born's perturbation method to calculate the elastic constants (tension coefficients). Since the crystal is noncentrosymmetric, internal displacements due to relative shifts between the two sublattices (B and N) contribute to the elastic constants. These internal displacements are responsible for piezoelectric and dielectric phenomena. The piezoelectric stress constant and the dielectric susceptibility of 2D h-BN are calculated.

Static structure factor for graphene in a magnetic field

A close study is made of the static structure factor for graphene in a magnetic field at integer filling factors $\ensuremath{\nu}$, with focus on revealing possible signatures of ``relativistic'' quantum field theory in the low-energy physics of graphene. It is pointed out, in particular, that for graphene even the vacuum state has a nonzero density spectral weight, which, together with the structure factor for all $\ensuremath{\nu}$, grows significantly with increasing wave vector; such unusual features of density correlations are a relativistic effect deriving from massless Dirac quasiparticles in graphene. Remarkably, it turns out that the zero-energy Landau levels of electrons or holes, characteristic to graphene, remain indistinguishable in density response from the vacuum state, although they are distinct in Hall conductance.

Calculation of the thermoelectric figure of merit for multilayer structures with quantum wells in the case of carrier scattering by polar optical phonons

The increase in the thermoelectric figure of merit in layered structures with quantum wells is calculated for the case of polar charge-carrier scattering by optical phonons. On the basis of previous and new calculations, it is concluded that the quantum confinement effect can give rise to the increase in the figure of merit only if the probability of carrier scattering decreases with increasing wave vector transfer.

Surface states and Fermi surface of orderedγ-like Ce films on W(110)

The surface electronic structure of structurally ordered Cerium films deposited on W(110) has been studied along the two surface high-symmetry directions of the close-packed surface. As in other trivalent rare-earth metals a surface state of d z 2-p z symmetry was found to dominate the electronic structure near the Fermi energy. This surface state lies exactly at the Fermi energy at r dispersing towards higher binding energies with increasing wave vector. Its effective mass amounts (-7.4′1.3) times the electron mass. The surface-state induced emission was found to dominate the Fermi-surface cuts near the Γ point of the first surface Brillouin zone (SBZ), while at the Γ point of the second SBZ the surface state lacks intensity.

Effects of coupling on plasmon modes and drift-induced instabilities in a pair of cylindrical nanotubes

We develop a theory of collective plasma excitations in a pair of parallel nonoverlapping cylindrical nanotubes. A general dispersion equation is obtained as a function of the angular momentum and linear momentum transfer. We use our results to calculate the phase velocity of the plasmon excitations when current flows parallel to the axis of the nanotube in either the same or neighboring nanotube as the plasma excitations. We demonstrate that the less energetic undamped plasmon excitations may have a phase velocity which is smaller than the Fermi velocity. The plasmons with the largest frequencies have phase velocities which decrease with increasing wave vector. We discuss the instabilities which may arise when the drift velocity of the electrons lies within a range which is determined by the phase velocity for the plasmon modes of the pair of cylindrical nanotubes.

X-ray synchrotron study of liquid-vapor interfaces at short length scales: effect of long-range forces and bending energies.

We have investigated the small-scale structure of the liquid-vapor interface using synchrotron x-ray scattering for liquids with different molecular structures and interactions. The effective momentum-dependent surface energy first decreases from its macroscopic value due to the effect of long-range forces, and then increases with increasing wave vector. The results are analyzed using a recent density functional theory. The large wave-vector increase is attributed to a bending energy for which local and nonlocal contributions are equally important.

Chain confinement effects on interdiffusion in polymer multilayers

We have measured interdiffusion in polystyrene on length scales approaching and below the overall dimensions of the polymer molecules, by using neutron reflectometry to follow the relaxation of the composition modulation in an isotopic polymer multilayer. After an initial transient, relaxation of the composition modulation is diffusive, even for times less than the reptation time. The diffusion coefficient decreases with increasing wave vector, in qualitative, but not quantitative, accord with theory.

Thinning transitions and fluctuations of freely suspended smectic-A films as studied by specular and diffuse X-ray scattering

The fluctuations in freely suspended smectic-A films have been studied using specular and diffuse X-ray scattering. Such films thin layer-by-layer above the bulk transition temperature of the smectic-A–nematic phase transition. The electron density profiles obtained from specular reflectivity demonstrate that thinning originates from nematic layers being expelled from the interior of the film. In addition, using diffuse scattering the spectral dependence of the displacement–displacement correlation function could be measured down to molecular dimensions, with a (2+2) scattering geometry at a synchrotron source. At long in-plane length scales the fluctuations of the smectic layers were found to be conformal; i.e. top and bottom of the film fluctuated in unison. However, at increasing wave vector transfers, conformality was progressively lost.

Single-particle excitations in quasi-zero- and quasi-one-dimensional electron systems.

Resonant inelastic light scattering is used to probe electronic excitations in shallow etched GaAs/AlGaAs quantum dots and wires. In both types of structures, intersubband excitations are observed in depolarized scattering geometries. They show significant blueshift with decreasing confinement length. In dot structures these transitions appear as dispersionless, whereas in wires they show strong broadening and an intensity dip at the energetic center of the excitation with increasing wave vector parallel to the wires, as expected for single-particle excitations. Their line shape correlates with the linear wave vector dispersion of additionally observed intrasubband excitations.

Dynamics of a bound membrane.

The dispersion relation for the overdamped bending modes of a membrane bound to a substrate by an attractive potential is determined. The damping rate \ensuremath{\gamma} as a function of the wave vector q behaves, for small q, like \ensuremath{\gamma}\ensuremath{\sim}${\mathit{q}}^{2}$ arising from the interplay between the hydrodynamic damping by the surrounding liquid and the restoring force in the binding potential. With increasing wave vector q, various crossovers can occur, leading to the possibility of nonmonotonic damping where \ensuremath{\gamma} decreases with q as \ensuremath{\sim}1/q.

Polarized neutron reflection as a probe of magnetic films and multilayers.

The application of polarized neutron reflection (PNR) to the study of the magnetic properties of thin films and multilayers is described. It is demonstrated that PNR provides a means of directly determining the magnetization-vector profile in multilayers of known layer thickness and layer density. Thus, the magnetization reversal process in these systems can be directly studied. A matrix method is presented which can be used to calculate the spin-dependent reflectivity from a multilayer with general in-plane orientation of the magnetic moment in each layer. In addition, we show that behavior of the spin asymmetry is dominated by multiple reflections and refraction just above the critical wave vector, but with increasing wave vector, such processes become progressively less important, and the response moves towards a ``diffraction limit'' in which a Fourier-transform approximation to the exact result can be used. The ideas in this paper are illustrated by a number of examples, including the exchange-biased structure Ag/Fe-Ni/Cu/Fe-Ni/Fe-Mn/Si.

Cu:Si(111) incommensurate (5.55 x 5.55) surface reconstruction: Helium-beam measurements of diffraction and surface phonons.

Elastic and inelastic atomic-helium scattering has been used to characterize the Cu:Si(111) ``quasi-(5\ifmmode\times\else\texttimes\fi{}5)'' surface. The surface superlattice is incommensurate with the underlying Si(111) structure, 5.55 times larger, appears to be limited to the outermost layers, yet is not a simple incommensurate overlayer. The helium diffraction indicates a long-range coherence of the reconstruction which, while not incompatible with a two-dimensional quasicrystal, would severely restrict any quasicrystal correlation or tiling rules. The surface phonons have intriguing characteristics including a lack of band gaps at fractional-order ``zone boundaries'' and what seems to be a continuous transition from extended mode to local oscillator mode with increasing wave vector.

Hydrodynamical theory of the LO-phonon-plasmon dispersion in Al xGa 1- xAs

In this work, we used the hydrodynamical theory to find a suitable description for the free-carrier electric susceptibility. This theory used also a phenomenological damping constant and is an extension of the Drude approach through the introduction of a diffusion term in the free-carrier equation of motion. A wave vector dependent susceptibility, corresponding to the contribution of a harmonic oscillator with an eigenfrequency, was obtained. Numerical results for Al x Ga 1- x As look similar to those for GaAs, although there are qualitative and quantitative differences. The free-carrier term is largest at zero frequency, as well as at zero wave vector, and decreases with increasing frequency and wave vector. The wave vector independent phonon contributions proceed parallel to the wave vector axis at the GaAs-like and AlAs-like resonance frequencies of lattice vibration. The L 1, L 2 and L 3 coupled modes approach the GaAs-like phonon, the AlAs-like phonon, and the plasma frequencies, respectively, with increasing wave vector. The plasma damping constant was used to calculate the electron mobility. The result was closer to the Hall mobility than the value obtained from using the coupled mode L 3.

Momentum dependence of the Stoner excitation spectrum of iron using spin-polarized electron-energy-loss spectroscopy.

The electron-hole excitations with different spin configurations have been separated and studied experimentally in iron, with use of spin-resolved electron-energy-loss spectroscopy with both a source and detector of spin-polarized electrons. The data are interpreted using a two-particle, exchange scattering model, and analyzed in the 4\ifmmode\times\else\texttimes\fi{}4 product spin space of the incident and target electrons. Stoner excitations in the form of majority-hole--minority-electron pairs are found to comprise up to one-third of the total electron-hole excitations in off-specular scattering, and exhibit a clear, broad peak due to excitations within the exchange-split d bands of iron. The width and energy loss at which this peak occurs increase with increasing wave vector of the Stoner excitation. These trends are also observed in the calculated Stoner density of states for iron.