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Brillouin zone

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


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TL;DR: In this paper, the authors presented the full in-plane phonon dispersion of graphite obtained from inelastic x-ray scattering, including the optical and acoustic branches, as well as the midfrequency range between the $K$ and $M$ points in the Brillouin zone, where the experimental data have been unavailable so far.
Abstract: We present the full in-plane phonon dispersion of graphite obtained from inelastic x-ray scattering, including the optical and acoustic branches, as well as the midfrequency range between the $K$ and $M$ points in the Brillouin zone, where the experimental data have been unavailable so far. The existence of a Kohn anomaly at the $K$ point is further supported. We fit a fifth-nearest neighbor force-constant model to the experimental data, making improved force-constant calculations of the phonon dispersion in both graphite and carbon nanotubes available.

391 citations

Journal ArticleDOI
TL;DR: In this paper, a complete description of the first-order Raman and Brillouin spectra of single-crystal aluminum nitride is provided, and the frequency has been measured and the symmetry identified of each of the Raman active zone-center optic modes, and five independent elastic constants have been measured.
Abstract: A complete description of the first-order Raman and Brillouin spectra of single-crystal aluminum nitride is provided. The frequency has been measured and the symmetry identified of each of the Raman-active zone-center optic modes, and the five independent elastic constants have been measured. The widths of the principal Raman modes increase with increasing oxygen content up to a critical value of approximately 1 at. %, after which they are constant. This behavior supports the hypothesis of a change in the nature of the oxygen defect at that concentration.

388 citations

Journal ArticleDOI
TL;DR: In this article, the static ground state energy of a two-dimensional Wigner crystal has been obtained for each of the five 2D Bravais lattices, and the dispersion curves for wave vectors along the symmetry directions in the first Brillouin zone for the hexagonal lattice are calculated.
Abstract: The static ground-state energy of a two-dimensional Wigner crystal has been obtained for each of the five two-dimensional Bravais lattices. At constant electron number density the hexagonal lattice has the lowest energy. Phonon dispersion curves have been calculated for wave vectors along the symmetry directions in the first Brillouin zone for the hexagonal lattice. In the long-wavelength limit one of the two branches of the dispersion relation vanishes with vanishing two-dimensional wave vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ as $q$, the second as ${q}^{\frac{1}{2}}$. The coefficient of $q$ in the former branch is pure imaginary for certain directions of propagation in the square lattice, implying a dynamical instability of this lattice; the hexagonal lattice is stable. The vibrational zero-point energy and low-temperature thermodynamic functions have been obtained for the hexagonal lattice. The dielectric susceptibility tensor of a two-dimensional Wigner crystal ${\ensuremath{\chi}}_{\ensuremath{\alpha}\ensuremath{\beta}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ has been determined in the long-wavelength limit, in the presence of a static magnetic field perpendicular to the crystal, and the result has been used to obtain the dispersion relation for plasma oscillations in the electron crystal.

386 citations

Book
01 Jan 1987
TL;DR: In this article, the effects of electron repulsion lattice distortions defects defects, impurities, and surfaces are discussed, and the Fermi-Dirac distribution function is described.
Abstract: Introduction spectroscopic methods electronic energy levels and chemical bonding elementary band theory the effects of electron repulsion lattice distortions defects, impurities, and surfaces Appendix A: The Fermi-Dirac distribution function Appendix B: Brillouin zones and the reciprocal lattice

385 citations

Journal ArticleDOI
TL;DR: First-principles calculations are used to show that field-gated silicene possesses two gapped Dirac cones exhibiting nearly 100% spin-polarization, situated at the corners of the Brillouin zone, and a design for asilicene-based spin-filter that should enable the spin- polarization of an output current to be switched electrically, without switching external magnetic fields is proposed.
Abstract: Silicene is a one-atom-thick two-dimensional crystal of silicon with a hexagonal lattice structure that is related to that of graphene but with atomic bonds that are buckled rather than flat. This buckling confers advantages on silicene over graphene, because it should, in principle, generate both a band gap and polarized spin-states that can be controlled with a perpendicular electric field. Here we use first-principles calculations to show that field-gated silicene possesses two gapped Dirac cones exhibiting nearly 100% spin-polarization, situated at the corners of the Brillouin zone. Using this fact, we propose a design for a silicene-based spin-filter that should enable the spin-polarization of an output current to be switched electrically, without switching external magnetic fields. Our quantum transport calculations indicate that the proposed designs will be highly efficient (nearly 100% spin-polarization) and robust against weak disorder and edge imperfections. We also propose a Y-shaped spin/valley separator that produces spin-polarized current at two output terminals with opposite spins.

384 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023430
2022957
2021463
2020543
2019568
2018587