Search

The semimetal MoTe$_2$ is studied by spin- and angle- resolved photoemission spectroscopy to probe the detailed electronic structure underlying its broad range of response behavior. A novel spin-texture is uncovered in the bulk Fermi surface of the non-centrosymmetric structural phase that is consistent with first-principles calculations. The spin-texture is three-dimensional, both in terms of momentum dependence and spin-orientation, and is not completely suppressed above the centrosymmetry-breaking transition temperature. Two types of surface Fermi arc are found to persist well above the transition temperature. The appearance of a large Fermi arc depends strongly on thermal history, and the electron quasiparticle lifetimes are greatly enhanced in the initial cooling. The results indicate that polar instability with strong electron-lattice interactions exists near the surface when the bulk is largely in a centrosymmetric phase.

Due to the existence of various views or representations in many real-world data, multi-view learning has drawn much attention recently. Multi-view spectral clustering methods based on similarity matrixes or graphs are pretty popular. Generally, these algorithms learn informative graphs by directly utilizing original data. However, in the real-world applications, original data often contain noises and outliers that lead to unreliable graphs. In addition, different views may have different contributions to data clustering. In this paper, a novel Multiview Subspace Clustering method unifying Adaptive neighbours and Metric learning (MSCAM), is proposed to address the above problems. In this method, we use the subspace representations of different views to adaptively learn a consensus similarity matrix, uncovering the subspace structure and avoiding noisy nature of original data. For all views, we also learn different Mahalanobis matrixes that parameterize the squared distances and consider the contributions of different views. Further, we constrain the graph constructed by the similarity matrix to have exact c (c is the number of clusters) connected components. An iterative algorithm is developed to solve this optimization problem. Moreover, experiments on a synthetic dataset and different real-world datasets demonstrate the effectiveness of MSCAM., Comment: 9 pages

The peculiar band structure of semimetals exhibiting Dirac and Weyl crossings can lead to spectacular electronic properties such as large mobilities accompanied by extremely high magnetoresistance. In particular, two closely neighbouring Weyl points of the same chirality are protected from annihilation by structural distortions or defects, thereby significantly reducing the scattering probability between them. Here we present the electronic properties of the transition metal diphosphides, WP2 and MoP2, that are type-II Weyl semimetals with robust Weyl points. We present transport and angle resolved photoemission spectroscopy measurements, and first principles calculations. Our single crystals of WP2 display an extremely low residual low-temperature resistivity of 3 nohm-cm accompanied by an enormous and highly anisotropic magnetoresistance above 200 million % at 63 T and 2.5 K. These properties are likely a consequence of the novel Weyl fermions expressed in this compound. We observe a large suppression of charge carrier backscattering in WP2 from transport measurements., Comment: Appeared in Nature Communications

Cryo-electron microscopy provides 2-D projection images of the 3-D electron scattering intensity of many instances of the particle under study (e.g., a virus). Both symmetry (rotational point groups) and heterogeneity are important aspects of biological particles and both aspects can be combined by describing the electron scattering intensity of the particle as a stochastic process with a symmetric probability law and therefore symmetric moments. A maximum likelihood estimator implemented by an expectation-maximization algorithm is described which estimates the unknown statistics of the electron scattering intensity stochastic process from images of instances of the particle. The algorithm is demonstrated on the bacteriophage HK97 and the virus N$\omega$V. The results are contrasted with existing algorithms which assume that each instance of the particle has the symmetry rather than the less restrictive assumption that the probability law has the symmetry., Comment: 16 pages, 10 figures

Basis functions which are invariant under the operations of a rotational point group $G$ are able to describe any 3-D object which exhibits the rotational point group symmetry. However, in order to characterize the spatial statistics of an ensemble of objects in which each object is different but the statistics exhibit the symmetry, a complete set of basis functions is required. In particular, for each irreducible representation (irrep) of $G$, it is necessary to include basis functions that transform according to that irrep. This complete set of basis functions is a basis for square-integrable functions on the surface of the sphere in 3-D. Because the objects are real-valued, it is convenient to have real-valued basis functions. In this paper, the existence of such real-valued bases is proven and an algorithm for their computation is provided for the icosahedral $I$ and the octahedral $O$ symmetries. Furthermore, it is proven that such a real-valued basis does not exist for the tetrahedral $T$ symmetry because some irreps of $T$ are essentially complex. The importance of these basis functions to computations in single-particle cryo-electron microscopy is described., Comment: 20 pages + supplemental materials

In 3-D reconstruction problems, the image data obtained from cryo electron microscopy is the projection of many heterogeneous instances of the object under study (e.g., a virus). When the object is heterogeneous but has an overall symmetry, it is natural to describe the object as stochastic with symmetrical statistics. This paper presents a maximum likelihood reconstruction approach which allows each object to lack symmetry while constraining the {\it statistics} of the ensemble of objects to have symmetry. This algorithm is demonstrated on bacteriophage HK97 and is contrasted with an existing algorithm in which each object, while still heterogeneous, has the symmetry. Reconstruction results show that the proposed algorithm eliminates long-standing distortions in previous heterogeneity calculations associated with symmetry axes, and provides estimates that make more biologically sense than the estimates of existing algorithms.

The basis of the identity representation of a polyhedral group is able to describe functions with symmetries of a platonic solid, i.e., 3-D objects which geometrically obey the cubic symmetries. However, to describe the dynamic of assembles of heterogeneous 3-D structures, a situation that each object lacks the symmetries but obeys the symmetries on a level of statistics, the basis of all representations of a group is required. While those 3-D objects are often transformed to real functions on $L_2$ space, it is desirable to generate a complete basis on real space. This paper deduces the existence of a basis on real space for each polyhedral group, and introduces a novel approach to explicitly compute these real basis functions, of which properties are further explored.