Showing papers on "Brillouin zone published in 1971"
TL;DR: In this paper, a three-axis crystal spectrometer was used to measure phonon dispersion in Ge at 80.5 K for all principal symmetry directions and on some lines at the boundary of the Brillouin zone.
Abstract: Phonon dispersion relations in Ge have been measured at 80 \ifmmode^\circ\else\textdegree\fi{}K for all principal symmetry directions and on some lines at the boundary of the Brillouin zone. The measurements were performed by neutron inelastic scattering using a three-axis crystal spectrometer. In order to achieve maximum accuracy, care was taken to reduce resolution widths as far as possible. In general, the estimated uncertainties of the measured phonon frequencies range from 0.3% to 0.5% for optical and from 0.3% to 1% for acoustic phonons. Frequencies of 238 phonons are tabulated and phonon linewidths are given for the symmetry directions.
197 citations
TL;DR: In this paper, a general formulation for studies of the vibrational properties of systems which have two-dimensional periodicity and one or two surfaces is given, which is applicable to reconstructed surfaces, surfaces with adsorbed impurity particles, etc., as well as unreconstructed clean surfaces, provided that the 2D periodicity is preserved.
Abstract: A general formulation is given for studies of the vibrational properties of systems which have two-dimensional periodicity and one or two surfaces. Although layered structures and other systems with interfaces fall within the scope of this formulation, the principal motivation is to provide a framework for calculating and interpreting vibrational surface properties. No assumption is made concerning crystal structure, surface orientation, the interaction between particles, or the number of particles per unit cell. Also, the treatment is applicable to reconstructed surfaces, surfaces with adsorbed impurity particles, etc., as well as unreconstructed clean surfaces, provided that the two-dimensional periodicity is preserved. A discussion is given of the properties of the vibrational modes: In general, the displacement ellipse for a given mode can have any orientation. For surfaces with "axial-inversion symmetry," however, one axis of the ellipse is always normal to the surface. If the surface has "complete reflection symmetry" with respect to a given plane, then for any two-dimensional wave vector parallel to the plane the modes will separate into two classes: one-third of the modes will be pure shear-horizontal (SH) modes, and the other two-thirds will be polarized strictly in the sagittal plane. It is possible for surface modes of one class to lie within the bulk subbands of the other class. If the crystal has either axial-inversion symmetry or a three-dimensional center of inversion, then the complex dynamical matrix can be reduced to a real, symmetric matrix of the same size. If both symmetries are present, as is the case for many surfaces of interest, then a further reduction is possible. Finally, notations are suggested for distinguishing two-dimensional vectors and for labeling symmetry points in the two-dimensional Brillouin zone associated with a surface.
178 citations
TL;DR: In this paper, a set of wavefunctions which are singly excited with respect to a given multiconfiguration wave function in the sense of the generalized Brillouin theorem are formed and the extended CI problem is solved by variation or perturbation methods.
120 citations
TL;DR: In this paper, the energy-momentum relation has been qualitatively studied below the one-phonon continuum, and the following new features have been found in the strong coupling region; (1) complete splitoff of the lowest branch in the whole Brillouin zone, and (2) split-off of second discrete branch.
Abstract: Optical properties of interacting exciton-phonon system have been theoretically studied in terms of a simple model consisting of Frenkel excitons and Einstein oscillators. The problem is characterized by two non-dimensional parameters B and S representing the exciton band width and the interaction energy, respectively. Approximate solutions have been obtained through the diagonalization of the Hamiltonian in special sub-spaces, and they reasonably describe the behavior of the system for all values of B and S . Absorption and emission spectra and the effective mass of the composite particle vary from free exciton type to self-trapped exciton type as we go from B > S to B < S . The energy-momentum relation has been qualitatively studied below the one-phonon continuum, and the following new features have been found in the strong coupling region; (1) complete split-off of the lowest branch in the whole Brillouin zone, and (2) the split-off of the second discrete branch. Furthermore, a clue to the mechanism of...
98 citations
89 citations
TL;DR: In this paper, a simple molecular I2 vapor filter is described which can attenuate the unshifted scattered light in Brillouin and Raman scattering by greater than 108 with a background attenuation of less than 10.
Abstract: A simple molecular I2 vapor filter is described which can attenuate the unshifted scattered light in Brillouin and Raman scattering by greater than 108 with a background attenuation of less than 10, i.e., a discrimination ratio of > 107 : 1.
80 citations
TL;DR: In this paper, the magnetoresistance, Hall effect, thermopower, thermal resistivity, and Nernst-Ettings-hausen effects are measured in magnetic fields to 10.3 T (103 kG) and at temperatures between 1.1 and 4.2 K. The major results are that majority-carrier electrons and holes are assigned to specific locations in the Brillouin zone; the electrons assigned to be around the center of the zone edge (point $K$).
Abstract: The magnetoresistance, Hall effect, thermopower, thermal resistivity, and Nernst-Ettings-hausen effects are measured in magnetic fields to 10.3 T (103 kG) and at temperatures between 1.1 and 4.2 K. Samples are highly ordered pressure-annealed pyrolytic graphite. The major results are that majority-carrier electrons and holes are assigned to specific locations in the Brillouin zone; the electrons are assigned to be around the center of the zone edge (point $K$). The first observation of spin-split Landau levels is made. A study of distorted line shapes of thermopower quantum oscillations shows agreement with a theory by Horton. Sugihara and Ono's theory, predicting field values for Landau level crossings of the Fermi energy in graphite, is confirmed for fields below 4 T.
47 citations
TL;DR: In this paper, the lattice vibrations of a layer compound having the MoS2 structure were derived using the Born-von Karman model in the nearest-neighbours approximation for single layers.
Abstract: The lattice vibrations of a layer compound having the MoS2 structure are derived using the Born-von Karman model in the nearest-neighbours approximation for single layers. The analysis produces a s...
42 citations
TL;DR: In this paper, a formalism is developed for calculating the normal modes of vibration of an ionic-crystal slab having the NaCl structure, which consists of a finite number of (100) planes oriented normal to the $z$ axis and is of infinite extent in the $x$ and $y$ directions.
Abstract: A formalism is developed for calculating the normal modes of vibration of an ionic-crystal slab having the NaCl structure. The slab consists of a finite number of (100) planes oriented normal to the $z$ axis and is of infinite extent in the $x$ and $y$ directions. The derivation of the dynamical matrix takes into account the free surfaces of the slab as well as the effect of retardation of the Coulomb interaction. Retardation is easily excluded from the theory by letting the speed of light $c$ become infinite in the Coulomb contributions to the dynamical matrix. The unretarded normal-mode frequencies and eigenvectors are calculated for a seven-layer slab for values of the wave vector chosen along the $x$ axis and ranging from zero out to the boundary of the two-dimensional first Brillouin zone. The properties of the optical surface modes are discussed in detail. If an electromagnetic wave is incident upon the slab, the optical properties of the slab can be found by calculating the total electric field which exists in the regions of space on either side of the slab as a superposition of the incident field and the induced field arising from the ionic motion within the slab. For both $P$ and $S$ polarizations of the incident field, peaks in the infrared absorption are found to occur at frequencies corresponding to certain optical modes of the slab. The calculated results offer a qualitative explanation of the transmittance of a thin LiF film as experimentally observed by Berreman.
42 citations
TL;DR: In this paper, the lattice dynamics of solid CO2 have been treated throughout the Brillouin zone and the molecular librational degrees of freedom has been treated by the use of Eulerian displacement coordinates.
Abstract: The lattice dynamics of solid CO2 has been treated throughout the Brillouin zone. The molecular librational degrees of freedom have been treated by the use of Eulerian displacement coordinates. The potential model assumes the molecule represented by two centers of interaction (diatomic model) and each molecular pair interaction term is written as a sum of 6–12 terms between interaction centers on different molecules. The three parameters of the potential are obtained by fitting to the five optic modes, from the crystal energy, and by invoking the condition of zero uniform stress. It is found that the interaction between translational and librational degrees of freedom is large inside the Brillouin zone. The low temperature specific heat was calculated and found to agree well with experimental data. In an appendix, the applicability of the classical harmonic oscillator treatment to small molecular solids is discussed, and it is concluded that this approach is justified for solid CO2.
TL;DR: In this article, the authors studied the uniform motion of a screw dislocation in a simple cubic lattice in which atoms interact piecewise harmonically with nearest neighbours, and the stress σ required for keeping the motion with velocity v is given exactly.
Abstract: Uniform motion of a screw dislocation is studied in a simple cubic lattice in which atoms interact piecewise harmonically with nearest neighbours. The stress σ required for keeping the motion with velocity v is given exactly. The dislocation excites lattice waves with k given by ω( k )= v · k , where ω( k ) is the dispersion relation of waves and k is not restricted within the first Brillouin zone. In contrast to continuum approximation, there is no singularity at v = c ; c is the sound velocity. At low velocities (\(v{\lesssim}c/3\)), σ( v ) has many singular points reflecting the van Hove singularities.
TL;DR: In this article, a detailed analysis of the generalized susceptibility function for paramagnetic chromium was made to investigate the effects of including realistic band-structure effects on both the unenhanced susceptibility and on the exchange enhancement.
Abstract: A detailed computation has been made of the generalized susceptibility function for paramagnetic chromium to investigate the effects of including realistic band-structure effects on both the unenhanced susceptibility and on the exchange enhancement. An augmented-plane-wave band-structure calculation for paramagnetic chromium has been performed to obtain energy bands and wave functions for the first six bands on a mesh of 1024 points in the Brillouin zone. An interpolation scheme was used to increase the effective mesh to 128 000 points in the zone and the unenhanced susceptibility function was calculated from these, both with and without the matrix elements. The matrix elements were seen to make a dramatic difference in the susceptibility, and, in fact, reduce the peak due to the "nesting" of the Fermi surface so that it is not an actual maximum of ${\ensuremath{\lambda}}^{(0)}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$. The exchange enhancement was then investigated by approximately solving the coupled self-consistent equations for the Fourier components of the response to an applied field including local-field corrections. This yields an exchange-enhanced susceptibility function which has the tendency to first become infinite at the nesting wave vector, indicating that the local-field corrections may play an important role in determining the wave vector for instability against formation of a spin-density wave. It is also shown that the exchange-enhanced susceptibility thus obtained displays quasilocalized spin behavior of the electron response to an applied oscillatory field.
TL;DR: In this paper, the Brillouin spectra of liquid CCl4 (at 20.0°C) have been investigated 20 scattering angles, from 40° to 145°.
Abstract: Brillouin spectra of liquid CCl4 (at 20.0°C) have been investigated 20 scattering angles, from 40° to 145°. The spectra were excited by 6328‐A radiation from a He‐Ne laser and analyzed with a pressure‐scanned Fabry‐Perot spectrometer. The measured frequency shifts and linewidths of the Brillouin component were used to determine velocities and attenuations of thermal waves in the frequency range 1.6–4.7 Gc/sec. A large dispersion (>10%) and corresponding change in attenuation were found, characteristic of a thermal relaxation process in this region. A broad new component in the spectrum of isotropic scattering was observed, which is also characteristic of a relaxation process. Analyses of these data were carried out in two ways: one is based on a simple extension of acoustic equations to light scattering, and the other, on Mountain's theory of light scattering in the region of a thermal relaxation. It is shown that the observed spectra and derived data agree with Mountain's theory in all respects. Also, fr...
TL;DR: In this article, a simple pseudopotential scheme is presented for calculating the effects of strain on the energy-band structure of diamond and zinc-blende structure crystals, including spin-orbit coupling, and good numerical agreement with experimentally determined deformation potential constants for silicon and germanium.
TL;DR: In this paper, the energy eigenvalues and wave functions for an equivalent of 256 k -points in the first Brillouin zone were calculated using the full Slater exchange potential.
TL;DR: In this paper, the temperature dependence of the frequency spectrum of a model NaCl-structure paraelectric exhibiting soft-mode behavior at the zone center is treated self-consistently.
Abstract: The temperature dependence of the frequency spectrum of a model NaCl-structure paraelectric exhibiting soft-mode behavior at the zone center is treated self-consistently. A variational formulation is employed, yielding a set of nonlinear integral equations which are solved iteratively. The difficulties associated with perturbative treatments are avoided by starting from a renormalized phonon basis which represents a stable state of equilibrium for the crystal. In particular, the soft-mode branches, which may be imaginary in the harmonic approximation, are renormalized and treated self-consistently. The model consists of rigid anions and cations of unequal masses interacting via long-range Coulomb forces plus a short-range interaction extending to second neighbors. Anharmonicity is introduced through a parametrized quartic interaction. Calculations are carried out for a wide range of model parameters, including the situation where the phase space subtended by the imaginary harmonic frequencies may constitute a large fraction of the Brillouin zone. The importance of including the effect of the soft-mode branches is discussed in detail. It is pointed out that the self-consistent equations do not admit a zero solution for the soft-zone-center optic mode. An explanation is given of why the Curie-law dependence of the soft-zone-center frequency squared may extend to lower temperatures than one might expect on simple qualitative grounds. Attention is given to the coupling of the soft TO branch to the TA branch of the same symmetry, and the anomalous temperature dependence of the acoustic branch at finite wave vector is displayed. Finally, the temperature dependence of the intersublattice correlation function is calculated, and it is pointed out that the soft-mode branches contribute significantly to the temperature dependence of this function. The implications of the latter for a transition to an ordered phase are discussed.
TL;DR: In this paper, the frequency of the de Haas-van Alphen type is measured over a wide range of angles between the magnetic field and the c axis of the Brillouin zone.
Abstract: Quantum oscillations as a function of magnetic field in the Hall effect and thermoelectric power are studied in two samples of pressure-annealed pyrolytic graphite. Only the oscillations originating from minority-Fermi-surface carriers are discussed. Frequencies of the de Haas-van Alphen type are measured over a wide range of angles between the magnetic field and the c axis of the Brillouin zone. Results are given graphically and analyzed.
TL;DR: In this article, the anisotropic spectra of edge absorption, photoconductivity, emission, and reflectivity of the tetragonal ZnP2 and CdP2 crystals have been experimentally investigated in the range 1 to 12.5 eV.
Abstract: The anisotropic spectra of edge absorption, photoconductivity, emission, and reflectivity of the tetragonal ZnP2 and CdP2 crystals have been experimentally investigated in the range 1 to 12.5 eV. The selection rules for interband transitions, the points of zero slope, and the dispersion relations at general points of the Brillouin zone have been derived by group-theoretical methods. From an analysis of the experimental and theoretical data conceivable energy band models of the tetragonal ZnP2 and CdP2 crystals are proposed.
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TL;DR: In this paper, the electronic energy band structure of the tetragonal crystallographic modification of germanium dioxide (GeO 2 ) has been calculated by the APW method.
TL;DR: In this article, the inelastic scattering of light by interband electronic transitions (interband electronic Raman scattering) in semiconductors and semimetals is examined, and the form and magnitude of the Raman efficiency associated with interband transitions near the $\ensuremath{Gamma}$ point of the Brillouin zone in materials with the gray-tin band structure in zero magnetic field.
Abstract: In this paper we examine the inelastic scattering of light by interband electronic transitions (interband electronic Raman scattering) in semiconductors and semimetals. A number of general features of the scattering process and the resulting Raman spectrum are examined. We also present detailed calculations of the form and magnitude of the Raman efficiency associated with interband transitions near the $\ensuremath{\Gamma}$ point of the Brillouin zone in materials with the gray-tin band structure in zero magnetic field.
TL;DR: In this article, the interband transitions of evaporated films of the noble metals copper, gold, and silver have been studied in reflectivity in the energy region 2.0 − 5.0 eV as a function of temperature, using wavelength modulation.
TL;DR: The electronic band structure of cubic silicon carbide (3C SiC) has been calculated using the non-local empirical pseudopotential method using the available experimental data as discussed by the authors, and the mysterious 42 eV absorption edge observed by Choyke and Patrick is identified with the Γ15v − L1c transition in the Brillouin zone.
TL;DR: In this article, the electroreflectance spectra of CdSnP2 chalcopyrite single crystals have been investigated in the spectral region 1.0 to 4.7 eV at room temperature using polarized light.
Abstract: The electroreflectance spectra of CdSnP2 chalcopyrite single crystals have been investigated in the spectral region 1.0 to 4.7 eV at room temperature using polarized light. The electroreflectance structure in the region of the fundamental absorption edge and its polarization dependence are found to be in good agreement with the relative location of the valence bands earlier predicted theoretically. A great number of electroreflectance peaks has been observed in the spectral region 2.4 to 4.7 eV and interpreted by optical transitions at the T, T, and N points of the Brillouin zone of the chalcopyrite lattice. The only transitions used were direct ones and responsible for the main structure in the optical spectra of sphalerite crystals. In addition, the fine structure of these optical transitions due to crystal field splitting has been included.
Russian text Ignored.
TL;DR: In this article, low-temperature measurements of the specific heat were reported for Ce 1−x La x Al 3 and Y 1 −x Th x Al3, where the observed maxima were attributed to crystalline field effects.
TL;DR: In this paper, the results of a nonspin polarized band calculation of the compound FeGe in its hexagonal phase B-35 are presented and the energy bands were obtained via the APW method and the energies were evaluated at 100 points in the first Brillouin zone.
Abstract: The results of a nonspin polarized band calculation of the compound FeGe in its hexagonal phase B-35 are presented. The energy bands were obtained via the APW method and the energies were evaluated at 100 points in the first Brillouin zone. Slater's free-electron approximation for the exchange operator was used. The density of states histogram was constructed for a grid in the energies of 0.03 Ryd.
TL;DR: In this article, De Haas-van Alphen oscillations in vanadium single crystals using large impulsive fields were investigated in terms of distorted ellipsoids located at the symmetry points N in the Brillouin zone.
TL;DR: In this article, the usual formalism of second quantization is generalized to include the case in which liquid helium contains atoms in electronic excited states, where the dipolar coupling between excited and normal atoms is included as perturbation.
Abstract: The usual formalism of second quantization is generalized to include the case in which liquid helium contains atoms in electronic excited states. The formalism is applied to sccatter ing of the photon, where the dipolar coupling between excited and normal atoms is included as perturbation. The resulting cross sections for Brillouin and Raman scattering agree with those obtained by the semi-phenomenological theory of Stephen. The relation with the recent theory of Iwamoto is also discussed in terms of Green functions.