Brillouin zone

About: Brillouin zone is a research topic. Over the lifetime, 13849 publications have been published within this topic receiving 383077 citations.

de Haas-van Alphen Effect and Fermi Surface of LaB6

Abstract: The de Haas-van Alphen (dHvA) effect in LaB 6 single crystal has been studied in detail using the field modulation technique. Observed dHvA frequencies in the (010) and (1\bar10) planes range from the order of 10 6 to 10 8 gauss. The angular dependence of the dHvA frequencies and the disappearance of the oscillation in some angular regions indicate that the Fermi surface of LaB 6 consists of a multiply connected surface, large pieces of which are centered at the point X (or M) in the simple cubic Brillouin zone. The electron density calculated from the Fermi surface is 1.39×10 22 cm -3 which corresponds to just one electron per unit cell.

Ab initio determination of the bulk properties of MgO

Abstract: Ab initio periodic Hartree-Fock (HF) theory was used to determine the elastic constants and selected phonon frequencies of bulk MgO; the accuracy of a posteriori correlation corrections to the periodic Hartree-Fock calculations is also discussed. Inclusion of diffuse atomic orbitals in the MgO basis was necessary to accurately describe elastic distortions and phonon vibrations of the solid. The computed HF lattice constant (4.195 \AA{}) agrees with experiment (4.19 \AA{}) and the elastic constants are within +15% of the observed values. Correlation corrections to these energetics shorten the lattice parameter to 4.09 \AA{} and further stiffen the elastic constants. The HF phonon frequencies at the (\ensuremath{\Gamma}, X, and L) points in the Brillouin zone were within 15% of experiment and the correlation corrections softened the modes improving agreement with experiment. These data will be used to parametrize electrostatic shell models of MgO.

Pseudospin and Deformation-Induced Gauge Field in Graphene

Abstract: The electronic properties of a single layer of graphite, graphene1)–4) have attracted much attention due to the “relativistic” character of π-electrons near the Fermi level. The energy band structure of graphene exhibits a linear energy dispersion relation around the two inequivalent, hexagonal corners of the first Brillouin zone in the k-space (the K and K′ points).5),6) The wavefunction (Hamiltonian) of π-electrons has two component (a 2 × 2 matrix) form due to the fact that the unit cell of graphene consists of two carbon atoms (A and B atoms). The effective-mass Hamiltonian of π-electrons around the K point or the K′ point is given by linear momentum operator, which is relevant to the linear energy dispersion relation of graphene. The effective-mass equation is similar to the massless Dirac equation or the Weyl equation.7) The original Dirac equation for an electron has the form

Elastic anomalies accompanying phase transitions in (Ca,Sr)TiO3 perovskites: Part I. Landau theory and a calibration for SrTiO3

Abstract: Landau theory has been used to develop expressions for the elastic anomalies that accompany octahedral tilting transitions in perovskites that are associated with the M and R points of the Brillouin zone. The master equation is a 246 Landau potential with saturation terms that provides phenomenological descriptions of transition sequences from a parent cubic structure through tetragonal or rhombohedral intermediates to orthorhombic or monoclinic product structures. Data from the literature have been used to determine values for all the coefficients required to generate a quantitative description of the Pm 3 m ↔ I 4/ mcm transition in SrTiO 3 , which is taken as a model system. Solutions to the Landau expansion have been adapted to include the general influence of hydrostatic pressure and non-hydrostatic stress on transition temperature and the evolution of the order parameter. Critical examination of elastic constant data from the literature reveals inconsistencies between the results of measurements on tetragonal samples using ultrasonic rather than Brillouin scattering methods. An internally consistent data set has, nevertheless, been assembled. Good qualitative agreement was obtained between the general pattern of calculated and observed variations of all the single crystal elastic constants, and semi-quantitative agreement was obtained for C 11 , C 33 , C 12 , and C 13 . Some inconsistencies remain in relation to the temperature dependence of the square of the soft mode frequencies in the tetragonal phase, which follow the square of the order parameter rather than its inverse susceptibility, but the 246 potential seems to provide a good description of the structural evolution of SrTiO 3 over a wide temperature interval up to the cubic-tetragonal transition point.

Loop structure of the lowest Bloch band for a Bose-Einstein condensate

Abstract: We investigate analytically and numerically Bloch waves for a Bose-Einstein condensate in a sinusoidal external potential. At low densities the dependence of the energy on the quasimomentum is similar to that for a single particle, but at densities greater than a critical one the lowest band becomes triple valued near the boundary of the first Brillouin zone and develops the structure characteristic of the swallowtail catastrophe. We comment on the experimental consequences of this behavior.