Topic
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 article, the electronic band structures of bulk Ge1-xSnx alloys were investigated using the empirical pseudopotential method (EPM) for Sn composition x varying from 0 to 0.2.
Abstract: This work investigates the electronic band structures of bulk Ge1-xSnx alloys using the empirical pseudopotential method (EPM) for Sn composition x varying from 0 to 0.2. The adjustable form factors of EPM were tuned in order to reproduce the band features that agree well with the reported experimental data. Based on the adjusted pseudopotential form factors, the band structures of Ge1-xSnx alloys were calculated along high symmetry lines in the Brillouin zone. The effective masses at the band edges were extracted by using a parabolic line fit. The bowing parameters of hole and electron effective masses were then derived by fitting the effective mass at different Sn compositions by a quadratic polynomial. The hole and electron effective mass were examined for bulk Ge1-xSnx alloys along specific directions or orientations on various crystal planes. In addition, employing the effective-mass Hamiltonian for diamond semiconductor, band edge dispersion at the Γ-point calculated by 8-band k.p. method was fitted...
198 citations
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TL;DR: In this article, an efficient formula for Z 2 topological invariants characterizing the quantum spin Hall effect is derived in a lattice Brillouin zone, which enables us to implement numerical calculations for realistic models even in three dimensions.
Abstract: We derive an efficient formula for Z 2 topological invariants characterizing the quantum spin Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numerical calculations for realistic models even in three dimensions. Based on this, we study the quantum spin Hall effect in Bi and Sb in quasi-two and three dimensions using a tight-binding model.
198 citations
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TL;DR: In this paper, a three-axis crystal spectrometer was used to measure phonon dispersion in Ge at 80.5 K for all principal symmetry directions and on some lines at the boundary of the Brillouin zone.
Abstract: Phonon dispersion relations in Ge have been measured at 80 \ifmmode^\circ\else\textdegree\fi{}K for all principal symmetry directions and on some lines at the boundary of the Brillouin zone. The measurements were performed by neutron inelastic scattering using a three-axis crystal spectrometer. In order to achieve maximum accuracy, care was taken to reduce resolution widths as far as possible. In general, the estimated uncertainties of the measured phonon frequencies range from 0.3% to 0.5% for optical and from 0.3% to 1% for acoustic phonons. Frequencies of 238 phonons are tabulated and phonon linewidths are given for the symmetry directions.
197 citations
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TL;DR: AlPt is shown to be a chiral topological material with four-fold and six-fold degeneracies in the band structure as discussed by the authors, which can be viewed as a higher spin generalization of Weyl fermions.
Abstract: Topological semimetals in crystals with a chiral structure (which possess a handedness due to a lack of mirror and inversion symmetries) are expected to display numerous exotic physical phenomena, including fermionic excitations with large topological charge1, long Fermi arc surface states2,3, unusual magnetotransport4 and lattice dynamics5, as well as a quantized response to circularly polarized light6. So far, all experimentally confirmed topological semimetals exist in crystals that contain mirror operations, meaning that these properties do not appear. Here, we show that AlPt is a structurally chiral topological semimetal that hosts new four-fold and six-fold fermions, which can be viewed as a higher spin generalization of Weyl fermions without equivalence in elementary particle physics. These multifold fermions are located at high symmetry points and have Chern numbers larger than those in Weyl semimetals, thus resulting in multiple Fermi arcs that span the full diagonal of the surface Brillouin zone. By imaging these long Fermi arcs, we experimentally determine the magnitude and sign of their Chern number, allowing us to relate their dispersion to the handedness of their host crystal. AlPt is shown to be a chiral topological material with four-fold and six-fold degeneracies in the band structure. Fermi arc edge states span the whole Brillouin zone and their dispersion enables identification of the handedness of the chiral material.
196 citations
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TL;DR: In this article, the generalized Brillouin zone (GBZ) is calculated analytically in one-dimensional non-Hermitian systems, which helps us to understand the non-hermitian bulk-boundary correspondence.
Abstract: We provide a systematic and self-consistent method to calculate the generalized Brillouin zone (GBZ) analytically in one-dimensional non-Hermitian systems, which helps us to understand the non-Hermitian bulk-boundary correspondence. In general, a $n$-band non-Hermitian Hamiltonian is constituted by $n$ distinct sub-GBZs, each of which is a piecewise analytic closed loop. Based on the concept of resultant, we can show that all the analytic properties of the GBZ can be characterized by an algebraic equation, the solution of which in the complex plane is dubbed as auxiliary GBZ (aGBZ). We also provide a systematic method to obtain the GBZ from aGBZ. Two physical applications are also discussed. Our method provides an analytic approach to the spectral problem of open boundary non-Hermitian systems in the thermodynamic limit.
196 citations