Weyl semimetals are a class of materials that can be regarded as three-dimensional analogs of graphene upon breaking time-reversal or inversion symmetry. Electrons in a Weyl semimetal behave as Weyl fermions, which have many exotic properties, such as chiral anomaly and magnetic monopoles in the crystal momentum space. The surface state of a Weyl semimetal displays pairs of entangled Fermi arcs at two opposite surfaces. However, the existence of Weyl semimetals has not yet been proved experimentally. Here, we report the experimental realization of a Weyl semimetal in TaAs by observing Fermi arcs formed by its surface states using angle-resolved photoemission spectroscopy. Our first-principles calculations, which match remarkably well with the experimental results, further confirm that TaAs is a Weyl semimetal.

Weyl semi-metal is the three dimensional analog of graphene. According to the quantum field theory, the appearance of Weyl points near the Fermi level will cause novel transport phenomena related to chiral anomaly. In the present paper, we report the first experimental evidence for the long-anticipated negative magneto-resistance generated by the chiral anomaly in a newly predicted time-reversal invariant Weyl semi-metal material TaAs. Clear Shubnikov de Haas oscillations (SdH) have been detected starting from very weak magnetic field. Analysis of the SdH peaks gives the Berry phase accumulated along the cyclotron orbits to be π, indicating the existence of Weyl points.When two non-degenerate bands cross in three dimensional momentum space, the crossing points are called Weyl points, which can be viewed as magnetic monopoles(1) or topological defects (2) in band structure, like "knots" on a rope. Near Weyl points, the low energy physics can be described by Weyl equations (3) with distinct chirality (either left-or right-handed), which mimics the relativistic field theory in particle physics. On lattice system, Weyl points always appear in pairs with opposite chirality and are topologically stable against perturbations that keep translational symmetry (4-7). If two weyl points with opposite chirality meet in the momentum space, they will generally annihilate each other, but may also be stabilized as 3D Dirac points by additional (such as crystalline) symmetry (8-11). For materials withWeyl points located near the Fermi level, called as Weyl semi-metals (WSMs), exotic low energy physics will be expected, such as the Fermi arcs on the surfaces (5,6), and the chiral-anomaly induced quantum transport (12)(13)(14)(15). Recently, 3D Dirac semimetals, Na 3 Bi and Cd 3 As 2 , have been theoretically predicted (9,10) and experimentally confirmed (16)(17)(18)(19)(20), while WSM are still waiting for its experimental verification in spite of various theoretical proposals (5,6,(21)(22)(23)(24)(25).The anomalous DC transport properties are important consequence of the topological band structure (14,26,27). In topological insulators (TI), the transport properties are dominated by the topological surfaces states (SS), where the lack of back scattering caused by the unique spin structure of the SS leads to the weak anti-localization (WAL) behavior. While in Weyl semi-metals, the bulk states are semi-metallic and dominate the DC transport. In relativistic field theory, for a continue system described by Weyl equation, chiral anomaly can be understood as the non-conservation of the particle number with given chirality, which only happens under the presence of

In 1929, H. Weyl proposed that the massless solution of the Dirac equation represents a pair of a new type of particles, the so-called Weyl fermions 1 . However, their existence in particle physics remains elusive after more than eight decades. Recently, significant advances in both topological insulators and topological semimetals have provided an alternative way to realize Weyl fermions in condensed matter, as an emergent phenomenon: when two non-degenerate bands in the three-dimensional momentum space cross in the vicinity of the Fermi energy (called Weyl nodes), the low-energy excitations behave exactly as Weyl fermions. Here we report the direct observation in TaAs of the long-sought-after Weyl nodes by performing bulk-sensitive soft X-ray angle-resolved photoemission spectroscopy measurements. The projected locations at the nodes on the (001) surface match well to the Fermi arcs, providing undisputable experimental evidence for the existence of Weyl fermionic quasiparticles in TaAs.The massless Dirac equation in the three-dimensional (3D) momentum space can be regarded as the overlap of two Weyl fermions with opposite chirality 1,2 . The Dirac fermionic quasiparticle is stable under the protection of some crystal symmetry in topological Dirac semimetals such as Na 3 Bi (ref. 3) and Cd 3 As 2 (ref. 4). However, a separated single Weyl node is much more robust and requires no protection of crystal symmetry. An isolated Weyl node is a sink or source of gauge field of Berry curvature, like a monopole in momentum space, and the chirality corresponds to its topological charge [5][6][7] . Weyl nodes appear in pairs of opposite chirality in a real material due to the 'No-go theorem' 8,9 . To obtain isolated Weyl nodes, the spin degeneracy of the electronic bands has to be removed by breaking either inversion symmetry or time-reversal symmetry. Although non-degenerate band crossing is not rare, finding a material with only Weyl nodes near the Fermi energy (E F ) is a big challenge. Recently, the noncentrosymmetric and non-magnetic transition-metal monoarsenide TaAs has been predicted to be a Weyl semimetal (WSM), and twelve pairs of Weyl nodes are expected in its 3D Brillouin zone (BZ; refs 10,11). Compared with other proposals 6,7,12-22 for realizing a Weyl state, the TaAs family features easy sample fabrication, a non-magnetic state and no fine-tuning of the electronic states is necessary, making experimental studies of Weyl semimetals possible. Many exotic properties induced by the Weyl nodes have been predicted and observed recently, such as surface states with Fermi arcs 23,24 and a negative magneto-resistivity 25,26 due to the chiral anomaly 27-29 . However, crucial evidence for Weyl nodes in the bulk states has not been observed. In this paper, by using soft X-ray angle-resolved photoemission spectroscopy (ARPES), which is sensitive to the bulk states, we report the first experimental observation of Weyl nodes in TaAs.TaAs crystallizes in a body-centred-tetragonal structure with the nonsymmorphic space group...

The topological materials have attracted much attention for their unique electronic structure and peculiar physical properties. ZrTe5 has host a long-standing puzzle on its anomalous transport properties manifested by its unusual resistivity peak and the reversal of the charge carrier type. It is also predicted that single-layer ZrTe5 is a two-dimensional topological insulator and there is possibly a topological phase transition in bulk ZrTe5. Here we report high-resolution laser-based angle-resolved photoemission measurements on the electronic structure and its detailed temperature evolution of ZrTe5. Our results provide direct electronic evidence on the temperature-induced Lifshitz transition, which gives a natural understanding on underlying origin of the resistivity anomaly in ZrTe5. In addition, we observe one-dimensional-like electronic features from the edges of the cracked ZrTe5 samples. Our observations indicate that ZrTe5 is a weak topological insulator and it exhibits a tendency to become a strong topological insulator when the layer distance is reduced.

Two-dimensional topological insulators with a large bulk band gap are promising for experimental studies of quantum spin Hall effect and for spintronic device applications. Despite considerable theoretical efforts in predicting large-gap two-dimensional topological insulator candidates, none of them have been experimentally demonstrated to have a full gap, which is crucial for quantum spin Hall effect. Here, by combining scanning tunneling microscopy/spectroscopy and angle-resolved photoemission spectroscopy, we reveal that ZrTe 5 crystal hosts a large full gap of ∼100 meV on the surface and a nearly constant density of states within the entire gap at the monolayer step edge. These features are well reproduced by our first-principles calculations, which point to the topologically nontrivial nature of the edge states.

We have investigated the spin texture of surface Fermi arcs in the recently discovered Weyl semimetal TaAs using spin-and angle-resolved photoemission spectroscopy. The experimental results demonstrate that the Fermi arcs are spin polarized. The measured spin texture fulfills the requirement of mirror and timereversal symmetries and is well reproduced by our first-principles calculations, which gives strong evidence for the topologically nontrivial Weyl semimetal state in TaAs. The consistency between the experimental and calculated results further confirms the distribution of chirality of the Weyl nodes determined by firstprinciples calculations.

Flow visualization research has made rapid advances in recent years, especially in the area of topology-based flow visualization. The ever increasing size of scientific data sets favors algorithms that are capable of extracting important subsets of the data, leaving the scientist with a more manageable representation that may be visualized interactively. Extracting the topology of a flow achieves the goal of obtaining a compact representation of a vector or tensor field while simultaneously retaining its most important features. We present the state of the art in topology-based flow visualization techniques. We outline numerous topology-based algorithms categorized according to the type and dimensionality of data on which they operate and according to the goal-oriented nature of each method. Topology tracking algorithms are also discussed. The result serves as a useful introduction and overview to research literature concerned with the study of topology-based flow visualization.

The performance of graph neural nets (GNNs) is known to gradually decrease with increasing number of layers. This decay is partly attributed to oversmoothing, where repeated graph convolutions eventually make node embeddings indistinguishable. We take a closer look at two different interpretations, aiming to quantify oversmoothing. Our main contribution is PAIRNORM, a novel normalization layer that is based on a careful analysis of the graph convolution operator, which prevents all node embeddings from becoming too similar. What is more, PAIRNORM is fast, easy to implement without any change to network architecture nor any additional parameters, and is broadly applicable to any GNN. Experiments on real-world graphs demonstrate that PAIRNORM makes deeper GCN, GAT, and SGC models more robust against oversmoothing, and significantly boosts performance for a new problem setting that benefits from deeper GNNs.