Brillouin zone

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

Quick iterative scheme for the calculation of transfer matrices: application to Mo (100)

Abstract: The transfer matrix of a solid described by the stacking of principal layers is obtained by an iterative procedure which takes into account 2 layers after n iterations, in contrast to usual schemes where each iteration includes just one more layer. The Green function and density of states at the surface of the corresponding semi-infinite crystal are then given by well known formulae in terms of the transfer matrix. This method, especially convenient near singularities, is applied to the calculation of the spectral as well as the total densities of states for the (100) face of molybdenum. The Slater-Koster algorithm for the calculation of tight-binding parameters is used with a basis of nine orbitals per atom (4d, 5s, 5p). Surface states and resonances are first identified and then analysed into orbital components to find their dominant symmetry. Their evolution along the main symmetry lines of the two-dimensional Brillouin zone is given explicitly. The surface-state peak just below the Fermi level (Swanson hump) is not obtained. This is traced to the difficulty in placing an appropriate boundary condition at the surface with the tight-binding parameterisation scheme.

Distributions of phonon lifetimes in Brillouin zones

Abstract: A collaboration of researchers from Japan and France present a comprehensive study of phonon lifetimes and thermal conductivity for 33 zincblende- and wurtzite compounds using linearized phonon Boltzmann equation and first-principles anharmonic phonon calculations. The software that the authors created for this study will be released as an open source package and should be of help in the search of new materials for thermoelectric applications.

Origin of dispersive effects of the Raman D band in carbon materials

Abstract: The origin and dispersion of the anomalous disorder-induced Raman band $(D$ band) observed in all ${\mathrm{sp}}^{2}$ hybridized disordered carbon materials near 1350 ${\mathrm{cm}}^{\ensuremath{-}1}$ is investigated as a function of incident laser energy. This effect is explained in terms of the coupling between electrons and phonons with the same wave vector near the K point of the Brillouin zone. The high dispersion is ascribed to the coupling between the optic phonons associated with the D band and the transverse acoustic branch. The large Raman cross section is due to the breathing motion of these particular phonons near the K point. Our model challenges the idea that the Raman D peak is due to laser-energy-independent features in the phonon density of states, but rather is due to a resonant Raman process.

Direct measurement of the Zak phase in topological Bloch bands

Abstract: Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the band theory of solids. Here we report on the measurement of the geometric phase acquired by cold atoms moving in one-dimensional optical lattices. Using a combination of Bloch oscillations and Ramsey interferometry, we extract the Zak phase—the Berry phase gained during the adiabatic motion of a particle across the Brillouin zone—which can be viewed as an invariant characterizing the topological properties of the band. For a dimerized lattice, which models polyacetylene, we measure a difference of the Zak phase’ Zak D 0:97(2) for the two possible polyacetylene phases with different dimerization. The two dimerized phases therefore belong to different topological classes, such that for a filled band, domain walls have fractional quantum numbers. Our work establishes a new general approach for probing the topological structure of Bloch bands in optical lattices.