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Weyl Semimetals, Fermi Arcs and Chiral Anomalies Shuang Jia, Su-Yang Xu and M commentary Weyl semimetals, Fermi arcs and chiral anomalies Shuang Jia, Su-Yang Xu and M. Zahid Hasan Physicists have discovered a new topological phase of matter, the Weyl semimetal, whose surface features a non-closed Fermi surface whereas the low-energy quasiparticles in the bulk emerge as Weyl fermions. A brief review of these developments and perspectives on the next steps forward are presented. eyl semimetals are semimetals these lines, highlighting the experimental of this line of research for materials or metals whose quasiparticle techniques and matching materials discovery were thoroughly discussed in Wexcitation is the Weyl fermion, a conditions that are necessary for realizing ref. 14, where the search was based on the particle that played a crucial role in quantum these research directions. Inorganic Crystal Structure Database of FIZ feld theory but has not been observed as a Karlsruhe27, which systematically records the fundamental particle in vacuum1–24. Weyl Topological material search lattice structure of crystals that have been fermions have defnite chiralities, either Although the theory of the Weyl semimetal synthesized over the course of a century. By lef-handed or right-handed. In a Weyl has been around for a long time in various following this approach and calculating the semimetal, the chirality can be understood as forms1–4, its discovery had to wait until band structure of materials that are likely a topologically protected chiral charge. Weyl recent developments. Tis is because to be semimetals, many experimentally nodes of opposite chirality are separated in experimental realization requires appropriate feasible Weyl semimetal candidates have momentum space and are connected only simulation and characterizations of been identifed10,14,28,29,34. through the crystal boundary by an exotic materials. Historically, the frst two materials Te theoretical prediction of Weyl non-closed surface state, the Fermi arcs. predicted to show the efect, the pyrochlore semimetal states in the TaAs class of Remarkably, Weyl fermions are robust while iridates R2Ir2O7 (ref. 4) and the magnetically compounds was independently reported in carrying currents, giving rise to exceptionally doped superlattice6, were both time-reversal- 2015 by two groups14,17. Te experimental high mobilities. Teir spins are locked to breaking (magnetic) materials. Perhaps realization of the frst Weyl semimetal in their momentum directions, owing to their infuenced by the early work, for a long while TaAs followed soon afer15,18. Both bulk character of momentum-space magnetic the community continued to focus on time- Weyl cones and topological Fermi-arc monopole confguration. Because of the reversal-breaking materials as candidates for surface states were directly reported by chiral anomaly, the presence of parallel Weyl semimetals 7,10. Tese candidates were photoemission, providing a topological electric and magnetic felds can break the extensively studied by many experimental proof 15 based on methods shown earlier16. apparent conservation of the chiral charge, groups. Unfortunately, their eforts were not Te negative magnetoresistance, which making a Weyl metal, unlike ordinary non- successful in either demonstrating Fermi serves as an early signature of the chiral magnetic metals, more conductive with arcs or isolating the Weyl quasiparticles. anomaly, was reported from transport an increasing magnetic feld. Tese new Later, it was realized that the ‘time-reversal- experiments in the TaAs family of topological phenomena beyond topological breaking’ route to fnding suitable materials materials19,20. Tis family of materials was insulators make new physics accessible and faces a number of obstacles such as the then experimentally shown to include suggest potential applications, despite the strong correlations in magnetic materials, NbAs and TaP (refs 10,21–24). A set of early stage of the research25–46. the destruction of sample quality upon experimental criteria was developed for In this Commentary, we will review magnetic doping, and the issue of magnetic directly detecting topological Fermi arcs key experimental progress and present an domains in photoemission experiments. in Weyl semimetals without the need for outlook for future directions of the feld. On the other hand, for a long period, detailed comparison with band-structure We aim to expound our perspectives on the inversion-breaking Weyl materials were calculation24. At present, the TaAs key results and the experimental approaches relatively unexplored. Following work on a family remain the only topological Weyl currently used to access the new physics, as semimetallic state located at a topological semimetals that have been clearly confrmed well as their limitations. Moreover, although phase transition point12, Singh and in experiments, independent of comparison most of the current experiments focus on collaborators13 discussed this possibility, but to band-structure calculations10,11. the discovery of new Weyl materials and they considered compositional fne-tuning of Te discovery of TaAs also established demonstration of novel Weyl physics such as spin–orbit strength in TlBi(S1−xSex)2, which a feasible materials method to search for the chiral anomaly, it is becoming clear that is challenging to fabricate. Looking for Weyl new Weyl semimetals that are more likely a crucial step forward is to develop schemes semimetal candidates in naturally occurring to be experimentally realizable. Shortly afer for achieving quantum control of the new inversion-breaking non-centrosymmetric TaAs, a number of new Weyl semimetal physics by electrical and optical means. We single crystals can, however, avoid the candidates along the same line of thinking discuss some theoretical proposals along difculties described above. Te advantages were proposed. 1140 NATURE MATERIALS | VOL 15 | NOVEMBER 2016 | www.nature.com/naturematerials commentary a b a 10 E 20 0 B –10 cm) cm) μΩ E B μΩ –20 ( 10 ( ρ ρ c ∆ ∆ –30 –40 0 –50 –1.5 –1.0 –0.5 0 0.5 1.0 1.5 –2.0 –1.0 0 1.0 2.0 B (T) B (T) c d e E B 2 10 c2 20 ϕ ) –1 a1 a WAL 3 C c cm 1 4 –1 Ta 10 3/2 c Ω c B W (m C 2 σ ∆ –2 0 10 10 As a a5 b 10–4 –100 –50 0 50 100 –10 0 10 20 30 40 ϕ (°) EF (eV) with respect to the Weyl node Figure 1 | Signatures of Adler–Bell–Jackiw chiral anomaly in TaAs. a,b, Longitudinal magnetoresistance data for TaAs. The red lines are the data, and the green lines are the theoretical fi ts. a and c are the lattice vectors along the in-plane and out-of-plane directions, respectively, of the TaAs tetragonal lattice. Background subtraction is discussed in ref. 20. c, The tetragonal crystal lattice of TaAs. d, Magnetoresistance data as a function of the angle between the electric (E) and magnetic (B) fi elds. e, Dependence of the chiral coef cient CWAL, normalized by other fi tting coef cients, on chemical potential, EF. Remarkably, the observed 2 2 scaling behaviour is 1/EF , as expected from the dependence of the Berry curvature on chemical potential in the simplest model of a Weyl semimetal, Ω ∝ 1/EF . CWAL is the coef cient describing the magnitude of the 3D weak anti-localization (WAL) ef ect. BC is a critical fi eld that characterizes a crossover between the WAL regime and the negative magnetoresistance regime. a1, a3, a5, c2 and c4 are dif erent samples measured in the experiments. These samples have slightly dif erent chemical potential levels because they were grown under slightly dif erent conditions. Adapted from ref. 20, Nature Publishing Group. Primary examples include Ta3S2, SrSi2, chirality that are separated in momentum chiral anomaly, diverges as the chemical Mo1−xWxTe 2 and LaAlGe. In particular, SrSi2 space. T is process violates the conservation potential approaches the energy of the Weyl realizes a quadratic double Weyl state29, of chiral charge and leads to an axial charge node (Fig. 1e), consistent with its relation while Mo1−xWxTe 2 (refs 30–33,35), LaAlGe current, making a Weyl semimetal more to the Berry curvature f eld. T ese transport (ref. 34) and Ta3S2 (ref. 28) are the ‘type-II’ conductive in an increasing magnetic f eld results, in combination with angle-resolved Weyl semimetals, where the Weyl fermion that is parallel to the electric f eld. photoemission spectroscopy (ARPES) manifests as a strongly Lorentz-violating, A clear identif cation of a Weyl semimetal data modelled to be consistent with them, tilted-over cone in the band structure30. with Fermi arcs in TaAs paved the way demonstrated the existence of the chiral Experimental evidence of the bulk Weyl for the detection of the chiral anomaly. As anomaly in TaAs driven by Weyl fermions. state has been shown in LaAlGe (ref. 34) and shown in Fig. 1a,b, the magnetoresistance It is worth noting that the chiral anomaly Mo1−xWxTe 2 (refs 35,36). Δρ decreases with increasing magnetic can also arise in a Dirac semimetal because f eld for a f nite range of f elds. T e the Dirac fermions can split into pairs of Transport response and chiral anomaly observed correct negative longitudinal Weyl fermions of opposite chirality under an Weyl fermions are expected to exhibit magnetoresistance serves as an important external magnetic f eld37. various forms of quantum anomalies f rst signature of the chiral anomaly. In In most metals, magnetoresistance such as a topological Fermi arc and chiral addition, a number of supporting pieces is known to be positive; so a negative anomaly. T e chiral anomaly is important of evidence were reported in ref. 20. magnetoresistance, especially a longitudinal in understanding some structures of the T ese include the following. (1) T ere one, is quite rare. But the chiral anomaly standard model of particle physics which is a sharp dependence of the negative is not the only possible origin.
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