Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Weyl and Dirac semimetals in three-dimensional solids

In recent years an increasing amount of attention has been devoted to quantum materials with topological characteristics that are robust against disorder and other perturbations. In this context it was discovered that topological materials can be classified with respect to their dimension and symmetry properties. This review provides an overview of the classification schemes of both fully gapped and gapless topological materials and gives a pedagogical introduction into the field of topological band theory.

Classification of topological quantum matter with symmetries

Fermions--elementary particles such as electrons--are classified as Dirac, Majorana or Weyl. Majorana and Weyl fermions had not been observed experimentally until the recent discovery of condensed matter systems such as topological superconductors and semimetals, in which they arise as low-energy excitations. Here we propose the existence of a previously overlooked type of Weyl fermion that emerges at the boundary between electron and hole pockets in a new phase of matter. This particle was missed by Weyl because it breaks the stringent Lorentz symmetry in high-energy physics. Lorentz invariance, however, is not present in condensed matter physics, and by generalizing the Dirac equation, we find the new type of Weyl fermion. In particular, whereas Weyl semimetals--materials hosting Weyl fermions--were previously thought to have standard Weyl points with a point-like Fermi surface (which we refer to as type-I), we discover a type-II Weyl point, which is still a protected crossing, but appears at the contact of electron and hole pockets in type-II Weyl semimetals. We predict that WTe2 is an example of a topological semimetal hosting the new particle as a low-energy excitation around such a type-II Weyl point. The existence of type-II Weyl points in WTe2 means that many of its physical properties are very different to those of standard Weyl semimetals with point-like Fermi surfaces.

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Type-II Weyl semimetals.

Weyl semimetals (WSMs) are topological quantum states wherein the electronic bands disperse linearly around pairs of nodes with fixed chirality, the Weyl points In WSMs, nonorthogonal electric and magnetic fields induce an exotic phenomenon known as the chiral anomaly, resulting in an unconventional negative longitudinal magnetoresistance, the chiral-magnetic effect However, it remains an open question to which extent this effect survives when chirality is not well-defined Here, we establish the detailed Fermi-surface topology of the recently identified WSM TaP via combined angle-resolved quantum-oscillation spectra and band-structure calculations The Fermi surface forms banana-shaped electron and hole pockets surrounding pairs of Weyl points Although this means that chirality is ill-defined in TaP, we observe a large negative longitudinal magnetoresistance We show that the magnetoresistance can be affected by a magnetic field-induced inhomogeneous current distribution inside the sample

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Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP

Experiments show that TaAs is a three-dimensional topological Weyl semimetal. 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 fermions1. 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.

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Observation of Weyl nodes in TaAs

Weyl points can be thought of as magnetic monopoles in momentum space that always appear in pairs. Magnetoresistance measurements indicate the existence of the long-anticipated chiral anomaly in Weyl semimetal TaAs single crystals.

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Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs

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 {\pi}, indicating the existence of Weyl points.

Observation of the chiral anomaly induced negative magneto-resistance in 3D Weyl semi-metal TaAs

Highly oriented PPy nanotubes are grown by in situ vapor phase polymerization within a nanoscale template under low temperature. As-fabricated PPy nanotubes are used for gas sensing, where an ultralow detection limit (0.05 ppb) and very fast response are achieved. Such an in situ mass-productive method for synthesizing highly oriented conducting polymers may pave a new step toward next-generation gas sensors.

High‐Oriented Polypyrrole Nanotubes for Next‐Generation Gas Sensor

A novel layered SnSSe material is designed as a high-performance anode for sodium-ion batteries with characteristics of high capacity, superior cyclability, facile synthetic method, and large-scale production ability. The transformation from bulk SnSSe particles into closely packed nanoplate aggregates with greater resistance to structure pulverization and the partial pseudocapacitive capacity contribution may engender excellent cycling performance and rate capability.

Novel Metal Chalcogenide SnSSe as a High-Capacity Anode for Sodium-Ion Batteries.

Two-dimensional (2D) chalcogenide materials are fundamentally and technologically fascinating for their suitable band gap energy and carrier type relevant to their adjustable composition, structure, and dimensionality. Here, we demonstrate the exfoliation of single-crystal SnS2-xSex (SSS) with S/Se vacancies into an atom-thin layer by simple sonication in ethanol without additive. The introduction of vacancies at the S/Se site, the conflicting atomic radius of sulfur in selenium layers, and easy incorporation with an ethanol molecule lead to high ion accessibility; therefore, atom-thin SSS flakes can be effectively prepared by exfoliating the single crystal via sonication. The in situ pyrolysis of such materials can further adjust their compositions, representing tunable activation energy, band gap, and also tunable response to analytes of such materials. As the most basic and crucial step of the 2D material field, the successful synthesis of an uncontaminated and atom-thin sample will further push ahead the large-scale applications of 2D materials, including, but not limited to, electronics, sensing, catalysis, and energy storage fields.

Zhanhai Yang

Papers

Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs

Observation of the chiral anomaly induced negative magneto-resistance in 3D Weyl semi-metal TaAs

High‐Oriented Polypyrrole Nanotubes for Next‐Generation Gas Sensor

Novel Metal Chalcogenide SnSSe as a High-Capacity Anode for Sodium-Ion Batteries.

Atom-Thin SnS2–xSex with Adjustable Compositions by Direct Liquid Exfoliation from Single Crystals