Point Of Brillouin Zone Research Articles

Transport study on pressure-induced band overlapped metallization of layered semiconductor black phosphorus

Hall effect experiments of a single crystal black phosphorus (black P) under pressure have been carried out to study a pressure-induced band overlapped metallization at about 1.5 GPa. The Hall coefficient ( R H ) at 300 K showed a logarithmic decrease with increasing pressure and reached about 1 cm 3 C −1 at 1.5 GPa. This value was comparable to those of typical semimetals. The pressure coefficient of the energy gap was estimated to be −0.21 eV/GPa and in good agreement with the value of the theoretical prediction. Further decrease in R H observed above 1.5 GPa was ascribed to the precursor of the p- n conversion of carriers. The pressure dependence of R H at 77 K exhibited the p- n conversion at 1.8 GPa. The conversion has suggested a change on the bottom of the conduction and the top of valence bands near the Z point in Brillouin zone.

First-Principles Determination of the Soft Mode in CubicZrO2

A direct approach to calculate the phonon dispersion using an ab initio force constant method is introduced. The phonon dispersion and structural instability of cubic ${\mathrm{ZrO}}_{2}$ are found using a supercell method in the local-density approximation. The force constants are determined from the Hellmann-Feynman forces induced by the displacement of an atom in the $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ fcc supercell. This size of the supercell gives ``exact'' phonon frequencies at $\ensuremath{\gamma},X,L,W$ Brillouin zone points. The phonon dispersion curves show a pronounced soft mode at the $X$ point, in agreement with the experimentally observed cubic to tetragonal phase transition.

Giant Faraday rotation in diluted magnetic semiconductor Cd 1−χFe χTe χ

The Faraday rotation as a function of photon energy and composition for Cd 1− x Fe x Te with x=0.01, 0.03, 0.06 in temperature range 70 K to 300 K has been measured. The samples exhibit giant Faraday rotation characteristic of diluted magnetic semiconductors as in Cd 1− x Mn x Te. Exciton energy at Γ and band gap energy at L points of Brillouin zone for different composition have been obtained for the first time in terms of the multioscillator model.

Quasiparticle band structures of short-period superlattices and ordered alloys of AlN and GaN.

Quasiparticle band structures of short-period superlattices and ordered alloys of AlN and GaN are calculated using the GW approximation. The calculated gaps range from 3.1 eV to 5.8 eV. Two types of structural materials are studied: zinc-blende superlattices in the (111) direction and hexagonal wurtzite superlattices and ordered alloys in the (001) direction. Comparisons between band structures of these materials using folding of Brillouin zone points and the transition from an indirect to direct gap semiconductor in the zinc-blende compounds are discussed. All of the wurtzite structures studied are found to have direct band gaps with values between 3.5 and 5.8 eV. The 1\ifmmode\times\else\texttimes\fi{}1 and 1\ifmmode\times\else\texttimes\fi{}2 AlN/GaN zinc-blende superlattices have direct gaps of 4.4 eV and 4.3 eV, respectively, whereas the 2\ifmmode\times\else\texttimes\fi{}1 AlN/GaN superlattice gap is 4.6 eV and is indirect. Several fundamental gaps are predicted and remain to be tested by experiment.

Nonlinear Spectroscopy of Deep Levels in Ferroelectric SbSI Crystals

Local lattice defects in SbSI crystals and the optical transitions associated with defects, which drastically change under ferroelectric phase transformation, are investigated by means of the spectroscopy of photo-induced absorption (PIA). The thermal changes in the spectra are caused by the replacement of the predominating type of optical modulation of deep level occupation: by direct optical ionization of the center or by capture of non-equilibrium free carriers generated by two-photon absorption of laser radiation. The results are explained by considerable modifications in the band structure under phase transition. It is accompanied by the replacement of impurity absorption from one point of Brillouin zone to the other, thus reflecting a splitting of the valence band. These processes are confirmed by the band-structure calculations for SbSI.

Infrared absorption in 76Ge and natural Ge crystals: Effects of isotopic disorder on q

Self-energy effects (frequency shifts and line broadenings) due to isotopic disorder on the off-zone-center (q\ensuremath{\ne}0) phonon spectra in natural Ge have been investigated by comparing infrared transmission spectra of an isotopically enriched germanium crystal (86% $^{76}\mathrm{Ge}$) and a natural Ge crystal at temperatures of 25, 100, and 300 K. Because selection rules only allow for the observation of two-phonon (and higher-order) absorption in Ge, q\ensuremath{\ne}0 phonons at Brillouin-zone points with high two-phonon density of states were investigated. Besides the trivial dependence of the phonon energies on the average isotopic mass m\ifmmode\bar\else\textasciimacron\fi{} (proportional to m${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}^{\mathrm{\ensuremath{-}}1/2}$), isotopic disorder leads to additional Ienergy shiftsR and Iline broadeningsR in natural Ge. The observed self-energy effects depend strongly on the phonon energy and are only significant for the transverse optical vibrations at the zone boundary (L, K, W, and X critical points), in agreement with coherent-potential-approximation calculations.

Calculation of Dielectric Constants for Semiconductors-an Application of Ab Initio Pseudopotential Method

We have used ab initio pseudopotential method to generate basis wavefunctions and eigen energies to carry out first principle calculations of the static macroscopic dielectric constant for GaAs and GaP. The resulted converged random phase approximation (RPA) value is 12.55 and 10.71, in excellent agreement to the experimental value of 12.4 and 10.86, respectively. The inclusion of the exchange correlation contribution makes the calculated result slightly worsen. A convergence test with respect to the number of k points in Brillouin zone (BZ) integration was carried out. Sixty irreducible BZ k points were used to achieve the converged results. Integration with only 10 special k points increased the RPA value by 15%.

Interaction of Excitons Bound to 3d Transition Metal Ions with Lattice Vibrations in II-VI Semiconductors

A large body of experimental information on the interaction of lattice vibration with donor and acceptor excitons (DE and ΑE) bound to isoeIectronic impurities has recently been accumulated. This interaction is very strong. Apart from this, the observed peak position often does not correspond to the phonons from the centre of the Brillouin zone [1]. The analysis of experimental results is based on the fact that DE and ΑE substantially distort ionic oscillations near the impurity, owing to strong localization of the carrier captured by a non-Coulomb potential. This results in a phonon spectum exhibiting normal modes of a cluster that consists of an impurity and some lattice ions surrounding it [2]. Excitons localized on an impurity interact with normal oscillations of a given claster. When an impurity is introduced into the lattice, the motion of the ions that surround the impurity acquires the point symmetry of the impurity site, e.g. Td for crystals with zincblende stucture. Combinations of atomic displacements near the impurity (normal modes) are described by irreducible representations Α1 (breathing mode), E and 2Τ2 of Td group. These are expressed in terms of irreducible representations of phonons of a perfect crystal. The contribution to normal modes originates from phonons from different Brillouin zone points, and the total number of phonons, that is, the projected density of phonon states, is calculated by a computer. Results of such computations for normal modes A1(ZnS), E and Τ2 (in ZnS, ZnSe, ZnTe) are given in [2]. When the difference in force constants and/or ion masses is large, local or quasilocal lattice vibrations may appear.

Flexural Waves in a Periodic Beam

The flexural wave propagation in the periodic beam can be interpreted as the superposition of two pairs of waves propagating in opposite directions. One of them forms an attenuated standing wave. The dispersion spectrum of the other pair of waves shows the band structure, consisting of stopping and passing bands. For the symmetry structure, the dispersion equation at the end points of Brillouin zone is uncoupled into two equations. Each of them corresponds to a standing wave which is either symmetric or antisymmetric about the midplane of the layers.

Surface electronic structure of metals

The surface electronic structure calculations of Sr(001), Cd(0001), In(001), Ba(001), Pb(001), and Hf(001) are performed using the self-consistent pseudopotential method. It is shown that there is a developed system of unoccupied surface states at Sr, Ba, Pb, and Hf surfaces. For Sr an occupied surface state is found at the X̄ point of the two-dimensional Brillouin zone. In the energy gap at \\ ̄ gG the surface state is located above the Fermi level. In the case of Cd the surface state is not observed in the gap at \\ ̄ gG. The 5% contraction of the top interlayer spacing does not change the result. For the Cd(0001) surface with the ideal casec a axial ratio the calculation of the electronic structure showed that in such a hypothetical lattice there exists a surface state in the energy gap at \\ ̄ gG. The electronic structure of the In(001) surface is similar, in many respects, to the band structure of the Al(001) surface. On the Ba(001) surface the occupied surface state is found only at the X̄ point. On the Pb(001) surface occupied surface states are observed at X̄ and M̄. Like a Cd surface there is no surface state in the energy gap at the \\ ̄ gG point of the Brillouin zone of Pb(001). The electronic states of the Hf(001) surface can be obtained by means of energy shifts from the electronic states of the Ba(001) surface.

Brillouin zone treatment in total energy calculations of Peierls distorted chains

Most band structure calculations approximate the integral over the Brillouin zone of momentum (i.e., wave vector) dependent properties with an appropriately weighted sum over a discrete set of points in the Brillouin zone. The best choice for such a set of points has long been a point of discussion in crystalline band structure calculations. For one-dimensionally periodic systems, however, the usual choice of points has been evenly spaced points in the one-dimensional Brillouin zone with equal weights. We have analyzed the exact error for the integral over the π band of a tight-binding model of trans-polyacetylene as a function of bond alternation. We find that the error in π band energy decreases in magnitude as q−2, where q is the total number of points treated in the Brillouin zone, for the metallic polyacetylene system with equal bond lengths. As bond alternation increases, however, we find that the error in π band energy decreases in magnitude roughly exponentially as a function of bond alternation for any given value of q. We find that this systematic change in error as a function of bond alternation can lead to either apparent overestimation or underestimation of the equilibrium dimerization and stabilization energy of Peierls distorted systems using first-principles total energy calculations.

Angle-resolved x-ray photoemission from the valence bands of tungsten with high angular resolution and temperature variation.

Angle-resolved valence photoemission spectra have been obtained for W(011) and W(001) using Al K\ensuremath{\alpha} and Mg K\ensuremath{\alpha} excitation and with both normal and off-normal emission directions. The angular resolution was \ensuremath{\lesssim}\ifmmode\pm\else\textpm\fi{}1.0\ifmmode^\circ\else\textdegree\fi{}, and thus the highest to date in this energy regime, and the temperature also was varied from 295 to 1000 K. These spectra exhibit features very strongly dependent on emission direction and temperature that can be more precisely associated with direct-transition emission from different Brillouin-zone points than in prior studies. Data obtained at different temperatures are used to deconvolute direct- and nondirect-transition components. The direct-transition components are found to include residual intensity due to nondirect transitions. The simple direct-transition model applied previously to the analysis of such data is also extended to include the effects of correlated lattice vibrations via a cylindrical broadening in k space. This model is found to describe semiquantitatively the effects of phonon-assisted nondirect transitions on spectra.

Solution of the ground state problem of a solid solution for interaction potentials of finite radius

A method is proposed for finding the energetically favorable superstructure of a solid solution or a magnet on a pc-, bcc- and fcc-lattice. A hierarchical classification is made of the Brillouin zone points corresponding to energetically suitable superstructures.

APW-LCAO energy bands and fundamental absorption in silver chloride crystal

The band structure of AgCl has been calculated by the augmented plane wave method in the seven high-symmetry points. While obtaining the spectral characteristics the Slater—Koster's scheme was applied for interpolation of the electron spectrum in 17,585 points of Brillouin zone. The distribution curves of complete electron density of states and its partial components have been constructed for AgCl by tetrahedron method. In order to interpret the optical absorption spectrum for AgCl the joint density of states has been calculated.

Band structure of semiconductors with cadmium thiogallate lattice

The energy band structure of a number of AIIBIIICVI semiconductors with highly symmetric Brillouin zone points Γ, T, P, N is analyzed by the method of a pseudopotential. It is established that the vertex of the valence band and the bottom of the conduction band are at the point Γ. The values obtained for the forbidden bound width are in satisfactory agreement with experimental results.

Magneto-Optical Studies of Direct Exciton State in Thallous Chloride

The magneto-optical properties of the ls exciton in TIC! associated with the direct transition at the X point in Brillouin zone are .studied theoretically and experimentally. It is found that the triplet exciton state as well as the longitudinal exciton state becomes observable in a certain configuration of the light and the magnetic field. These results are analyzed by the theory based on the exciton exchange interaction. The electron-hole intravalley exchange energies for the two exciton polarizations are obtained as 2. 7 and 1.5 me V. The effective g value of exciton parallel to the valley direction is estimated to be 3.4.

Simple group-theoretical method to determine the symmetry of soft modes in general second order phase transitions

It is shown how one can obtain, extending Birman's method, the symmetry of the soft modes in general second order phase transitions which occurs at k ≠0 points in Brillouin zone accompanying the primitive cell volume enlargement. This method is much simpler than the usual Landau method which utilizes the free energy expansion and its minimization. Gd 2(MoO 4) 3 is taken as an example. The case in which several arms of star- k contribute to the transition is also discussed using the example of C 6 4 h → C 6 2 h .

Hydrostatic Pressure Coefficients and Deformation Potentials for II–VI Compounds

AbstractCalculations of the pressure coefficients of the gaps and spin—orbit splittings at the Γ and L Brillouin zone points have been performed for cubic ZnS, ZnSe, ZnTe, and CdTe using the KKR method. Special emphasis was placed on the determination of the pressure coefficients of spin—orbit splittings. These coefficients were found to be considerably smaller than those predicted from the wave function renormalization due to the change of volume. We also calculated pressure coefficients and deformation potentials for the smallest gaps of hexagonal ZnO, ZnS, CdS, and CdSe. The results of the calculations are compared with experimental data.

Some Properties of Iron deduced from a Tight-Binding Calculation

The first constant K1 of the magnetocrystalline energy of Fe has been evaluated by introducing the spin-orbit coupling as a perturbation as compared with the effects of the crystal field and the exchange energy. The latter has been treated as an additional energy ±δ to the various levels depending on the direction of the electron spin. Previous results obtained with the tight-binding approximation are used. A histogram of K1 as a function of the energy of the levels has been constructed which shows that the levels in the lower half of the band give a negligible contribution compared to that due to the ones in the upper half. Using 284 nonequivalent points of Brillouin zone, K1 is found to be positive, in agreement with the experimental data on the directions of easy magnetization, but its value is lower than expected. The 3d electron charge distributions for the t2g and eg symmetries are given as a function of energy. They show two peaks with a minimum in the middle of the band and the eg character predominates at the top and at the bottom of the band. Both the charge and spin densities show the same kind of deviation from spherical symmetry as the ones deduced respectively by x-ray and neutron-diffraction experimental results.