Topological Materials: Weyl Semimetals

Topological insulators and topological semimetals are both new classes of quantum materials, which are characterized by surface states induced by the topology of the bulk band structure. Topological Dirac or Weyl semimetals show linear dispersion round nodes, termed the Dirac or Weyl points, as the three-dimensional analogue of graphene. We review the basic concepts and compare these topological states of matter from the materials perspective with a special focus on Weyl semimetals. The TaAs family is the ideal materials class to introduce the signatures of Weyl points in a pedagogical way, from Fermi arcs to the chiral magneto-transport properties, followed by the hunting for the type-II Weyl semimetals in WTe2, MoTe2 and related compounds. Many materials are members of big families and topological properties can be tuned. As one example, we introduce the multifuntional topological materials, Heusler compounds, in which both topological insulators and magnetic Weyl semimetals can be found. Instead of a comprehensive review, this article is expected to serve as a helpful introduction and summary by taking a snapshot of the quickly expanding field.Comment: 19 pages, 7 figures, an invited review article for Annual Review of Condensed Matter Physic

Berry-curvatures and anomalous Hall effect in Heusler compounds

Berry curvatures are computed for a set of Heusler compounds using density functional (DF) calculations and the wave functions that DF provide. The anomalous Hall conductivity is obtained from the Berry curvatures. It is compared with experimental values in the case of Co$_2$CrAl and Co$_2$MnAl. A notable trend cannot be seen but the range of values is quite enormous. The results for the anomalous Hall conductivities and their large variations can be qualitatively understood by means of the band structure and the Fermi-surface topology

Non-collinear Antiferromagnets and the Anomalous Hall Effect

The anomalous Hall effect is investigated theoretically by means of density functional calculations for the non-collinear antiferromagnetic order of the hexagonal compounds Mn$_3$Ge and Mn$_3$Sn using various planar triangular magnetic configurations as well as unexpected non-planar configurations. The former give rise to anomalous Hall conductivities (AHC) that are found to be extremely anisotropic. For the planar cases the AHC is connected with Weyl-points in the energy-band structure, which are described in detail. If this case were observable in Mn$_3$Ge, a large AHC of about 900 S/cm should be expected. However, in Mn$_3$Ge it is the non-planar configuration that is energetically favored, in which case it gives rise to an AHC of 100 S/cm. The non-planar configuration allows a quantitative evaluation of the topological Hall effect that is seen to determine this value of the conductivity to a large extent. For Mn$_3$Sn it is the planar configurations that are predicted to be observable. In this case the AHC can be as large as 250 S/cm.Comment: 5 pages, 7 figure

Language Processing Evidence for Linguistic Structure

This article illustrates how data from language processing experiments might bear on theoretical linguistic issues and controversies. Based on the results from real-time processing studies of subject raising vs. subject control structures and successive-cyclic wh-movement in English, and of long-distance scrambling in Japanese, this article examines how language processing data can help shed light on the nature of the linguistic representations of different types of non-canonically ordered sentences.Este artículo ilustra cómo datos provenientes de experimentos de procesamiento del lenguaje pueden arrojar luz sobre algunos temas (algunos controvertidos) relacionados con la teoría lingüística. Basado en los resultados de estudios de procesamiento a tiempo real de estructuras de ascenso de sujeto vs. estructuras de control de sujeto y movimiento qusucesivamente cíclico en inglés, así como desplazamiento libre (scrambling) de larga distancia en japonés, este artículo examina cómo los datos de procesamiento del lenguaje pueden ayudar a dilucidar la naturaleza de las representaciones lingüísticas de distintos tipos de oraciones ordenadas de forma no canónica.Este artigo ilustra de que forma dados experimentais do processamento de linguagem podem ser suportados por questões linguísticas teóricas e por controvérsias. Com base nos resultados de processamento em tempo real em estudos de subida de sujeito vs. estruturas de controlo de sujeito e movimento wh- sucessivo cíclico em inglês, e de scrambling de longa distância em japonês, este artigo analisa a forma como os dados de processamento de linguagem podem ajudar a esclarecer a natureza das representações linguísticas dos diferentes tipos de orações nãocanónicas

A large energy-gap oxide topological insulator based on the superconductor BaBiO3

Mixed-valent perovskite oxides based on BaBiO3 (BBO) are, like cuperates, well-known high-Tc superconductors. Recent ab inito calculations have assigned the high-Tc superconductivity to a correlation-enhanced electron--phonon coupling mechanism, stimulating the prediction and synthesis of new superconductor candidates among mixed-valent thallium perovskites. Existing superconductivity has meant that research has mainly focused on hole-doped compounds, leaving electron-doped compounds relatively unexplored. Here we demonstrate through ab inito calculations that BBO emerges as a topological insulator (TI) in the electron-doped region, where the spin-orbit coupling (SOC) effect is significant. BBO exhibits the largest topological energy gap of 0.7 eV among currently known TI materials, inside which Dirac-type topological surface states (TSSs) exit. As the first oxide TI, BBO is naturally stable against surface oxidization and degrading, different from chalcoginide TIs. An extra advantage of BBO lies in its ability to serve an interface between the TSSs and the superconductor for the realization of Majorana Fermions

Graphene-like Dirac states and Quantum Spin Hall Insulators in the square-octagonal MX2 (M=Mo, W; X=S, Se, Te) Isomers

We studied the square-octagonal lattice of the transition metal dichalcogenide MX$_2$ (with $M$=Mo, W; $X$=S, Se and Te), as an isomer of the normal hexagonal compound of MX$_2$. By band structure calculations, we observe the graphene-like Dirac band structure in a rectangular lattice of MX$_2$ with nonsymmorphic space group symmetry. Two bands with van Hove singularity points cross each at the Fermi energy, leading to two Dirac cones that locates at opposite momenta. Spin-orbit coupling can open a nontrivial gap at these Dirac points and induce the quantum spin Hall (QSH) phase, the 2D topological insulator. Here, square-octagonal MX$_2$ structures realize the interesting graphene physics, such as Dirac bands and QSH effect, in the transition metal dichalcogenides.Comment: 4 pages, 3 figures, 1 Tabl