Brillouin zone

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

Analysis of Bloch’s Method and the Propagation Technique in Periodic Structures

Abstract: Bloch analysis was originally developed by Bloch to study the electron behavior in crystalline solids. His method has been adapted to study the elastic wave propagation in periodic structures. The absence of a rigorous mathematical analysis of the approach, as applied to periodic structures, has resulted in mistreatment of internal forces and misapplication to nonlinear media. In a previous article (Farzbod and Leamy, 2009, "The Treatment of Forces in Bloch Analysis, " J. Sound Vib., 325(3), pp. 545―551), we clarified the treatment of internal forces. In this article, we borrow the insight from the previous work to detail a mathematical basis for Bloch analysis and thereby shed important light on the proper application of the technique. For example, we conclusively show that translational invariance is not a proper justification for invoking the existence of a "propagation constant, " and that in nonlinear media, this results in a flawed analysis. We also provide a simple, two-dimensional example, illustrating what the role stiffness symmetry has on the search for a band gap behavior along the edges of the irreducible Brillouin zone. This complements other treatments that have recently appeared addressing the same issue.

Energy band structure of graphite

Abstract: The energy band structure of graphite is described in the region of the Fermi surfaces by the Slonczewski-Weiss model. The electron and hole Fermi surfaces are highly elongated and are aligned along the six Brillouin zone edges which are parallel to the trigonal axis of the crystal. The energy is a nonparabolic function of wavenumber and the Fermi surfaces are not ellipsoids. Galvanomagnetic, de Haasvan Alphen, and other experiments have established that: the band overlap is about 0.03 to 0.04 eV, the carrier densities of electrons and holes are each about 3 × 1018 cm-3 at low temperatures, the effective masses perpendicular to the trigonal axis are about 0.04 m0 for electrons and 0.06 m0 for holes, and the length-to-width ratio of the Fermi surfaces is about 12. The only important effect not included in the Slonczewski-Weiss model is the correlation of electron motion due to the coulomb interaction. Though this effect is expected to be important a priori, it is not yet clear if it causes important discrepancies between the predictions of the model and the experimental results.

Few-Layer PdSe2 Sheets: Promising Thermoelectric Materials Driven by High Valley Convergence.

Abstract: Herein, we report a comprehensive study on the structural and electronic properties of bulk, monolayer, and multilayer PdSe2 sheets. First, we present a benchmark study on the structural properties of bulk PdSe2 by using 13 commonly used density functional theory (DFT) functionals. Unexpectedly, the most commonly used van der Waals (vdW)-correction methods, including DFT-D2, optB88, and vdW-DF2, fail to provide accurate predictions of lattice parameters compared to experimental data (relative error > 15%). On the other hand, the PBE-TS series functionals provide significantly improved prediction with a relative error of <2%. Unlike hexagonal two-dimensional materials like graphene, transition metal dichalcogenides, and h-BN, the conduction band minimum of monolayer PdSe2 is not located along the high symmetry lines in the first Brillouin zone; this highlights the importance of the structure–property relationship in the pentagonal lattice. Interestingly, high valley convergence is found in the conduction a...

On occurrence of spectral edges for periodic operators inside the Brillouin zone

Abstract: The paper discusses the following frequently arising question on the spectral structure of periodic operators of mathematical physics (e.g., Schrodinger, Maxwell, waveguide operators, etc). Is it true that one can obtain the correct spectrum by using the values of the quasimomentum running over the boundary of the (reduced) Brillouin zone only, rather than the whole zone? Or, do the edges of the spectrum occur necessarily at the set of 'corner' high symmetry points? This is known to be true in 1D, while no apparent reasons exist for this to be happening in higher dimensions. In many practical cases, though, this appears to be correct, which sometimes leads to the claims that this is always true. There seems to be no definite answer in the literature, and one encounters different opinions about this problem in the community. In this paper, starting with simple discrete graph operators, we construct a variety of convincing multiply-periodic examples showing that the spectral edges might occur deeply inside the Brillouin zone. On the other hand, it is also shown that in a 'generic' case, the situation of spectral edges appearing at high symmetry points is stable under small perturbations. This explains to some degree why in many (maybe even most) practical cases the statement still holds.

Polarization-Resolved Study of High Harmonics from Bulk Semiconductors.

Abstract: The polarization property of high harmonics from gallium selenide is investigated using linearly polarized midinfrared laser pulses. With a high electric field, the perpendicular polarization component of the odd harmonics emerges, which is not present with a low electric field and cannot be explained by the perturbative nonlinear optics. A two-dimensional single-band model is developed to show that the anisotropic curvature of an energy band of solids, which is pronounced in an outer part of the Brillouin zone, induces the generation of the perpendicular odd harmonics. This model is validated by three-dimensional quantum mechanical simulations, which reproduce the orientation dependence of the odd-order harmonics. The quantum mechanical simulations also reveal that the odd- and even-order harmonics are produced predominantly by the intraband current and interband polarization, respectively. These experimental and theoretical demonstrations clearly show a strong link between the band structure of a solid and the polarization property of the odd-order harmonics.