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

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Over the past 30 years, significant commercial and academic progress has been made on Li-based battery technologies. From the early Li-metal anode iterations to the current commercial Li-ion batteries (LIBs), the story of the Li-based battery is full of breakthroughs and back tracing steps. This review will discuss the main roles of material science in the development of LIBs. As LIB research progresses and the materials of interest change, different emphases on the different subdisciplines of material science are placed. Early works on LIBs focus more on solid state physics whereas near the end of the 20th century, researchers began to focus more on the morphological aspects (surface coating, porosity, size, and shape) of electrode materials. While it is easy to point out which specific cathode and anode materials are currently good candidates for the next-generation of batteries, it is difficult to explain exactly why those are chosen. In this review, for the reader a complete developmental story of LIB should be clearly drawn, along with an explanation of the reasons responsible for the various technological shifts. The review will end with a statement of caution for the current modern battery research along with a brief discussion on beyond lithium-ion battery chemistries.

30 Years of Lithium-Ion Batteries.

Carbon nanotube–polymer composites: Chemistry, processing, mechanical and electrical properties

Thermal conductivity of carbon nanotubes and their polymer nanocomposites: A review

Observations of topological surface states provide strong evidence that MoTe2 is a type-II Weyl semimetal, hosting Weyl fermions that have no counterpart in high-energy physics.

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Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2

Aligned Carbon Nanotube Composite Films for Thermal Management

The intricate interplay between non-trivial topology and magnetism in two-dimensional materials can lead to the emergence of interesting phenomena such as the quantum anomalous Hall effect. Here we investigate the quantum transport of both bulk crystal and exfoliated MnBi2Te4 flakes in a field-effect transistor geometry. For the six septuple-layer device tuned into the insulating regime, we observe a large longitudinal resistance and zero Hall plateau, which are characteristics of an axion insulator state. The robust axion insulator state occurs in zero magnetic field, over a wide magnetic-field range and at relatively high temperatures. Moreover, a moderate magnetic field drives a quantum phase transition from the axion insulator phase to a Chern insulator phase with zero longitudinal resistance and quantized Hall resistance h/e2, where h is Planck’s constant and e is electron charge. Our results pave the way for using even-number septuple-layer MnBi2Te4 to realize the quantized topological magnetoelectric effect and axion electrodynamics in condensed matter systems. A large longitudinal resistance and zero Hall plateau—hallmarks of an axion insulator—are found in MnBi2Te4. Moreover, a moderate magnetic field drives a quantum phase transition to a Chern insulator phase with zero longitudinal resistance and quantized Hall resistance h/e2.

Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator

Topological semimetals have recently attracted extensive research interests as host materials to condensed matter physics counterparts of Dirac and Weyl fermions originally proposed in high energy physics. Although Lorentz invariance is required in high energy physics, it is not necessarily obeyed in condensed matter physics, and thus Lorentz-violating type-II Weyl/Dirac fermions could be realized in topological semimetals. The recent realization of type-II Weyl fermions raises the question whether their spin-degenerate counterpart—type-II Dirac fermions—can be experimentally realized too. Here, we report the experimental evidence of type-II Dirac fermions in bulk stoichiometric PtTe2 single crystal. Angle-resolved photoemission spectroscopy measurements and first-principles calculations reveal a pair of strongly tilted Dirac cones along the Γ-A direction, confirming PtTe2 as a type-II Dirac semimetal. Our results provide opportunities for investigating novel quantum phenomena (e.g., anisotropic magneto-transport) and topological phase transition. Whether the spin-degenerate counterpart of Lorentz-violating Weyl fermions, the Dirac fermions, can be realized remains as an open question. Here, Yan et al. report experimental evidence of such type-II Dirac fermions in bulk PtTe2 single crystal with a pair of strongly tilted Dirac cones.

http://inspirehep.net/record/1475773/files/3fb91327-3bae-469c-aba6-b3437e8512f2-1607.03643.pdf

Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide PtTe 2

The quantum Hall effect (QHE) with quantized Hall resistance of h/νe2 started the research on topological quantum states and laid the foundation of topology in physics. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C| = 1, which has been experimentally observed at relatively low temperatures. For emerging physics and low-power-consumption electronics, the key issues are how to increase the working temperature and realize high Chern numbers (C > 1). Here, we report the experimental discovery of high-Chern-number QHE (C = 2) without Landau levels and C = 1 Chern insulator state displaying a nearly quantized Hall resistance plateau above the Neel temperature in MnBi2Te4 devices. Our observations provide a new perspective on topological matter and open new avenues for exploration of exotic topological quantum states and topological phase transitions at higher temperatures.

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Yang Wu

Papers

Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2

Aligned Carbon Nanotube Composite Films for Thermal Management

Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator

Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide PtTe 2

High-Chern-number and high-temperature quantum Hall effect without Landau levels.