Minigap plasmons in a two-dimensional electron gas subjected to a one-dimensional periodic potential

We investigate the plasmon excitations in a two-dimensional electron gas subjected to a one-dimensional weak periodic potential. We derive and discuss the dispersion relations for both intrasubband and intersubband excitations within the framework of Bohm-Pines' random-phase approximation. For such an anisotropic system with spatially modulated charge density, we observe a splitting of the 2D plasmon dispersion. The splitting is caused by the superlattice effect of the charge-density modulation on the collective excitation spectrum. We also discuss how the tunneling and the potential amplitude affect the plasmon excitations.     

Anisotropic Intervalley Plasmon Excitations in Graphene

We investigate theoretically the intervalley plasmon excitations(IPEs) in graphene monolayer within the random-phase approximation. We derive an analytical expression of the real part of the dielectric function. We find a lowenergy plasmon mode with a linear anisotropic dispersion which depends on the Fermi energy and the dielectric constant of substrate. The IPEs show strongly anisotropic behavior, which becomes significant around the zigzag crystallographic direction. More interestingly, the group velocity of IPE varies from negative to positive, and vanishes at special energy.     

Collective modes in semiconductor superlattices

Electronic collective modes in a semiconductor superlattice structure are studied within the self-consistent field approach. Plasmon and magneto-plasmon dispersion relations are obtained for the cases of strong and weak coupling between layers. The interaction of these collective modes with optical phonons is also investigated.     

Model boson fluid with disorder in the self-consistent field approximation

We study the ground-state properties of a model neutral boson fluid in the presence of disorder effects. The effective interaction between the bosons is obtained through the self-consistent field method which renormalizes the bare interaction consisting of a hard-core repulsive potential with an attractive tail at zero temperature. We introduce disorder effects within a number-conserving approximation by modifying the density–density response function. Our results for the static structure factor and the collective mode dispersion reflect the effect of disorder in qualitative agreement with other calculational approaches.     

Anisotropic exchange and magnetic excitations in KCoF3

A superexchange mechanism is used for the determination of the form of the exchange Hamiltonian in KCoF₃ introducing only two independent parameters. The Co²⁺ ions are orbitally degenerate and this leads to the anisotropic exchange in KCoF₃. The collective excitations are introduced being based on the space of selfconsistently determined states of Co²⁺ ions in the low temperature approximation. The effective exchange field is introduced in this many-level system so that the one-ion eigenvalue problem can be solved. The agreement with two lowest branches of magnetic excitation spectra is satisfactory. It is emphasized that the appropriate general form of the exchange Hamiltonian which includes the orbital operators should be used for the interpretation of experimental data instead of the simple isotropic form. In the case of KCoF₃, however, it appears that the dispersion relation for magnetic excitations is rather insensitive on the form of the model Hamiltonian.     

Theory of plasmon excitations in (SN)x

The anomalous anisotropy and dispersion of plasmons in polymeric sulfur nitride (SN)_x are explained within a model of an electron gas with an anisotropic effective mass ratio. Calculations in the random phase approximation yield very good agreement with the electron loss data. Exchange corrections for the model are shown to be small for systems of the (SN)_x type which exhibit reduced dimensionality.     

Theoretical investigation of Stoneley-wave attenuation and dispersion in a fluid filled fracture in transversely isotropic formation

The wave motion in a fluid-filled fracture embedded in an anisotropic medium is investigated using the technique of partial waves. A model is derived to calculate the complex dispersion relation of the Stoneley-wave mode in a fluid layer between two infinite transversely isotropic half-spaces. The effect of the anisotropic parameters on the Stoneley-wave in the fracture is investigated. The numerical results indicate that the velocity of the Stoneley-wave mode has significant dependence on the transversely isotropic constants. For a weakly anisotropic medium, the Stoneley-wave dispersion is almost the same as in an isotropic medium.     

A new method for calculation of the magnetic properties in one- and two-dimensional spin systems with anisotropic Heisenberg exchange

A new approximation method is proposed for the calculation of the magnetic susceptibility of one-dimensional assembly of spins and the critical temperature of two-dimensional one both with the anisotropic Heisenberg exchange. In a linear chain system, every spins are grouped into pairs of adjacent spins (pair-approximation) or clusters of adjacent three spins ((q+1)-approximation), and the partition function of the total spin system is approximated as a sum of products of the partitions functions for the pairs or the clusters. Then the partition function of the anisotropic Heisenberg spin system is shown to reduce into a form of the Ising spin system with modified coupling constants. The exact result for the Ising chain system enables us to obtain an analytical expression for the magnetic susceptibility of anisotropic Heisenberg chain system. The same approximations are also applied to two-dimensional lattices, and the critical temperatures of the square, triangular, and honeycomb lattices with anisotropic Heisenberg exchange are calculated as a function of anisotropy parameter. The results are compared with those of the existing theories and shown to be quite excellent.     

Band structure of collective modes and effective properties of binary magnonic crystals

In this paper a theoretical study of the band structure of collective modes of binary ferromagnetic systems formed by a submicrometric periodic array of cylindrical cobalt nanodots partially or completely embedded into a permalloy ferromagnetic film is performed. The binary ferromagnetic systems studied are two-dimensional periodic, but they can be regarded as three-dimensional, since the magnetization is non uniform also along the z direction due to the contrast between the saturation magnetizations of the two ferromagnetic materials along the thickness. The dynamical matrix method, a finite-difference micromagnetic approach, formulated for studying the dynamics in one-component periodic ferromagnetic systems is generalized to ferromagnetic systems composed by F ferromagnetic materials. It is then applied to investigate the spin dynamics in four periodic binary ferromagnetic systems differing each other for the volume of cobalt dots and for the relative position of cobalt dots within the primitive cell. The dispersion curves of the most representative frequency modes are calculated for each system for an in-plane applied magnetic field perpendicular to the Bloch wave vector. The dependence of the dispersion curves on the cobalt quantity and position is discussed in terms of distribution of effective “surface magnetic charges” at the interface between the two ferromagnetic materials. The metamaterial properties in the propagative regime are also studied (1) by introducing an effective magnetization and effective “surface magnetic charges” (2) by describing the metamaterial wave dispersion of the most representative mode in each system within an effective medium approximation and in the dipole-exchange regime. It is also shown that the interchange between cobalt and permalloy does not necessarily lead to an interchange of the corresponding mode dispersion. Analogously to the case of electromagnetic waves in two-dimensional photonic crystals, the degree of localization of the localized collective modes is expressed in terms of an energy concentration factor.     

Strong Coulomb correlation effects in ZnO

The electronic structure, band parameters, and optical spectra of wurtzite-type ZnO were studied by first-principles calculations within different approximations of the density functional theory. The local-density approximation underestimates the band gap, the energy levels of the Zn-3d states, the band dispersion, the crystal-field splitting, the spin-orbit interaction, and location of peaks in the optical spectra. The generalized-gradient approximation slightly corrects the discrepancies with the experimental findings and it shows good agreement for the optical spectra with experimental data at energies 10-20 eV for E⊥c. Studies within the local-density approximation with the multiorbital mean-field Hubbard potential show that strong Coulomb correlations are in operation. From effective mass calculations it is found that holes are much heavier and more anisotropic than the conduction-band electrons in ZnO.     

Locally resonant acoustic metamaterials with 2D anisotropic effective mass density

A two-dimensional (2D) lattice model with anisotropic resonant microstructures is found to provide an anisotropic band gap structure. A 2D continuum with anisotropic effective mass density is introduced to represent this lattice system. Two methods are proposed to derive the equivalent continuum. In the first method, the effective mass density of the equivalent continuum is obtained by matching the dispersion relations for harmonic waves propagating in the principal directions. The second approach employs an approximate estimation of the effective mass density by volume-averaging an effective mass that represents the resonant microstructure. For both equivalent continuum models, the effective mass density is frequency-dependent and may become negative in certain frequency ranges. Subsequently, the effective mass density of the equivalent continuum assumes the form of a second-order tensor. Thus, it suffices to determine the effective mass density tensor with respect to the principle directions. It is shown numerically that the local-resonance effect is accurately described by the equivalent continuum model. In addition, the effect of anisotropic mass density on wave propagation is numerically illustrated and discussed.     

The paramagnetic properties of one-dimensional spin-1 single-ion anisotropic ferromagnet

One-dimensional single-ion anisotropic ferromagnet with spin-1 is investigated by means of Green's function treatment in this paper. The model Hamiltonian includes a Heisenberg ferromagnetic term, an external magnetic field, and a second-order single-ion anisotropy. The magnetic properties of the system are treated by the random phase approximation for the exchange interaction term and the Anderson-Callen approximation for the anisotropy term. Our paramagnetic results are in agreement with the other theoretical results.     

Anisotropic superfluidity in a dipolar Bose gas

We study the superfluid character of a dipolar Bose-Einstein condensate (DBEC) in a quasi-two dimensional geometry. We consider the dipole polarization to have some nonzero projection into the plane of the condensate so that the effective interaction is anisotropic in this plane, yielding an anisotropic dispersion relation. By performing direct numerical simulations of a probe moving through the DBEC, we observe the sudden onset of drag or creation of vortex-antivortex pairs at critical velocities that depend strongly on the direction of the probe's motion. This anisotropy emerges because of the anisotropic manifestation of a rotonlike mode in the system.     

Anisotropic magnetic exchange in orthorhombic RCu2 compounds (R = rare earth)

The magnetic excitations in the field induced ferromagnetic phase F3 of a NdCu₂ single crystal were investigated by means of inelastic neutron scattering experiments. A mean field model using the random phase approximation in connection with anisotropic magnetic bilinear R-R (R denotes a rare earth) exchange interactions is proposed to account for the observed dispersion. The relevance of this model to the analysis of the magnetic ordering process in other RCu₂ compounds is discussed. Received 21 April 1999     

Nucleus-nucleus potential within the semimicroscopic dispersive model on the basis of a corrected folding-model potential

A procedure is proposed for correcting the energy dependence of the mean-field component of the optical-model potential, this component being calculated within the double-folding model with allowance for exchange effects in the approximation of one-nucleon knockout exchange. The procedure is based on employing, for the mean field, an empirical energy dependence that is obtained from a dispersion analysis of integrated features of phenomenological optical-model potentials and is tested by applying it to calculating the mean field and to analyzing data on the elastic scattering of alpha particles on oxygen nuclei within the semimicroscopic dispersive optical model.     

Self-consistent many-body theory for the standard basis operator Green's functions

We propose a self-consistent many-body theory for the standard basis operator Green's functions and obtain an exact Dyson-type matrix equation for the interacting many-level systems. A zeroth order approximation, which neglects all the damping effects, is investigated in detail for the anisotropic Heisenberg model, the isotropic quadrupolar system and the Hubbard model. In the case of the anisotropic Heisenberg ferromagnet with both exchange and single-ion anisotropy the low-temperature renormalization of the spin-waves for the uniaxial ordering agrees with the Bloch-Dyson theory. For the spin-1 easy-plane ferromagnet, the critical parameters for the phase transition at zero temperature are determined and compared with other theories. The elementary excitation spectrum of the spin-1 isotropic quadrupolar system is calculated and compared with the random phase approximation and Callen-like decoupling schemes. Finally, the theory is applied to the study of the single-particle excitation spectrum of the Hubbard model.     

Vortices and magnetic structures of the target type in a two-dimensional ferromagnet with anisotropic exchange

Various types of magnetic structure in a two-dimensional Heisenberg ferromagnet are considered in a continuum approximation. The effect of anisotropic exchange and single-ion anisotropy on the vortex structure is analyzed. A new type of static magnetic structure (“target”) is predicted and investigated in an easy-plane ferromagnet.     

Excitations in a Dipolar Bose–Einstein Condensate

We study excitations in a dipolar Bose–Einstein condensate with Green’s function. In Bogoliubov approximation, we obtain the dispersion relation. The excitation energy is dependent on the angle between the momentum and the magnetic moment. In the long-wave limit, the dispersion relation reduces to an anisotropic phonon-like dispersion relation.     

Exchange and correlation effects in a semiconductor quantum-well wire

The exchange and correlation effects of a quasi-one-dimensional electron gas are investigated by using the self-consistent-field approximation theory proposed by Singwi, Tosi, Land and Sjölander for the response function of the electron system. The present results are applied to GaAs-GaAlAs rectangular quantum-well-wires with the appropriate form factors that take into account the influence of the finite width of the electron layer. The plasmon dispersion relation and structure factor are calculated as a function of electron density and thickness of the wire. Results for the total energy per electron including kinetic, exchange and correlation energies and electron effective mass are presented. The Hartree-Fock and the random-phase approximation (RPA) results are also presented for comparison. We have found that exchange and correlation effects are more evident in wires of reduced dimensions.     

Hysteresis behavior of the anisotropic quantum Heisenberg model

The effect of the anisotropy in the exchange interaction on the hysteresis loops within the anisotropic quantum Heisenberg model has been investigated with the effective field theory for two spin cluster. Particular attention has been devoted on the behavior of the hysteresis loop area, coercive field and remanent magnetization with the anisotropy in the exchange interaction for both ferromagnetic and paramagnetic phases.