Showing papers on "Brillouin zone published in 1983"

Polyacene and a new class of quasi-one-dimensional conductors

Abstract: Most one-dimensional conductors are quite similar since the Fermi surface is a point and the electron energy dispersion relation near the Fermi surface is linear. It is pointed out that in polyacene the Fermi surface lies at the edge of the Brillouin zone, but that an accidental degeneracy between the valence and conduction bands makes it metallic nonetheless. The dispersion relation is therefore quadratic, and the density of states diverges at the Fermi surface. Thus, polyacene [${({\mathrm{C}}_{4}{\mathrm{H}}_{2})}_{n}$] and its possible derivatives represent a conceptually new class of quasi-one-dimensional conductors. Moreover, we find that this class of materials has the possibility of possessing interesting condensed phases including high-temperature superconductivity and ferromagnetism.

Magnetic excitations in layered media: Spin waves and the light-scattering spectrum

Abstract: We present an analysis of the spin-wave spectrum of a semi-infinite stack of ferromagnetic films, each of which is separated by a gap filled by a nonmagnetic medium. This is done within a formalism which includes the Zeeman and dipolar contributions to the spin-wave energy, with exchange omitted. We then calculate the spin-wave contribution to the Brillouin spectrum of such a system, in the backscattering geometry. The aim is to compare the spectrum for scattering from a sample with this geometry, with that from an isolated film. Two features unique to the stack appear in the spectrum. Each film, in isolation, possesses surface spin waves on its boundaries (Damon-Eshbach waves). In the layered geometry these interact to form a band of excitations of the array, which has nonvanishing component of wave vector normal to the stack. We find a feature in the spectrum associated with scattering from this band of modes; the position of the peak is controlled by dispersion introduced by interfilm interactions. Under certain conditions, the semi-infinite stack possesses a surface spin wave, whose eigenfunction is a linear superposition of individual film states, with amplitude that decays to zero as one moves down into the stack interior. This mode also produces a distinct feature in the light-scattering spectrum. These points are illustrated with a series of calculations of the spectrum, for parameters characteristic of layered ultrathin coherent structures.

Special points of the brillouin zone and their use in the solid state theory

Abstract: Article de synthese en trois parties: 1) Considerations generales sur l'integration en des points particuliers de la zone de Brillouin; 2) Points de valeur moyenne et points particuliers de la zone de Brillouin pour des cristaux de differentes symetries; 3) Utilisation des points particuliers dans des calculs de structure de bande et de proprietes physiques de solides

Three-Dimensional Energy Band in Graphite and Lithium-Intercalated Graphite

Abstract: Angle-resolved inverse photoemission with tunable photon energies has been used to map out the unoccupied bands of graphite and lithium-intercalated graphite. At the Brillouin zone center the bottom of the lowest band is found at 4.0\ifmmode\pm\else\textpm\fi{}0.5 eV above the Fermi level in graphite. This band shows strong dispersion normal to the basal plane in excellent agreement with recent self-consistent band-structure calculations. A similar three-dimensional band is found in lithium-intercalated graphite shifted 3 eV to lower energy.

Electron densities and chemical bonding in TiC, TiN, and TiO derived from energy band calculations

Abstract: The chemical bonding in the interesting class of refractory transition metal compounds is illustrated for TiC, TiN, and TiO. Self-consistent augmented plane wave (APW) calculations are already available for these compounds. Using the respective potentials we have repeated the band calculations on a finer k grid with the linearized APW method to obtain accurate densities of states (DOS). These DOS can be divided into local partial contributions to characterize the bonding. Further information can be obtained from a decomposition of the metal dDOS into t2g and eg symmetry components. These partial local DOS are compared with the LCAO counterpart and give a first picture of the chemical bonding in these compounds. The electron densities corresponding to the occupied valence states are obtained from the LAPW calculations. They provide further insight into characteristic trends in the series from TiC to TiO: around the nonmetal site the density shows increasing localization; around the metal site the deviation from spherical symmetry changes from eg to t2g. These effects can be traced back to the three types of valence bands. Electron density plots of characteristic band states (all energies of a selected k point in the Brillouin zone) will be shown. These plots can describe the different types of bonding occurring in these systems.

Leaky surface‐elastic waves on both flat and strongly corrugated surfaces for isotropic, nondissipative media

Abstract: The dispersion relation for Rayleigh waves propagating across a grating, on the surface of a semi‐infinite, nondissipative, isotropic elastic medium was recently calculated by Rayleigh’s method and equivalently by a formally exact method based on Green’s theorem. Now, using a complex wave‐vector k or complex frequency ω in the present work, we continue the solutions of the dispersion relation into the radiative region of the kω‐plane (i.e., above the bulk transverse sound line) and into the first frequency‐gap on the boundary of the Brillouin zone caused by the grating periodicity. Here the solutions for the surface waves have components that radiate outwardly into the bulk. The acoustic attenuation for the Rayleigh waves, calculated from the imaginary part of complex k, agrees very well with experiment: all the observed peaks, including those missed by previous perturbation scattering theories, are found. Moreover, a branch is found in the dispersion relation, to which a corresponding complex solution is...

Theory of Brillouin scattering from surface acoustic phonons in supported films

Abstract: The theory of the Brillouin scattering from the surface of a semi-infinite medium, developed previously, is extended to coated surfaces of cubic materials. The Brillouin cross section is obtained for any scattering geometry and for p and s polarisation of the incident and scattered light. The formulae for the cross section contain contributions from the ripple and the elasto-optic scattering mechanisms for the film as well as for the substrate. The theory is applied to a silica film deposited on crystalline silicon and the behaviour of the cross section against the film thickness is investigated. The authors find that there are strong interference effects among the various contributions to the cross-section, so that the intensity of the spectral lines dramatically oscillates by changing the thickness. Although in general the ripple scattering mechanism is the dominant one it is found that the elasto-optic coupling in the silica film is not negligible and sometimes is even prevailing. The discrete phonon spectrum (Rayleigh, Sezawa, Lamb modes) and the continuous spectrum (resonances, mixed modes) are both studied.

Measurement of the Rayleigh surface-phonon dispersion curve for NaCl(001) from high-resolution He time-of-flight spectroscopy and from kinematical focusing angles

Abstract: Angular distributions and time-of-flight spectra have been measured for the collisions of 20-meV He atoms with a NaCl(001) surface in the 100g direction. Structures in the angular distribution and in the time-of-flight spectra due to elastic and inelastic scattering are measured and used to extract (1) a corrugation parameter of the rigid-atom surface potential ${\ensuremath{\zeta}}_{0}=0.34$ \AA{}, (2) three bound-state energies of the He-surface potential, and (3) a surface-phonon Rayleigh dispersion curve out to the edge of the Brillouin zone. Furthermore, we were able to demonstrate that by rotating the crystal about the surface normal it is possible to unambiguously identify kinematical focusing features in the angular distributions. These features were then used to determine a surface-phonon dispersion curve in good agreement with that obtained from the time-of-flight experiments.

Ferroelectric Phase Transition in Li 2 Ge 7 O 15

Abstract: The dielectric, ferroelectric, DTA, thermal expansion, Raman scattering and ultrasonic measurements of Li 2 Ge 7 O 15 single crystal have been performed in a wide temperature range including the phase transition point at T c =283.5 K. It has turned out that Li 2 Ge 7 O 15 undergoes a ferroelectric phase transition of displacive-type and the transition is quite or almost continuous. The Raman spectra obtained support the idea that the phase transition is associated with a soft optic phonon at the Brillouin zone center of the space group Pbcn in the paraelectric phase.

Observation of a new surface state on Cu(001)

Abstract: High-resolution angle-resolved photoemission studies of the Cu(001) surface demonstrate the existence of a surface state which has not previously been reported. The state is located in a relative bulk band gap near the Fermi energy at the $\overline{X}$ point of the two-dimensional Brillouin zone. Its energy position and dispersion are in excellent agreement with recent calculation for this surface. Comparisons are made of this state's natural energy width and dispersion with similar states on other copper surfaces.

Self-consistent electronic structure of 6- and 18-layer Cu(111) films

Abstract: With the use of the self-consistent linear combination of Gaussian orbitals method, the energy bands of 6- and 18-layer Cu(111) films are calculated and compared with earlier calculations of 7- and 19-layer Cu(001) films. A large number of surface-state and surface-resonance bands are found, including one pushed out of the top of the $d$ bands throughout the two-dimensional Brillouin zone. A comparison is made of the actual surface excess electronic charge with that obtained from a projected density of states, and the meaning of the discrepancy is discussed.

High-resolution angle-resolved photoemission study of the Cu(011) surface state

Abstract: Recent high-resolution angle-resolved photoemission studies have shown that experimental peak widths can be governed by parallel momentum broadening in the photoemission process. An accurate characterization of this broadening is important from both a fundamental and a practical point of view. This paper presents results for the surface state on Cu(011) located at the $\overline{Y}$ point of the surface Brillouin zone which provide further insight into the source of the broadening. The observed broadening in this system of 0.015 ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ is half that previously observed on Cu(111) and provides evidence that the source of the broadening is defects or impurities at the surface.

Thermal conductivity of minerals at high pressure: The effect of phase transitions

Abstract: Theory predicts and measurements confirm that anharmonic properties such as the lattice thermal resistivity, the Gruneisen parameter, and the coefficient of thermal expansion generally decrease as a function of increasing density upon compression of solids. The Debye-Gruneisen continuum model further predicts a discontinuous decrease of anharmonic properties during a phase transition with a density increase, in contradiction with available experimental data on alkali halides. We present results calculated from a model based on interatomic potentials. This model correctly predicts an increase in anharmonic properties for simple compounds transforming from a six- to an eight-coordinated structure. These results stress the importance of interatomic spacing as well as density in determining changes in thermodynamic properties due to polymorphism. The change in crystal structure across a phase transition also affects the thermal conductivity via Brillouin zone summations over the interacting phonon modes. We have used in the calculations either the bulk sound speed, or the Debye average velocity calculated from the longitudinal and transverse velocities (in both cases, theoretically derived from the interatomic potentials). We have found that the pressure dependence of thermal conductivity determined from the bulk sound speed agrees much better with experimental data for each phase than that determined from the average velocity. Apparently, shear modes contribute less to the change of thermal conductivity with compression than has been thought.

Experimental band structure of cadmium sulfide

Abstract: We have investigated the bulk electronic structure of wurtzite CdS using angle-resolved photoelectron spectroscopy with synchrotron radiation. We find that direct transitions largely determine the shape of the experimental spectra. Information from all high-symmetry points in the Brillouin zone is available from normal- and off-normal-emission spectra with the aid of polarization selection rules. A comparison with our experimentally determined critical-point energies shows that existing theoretical band-structure calculations for wurtzite CdS are qualitatively correct, but underestimate the extent of the band dispersion. For example, we observe an upper-valence-band width of 4.5 eV, which is significantly larger than the predicted values of 2.7---3.3 eV. Our spectra also reveal fine structure in the Cd $4d$ core-level spectra. This suggests that the Cd $4d$ electrons are involved in the chemical bonding.

A brillouin-zone model for compositional variation in tetrahedrite

Abstract: A Brillouin-zone analysis based on a nearly-free electron model for tetrahedrite, an important copper antimony sulfide, successfully explains the observed compositional limits for synthetic and natural tetrahedrites. Tetrahedrite should occur with greater than 2M and up to 208 valence electrons per unit cell (filling the 52nd Brillouin zone); it should be most stable with 208 valence electrons. The classical formula CurzSblSlr is not expected to occur. This model predicts that filling a zone (e .g ., by substituting Fe or Zn for Cu) should cause electrical resistivity to increase. This is confirmed by experimental results which show that a tetrahedrite with about 208 valence electrons per unit cell (approximate composition Curo(Fe,Zn)z(Sb,As)aSs) has a resistivity 107 times higher than that of a tetrahedrite with approximately 205 valence electrons (composition Cutz rz Sba.6eS13). The Brillouin-zone model also agrees with observed limits to tetrahedrite composition: natural tetrahedrite samples are stoichiometric with compositions restricted to two divalent cations per formula unit, while synthetic samples, which are not stoichiometric, have compositions bounded by the line

Light Scattering from Parallel-Pump Instabilities in Yttrium Iron Garnet

Abstract: Brillouin light scattering has been observed from parametrically excited magnons by parallel pumping in a 4-\ensuremath{\mu}m yttrium-iron-garnet film at 9.4 GHz. Scattering from the spin waves could be observed continuously from the thermal level through the nonlinear region of parametrically excited magnons. Magnons with small wave vectors propagating perpendicular to the static field are seen to have the lowest critical field as predicted theoretically. The spectra of these parametric excitations show a pronounced structure.

Ion-trapping saturation of the Brillouin instability

Abstract: The ion acoustic wave and harmonics driven by stimulated Brillouin scattering are probed by space- and time-resolved ruby-laser Thomson scattering. Corresponding to the 6% backscatter observed, the ion wave is seen to saturate at (5--10)% amplitude, a level quantitatively predictable from the nonlinear frequency shift caused by ion trapping.

Calculation of the magnetic states of cobalt overlayers on copper (111)

Abstract: One- and two-atom layers of cobalt on a copper (111) surface were found to be magnetic with a spin polarization close to the bulk value. The calculation was performed in a tight-binding scheme, with single-site, full orbital interactions treated self-consistently. Antiferromagnetic and ferrimagnetic states with a two-atom periodicity were examined. A new type of ''spatially modulated'' state was found. The density of states and the spatial distribution of magnetization were obtained for each configuration. The ferromagnetic state was found to have the lowest total energy; the energy of the spatially modulated state was, however, calculated to be only 0.03 Ry per surface atom higher. Agreement with photoemission experiments is satisfactory: It is excellent for a one-atom layer of Co on Cu (111), but a theoretically predicted shift in peak location with Co layer thickness is not found experimentally. Calculations for both pure Cu (111) and Co on Cu (111) show that the spectral features observed at the corner of the surface Brillouin zone arise from the totally symmetric electronic states.

Angle-resolved photoelectron spectroscopy investigation of intrinsic surface states on the Ge(001)-(2 × 1) reconstructed surface

Abstract: Synchrotron-radiation-excited angle-resolved photoelectron spectra of the Ge(001)-(2 x 1) reconstructed surface reveal two surface states 0.6 and 1.3 eV below the bulk valence-band maximum at the GAMMA point of the surface Brillouin zone. These two states are similar to those observed previously for Si(001) and GaAs(001) surfaces. The dispersion of the Ge bands with k/sub parallel/ is qualitatively in agreement with the calculations of Chadi using his asymmetric dimer model for Si(001)-(2 x 1).

Band structure of TlGaSe2

Abstract: A model of the TlGaSe2-I band structure of the monoclinic modification is proposed. The monoclinic modification of TlGaSe2-I is considered as a deformed tetragonal one. The band structure of the metastable tetragonal modification of TlGaSe2-II is calculated by the pseudopotential method. The irreducible representations of the D184h group (TlGaSe2-II) are expanded in irreducible representations of the C4s group (TlGaSe2-I). It is found that the top of the valence band is located at the point Y (0,2π/bm, 0) of the TlGaSe2-I Brillouin zone and is formed from band states N2, N4 of the tetragonal modification. The bottom of the conduction band is located at the point Γ of the TlGaSe4-I Brillouin zone and is formed from T4 states. An additional extremum of the valence and conduction bands is located at the points Γ(A2) and Y(N6, N8), respectively. An interpretation of the absorption spectra of TlGaSe2-I near the fundamental edge is proposed. [Russion Text Ignored]

Wave vector-dependent spin susceptibility of iron above the Curie temperature

Abstract: Microscopic calculations are given of the wavevector- and temperature-dependent spin susceptibility, chi (q), of itinerant-electron magnets by generalising the approach initiated by Hubbard and Hasegawa (1979-1983). The expressions for chi (q) in the limit of q=0 and q=Q (the antiferromagnetic wavevector) are shown to reduce to the results obtained previously by the present author. Detailed calculations of chi (q) of paramagnetic iron are made using the density of states generated by the recursion method. The amplitude of local moments evaluated by summing chi (q) over the BCC Brillouin zone using the classical fluctuation-dissipation theorem is nearly in agreement with effective moments deduced from the susceptibility chi (0). The equal-time and spatial spin-spin correlation functions are also calculated, and discussed with reference to recent neutron diffraction experiments.

Structural phase transition in crystals with Fm3m symmetry

Abstract: A systematic study of the possible phase symmetries derived from a prototype phase with the space group Fm3m (Oh5) has been performed. These structural phase transitions involve the onset of an order parameter transforming according to one irreducible representation of the prototype space group. The investigation is performed on the basis of the Landau theory for continuous transitions. Accordingly, the irreducible representations of Fm3m are examined at the Gamma ,X,L and W high-symmetry points of the cubic face-centered Brillouin zone. The order parameters relevant to all the arms of a given star are considered. The results are summarised in several tables. These results are discussed and compared with the available experimental data relative to Fm3m subgroups.

Hartree‐fock exchange and LCAO approximation in the band structure calculations of solids

Abstract: It is shown that the use of the simple cubature formula for the approximate calculation of the density matrix Qrr in the non-local Hartree-Fock exchange for crystals leads to a non-physical divergence of the lattice sums. To overcome this difficulty it is proposed to introduce a weight function in the cubature formula for the numerical integration over the Brillouin zone in calculating non-local exchange. It is discussed the simple way to choose the nodes of the numerical integration which is based on the large unit cell transformation in the direct and reciprocal lattices. This choice allows to extend the special point technique of the Brillouin zone integration to the non-local exchange calculation. [Russsian Text Ignored.]