Nature Physics  Letter
Weyl semimetal phase in the noncentrosymmetric compound TaAs
 L. X. Yang^{1, 2, 3}^{, n1}
 Z. K. Liu^{4, 5}^{, n1}
 Y. Sun^{6}^{, n1}
 H. Peng^{2}^{, }
 H. F. Yang^{2, 7}^{, }
 T. Zhang^{1, 2}^{, }
 B. Zhou^{2, 3}^{, }
 Y. Zhang^{3}^{, }
 Y. F. Guo^{2}^{, }
 M. Rahn^{2}^{, }
 D. Prabhakaran^{2}^{, }
 Z. Hussain^{3}^{, }
 S.K. Mo^{3}^{, }
 C. Felser^{6}^{, }
 B. Yan^{5, 6}^{, }
 Y. L. Chen^{1, 2, 4, 5}^{, }
 Journal name:
 Nature Physics
 Volume:
 11,
 Pages:
 728–732
 Year published:
 DOI:
 doi:10.1038/nphys3425
Threedimensional (3D) topologicalWeyl semimetals (TWSs) represent a state of quantum matter with unusual electronic structures that resemble both a ‘3D graphene’ and a topological insulator. Their electronic structure displays pairs of Weyl points (through which the electronic bands disperse linearly along all three momentum directions) connected by topological surface states, forming a unique arclike Fermi surface (FS). Each Weyl point is chiral and contains half the degrees of freedom of a Dirac point, and can be viewed as a magnetic monopole in momentum space. By performing angleresolved photoemission spectroscopy on the noncentrosymmetric compound TaAs, here we report its complete band structure, including the unique Fermiarc FS and linear bulk band dispersion across the Weyl points, in agreement with the theoretical calculations^{1, 2}. This discovery not only confirms TaAs as a 3DTWS, but also provides an ideal platform for realizing exotic physical phenomena (for example, negative magnetoresistance, chiral magnetic effects and the quantum anomalous Hall effect) which may also lead to novel future applications.
Subject terms:
At a glance
Figures
Main
The discovery of quantum materials with nontrivial topological electronic structures, such as topological insulators, topological crystalline insulators and Dirac semimetals^{3, 4, 5, 6, 7, 8, 9}, has recently ignited worldwide interest owing to their rich scientific implications and broad application potentials^{3, 4, 5, 6, 7, 8, 9}. Although being the subject of condensed matter physics, the research on topological quantum matter has benefited from the connection to other fields of physics, such as highenergy physics, by the introduction of Dirac and Majorana fermions into the electronic spectra of crystals. Recently, another intriguing particle—the Weyl fermion—which was also originally introduced in highenergy physics (for example, as a description of neutrinos), is proposed to have its counterpart in solid state physics^{10}, leading to a new type of topological quantum matter, the topological Weyl semimetals (TWSs; refs 1, 2, 10, 11, 12).
A TWS exhibits unique band structures that resemble both a ‘3D graphene’ and a topological insulator. On one hand, the bulk conduction and valence bands of a TWS touch linearly at pairs of discrete points—the Weyl points, through which the bands disperse linearly along all three momentum directions (thus it is a 3D analogue of graphene); as Weyl points of opposite chirality can be either a ‘source’ or ‘sink’ of Berry curvature^{1, 2, 10} (Fig. 1a), they can also be viewed as magnetic monopoles in the momentum space. On the other hand, in a TWS, there exist unique surface Fermi arcs^{1, 2, 10, 11, 12} (Fig. 1a), or unclosed Fermi surfaces (FSs) originating from the topological surface states (similar to those in topological insulators) that start and end at the Weyl points of opposite chirality (Fig. 1a). The unique bulk Weyl fermions and the surface Fermi arcs can give rise to many unusual physical phenomena, such as negative magnetoresistance, the chiral magnetic effect, the quantum anomalous Hall effect, novel quantum oscillations (in magnetotransport) and quantum interference (in tunnelling spectroscopy)^{13, 14, 15, 16, 17}.
In principle, TWSs can be realized by breaking either timereversal symmetry or inversion symmetry^{12, 18} of recently discovered topological Dirac semimetals^{9, 19, 20, 21}. In this way, the bulk Dirac point in a topological Dirac semimetal can be split into two Weyl points (Fig. 1a), thus realizing the TWS state. However, this method does not generate intrinsic TWSs and the need for a high external magnetic field or mechanical strain requires complicated instrumentation and experimental setup (thus limiting the use and application of these materials). Under this circumstance, the pursuit of intrinsic materials with spontaneously broken symmetry has become the focus of current research. So far, several candidates with naturally broken timereversal symmetry have been proposed (for example, Y_{2}Ir_{2}O_{7} (ref. 10) and HgCr_{2}Se_{4} (ref. 11)), however, none of them have been experimentally confirmed, leaving the existence of the TWS elusive.
Recently, another type of TWS candidate with naturally broken inversion symmetry was proposed in several compound families, including finely tuned solid solutions LaBi_{1−x}Sb_{x}Te_{3}, LuBi_{1−x}Sb_{x}Te_{3} (ref. 22) and transition metal monoarsenides/phosphides (including TaAs, TaP, NbAs and NbP; refs 1, 2). In this work, by using angleresolved photoemission spectroscopy (ARPES), we systematically studied the electronic structure of singlecrystal TaAs and observed the unique surface Fermi arcs on its FS as well as the linear bulk band dispersions through the Weyl points. The excellent agreement between our experimental band structures and ab initio calculations (including previous theoretical predictions^{1, 2}) clearly establishes that TaAs is a TWS.
The crystal structure of TaAs is shown in Fig. 1b. There are four TaAs layers in a unit cell along the cdirection, forming a repeating ⋯ –A–B–C–D– ⋯ stacking structure^{23} without inversion symmetry (Fig. 1b). As the distances in the cdirection between the intra and interlayer Ta and As planes are 0.083c (0.966 Å) and 0.167c (1.944 Å), respectively, the crystal cleaves naturally between adjacent TaAs layers along the (001) plane (Fig. 1b, e(i)), which is ideal for the ARPES measurements. In recent theoretical investigations^{1, 2}, TaAs was proposed as a TWS candidate with twelve pairs of Weyl points in each Brillouin zone (BZ; Fig. 1c), with each pair of Weyl points connected by topologically nontrivial surface states, forming the unique surface Fermi arcs. The characteristic FS of TaAs with the surface Fermi arcs on the (001) surface from our ab initio calculations (details of the calculations can be found in Methods) is shown in Fig. 1d, in nice agreement with the previous theoretical works^{1, 2}.
Highquality TaAs crystals were synthesized (details of growth can be found in Methods) for our ARPES measurements (Fig. 1e(i)), showing flat and shiny cleaved surfaces. The Xray diffraction along different crystalline orientations (Fig. 1e(ii–iv)) confirmed the crystal structure. The corelevel photoemission spectrum (Fig. 1f) shows sharp characteristic Ta 5p, 4f and As 3d core levels and the broad FS mapping (Fig. 1g) illustrates the overall FS topology agreeing with the ab initio calculations in Fig. 1d (fine measurements with more details will be discussed below).
Owing to the intrinsic surface sensitivity, ARPES is an ideal tool to study the unusual surface states and search for the unique surface Fermi arcs in TaAs. In Fig. 2, we illustrate the overall FS geometry and the band structure evolution with different binding energies around both and points of the surface BZ.
The 3D band structures around both and regions are presented in Fig. 2a and d respectively, which illustrate the FS geometry with related band dispersions. In Fig. 2b, e, three constant energy contours at different binding energies are selected to show the band evolution around the and points—both vary from the crossshaped FSs to more complicated shapes at higher binding energy. Each set of crossshaped FSs (Fig. 2b(i), e(i)) is comprised of two orthogonal subsets of FSs, one forms spoonlike pockets (marked as αFSs) and the other forms bowtieshaped pockets (marked as βFSs)—all of these FSs agree well with our ab initio calculations (presented side by side in Fig. 2b, e).
Besides the FS topology, we also studied the band dispersions across the BZ (Fig. 2c, f). The comparison between the measurements and calculations again shows excellent agreement (see Supplementary Fig. 1 for more comparisons). The surface nature of the bands that form the spoonlike αFSs (Fig. 2a, b(i), d, e(i)) can be verified by photonenergydependent ARPES measurements^{24} (Fig. 2g, h), where the ARPES spectra clearly show no k_{z}dispersion (that is, vertical dispersions; see Supplementary Information), in contrast to the bulk band dispersion which we will discuss later.
After establishing the overall correspondence between the experimental and theoretical band structures, we zoom into the spoonlike αFSs by performing fine ARPES mapping with high resolution to study the detailed FS geometry and search for the unusual surface Fermi arcs—the unique signature of a TWS.
In Fig. 3a, our ab initio calculations show a clear surface Fermi arc (green curve, marked as FS1) terminating at the Weyl points (see Fig. 3a inset for clarity), whereas the other two FS segments (FS2, FS3) extend across the Weyl points. This unusual FS topology was indeed experimentally observed in Fig. 3b, which matches Fig. 3a excellently. The change in the FS segments across the Weyl points in the experiment can also be verified through the band dispersions (Fig. 3c). Evidently, measurements above the Weyl points (Fig. 3c(i–iii)) show three bands dispersing across E_{F}, whereas there are only two bands crossing E_{F} below the Weyl points (Fig. 3c(iv–vi)), caused by the termination of FS1 at the Weyl points. Further discussions on the nature (including the spin polarization) and evolution of each FS segment, as well as quantitative momentum distribution curve (MDC) analysis can be found in the Supplementary Information.
Interestingly, as a Fermi arc is an unclosed FS, we can also verify the existence of Fermi arcs by counting the total number of Fermi crossings along a closed loop in the BZ that encloses an odd number of Weyl points—and get an odd total number of Fermi crossings (see Supplementary Information for further details on the principles of Fermi crossing counting). We thus choose the loop in a BZ (see Fig. 3d(iv)) which encloses three Weyl points, including two degenerate points (red colour, at different k_{z}, but projected to the surface BZ at the same location, see Fig. 1c, d for details) and a singular point (blue colour). In Fig. 3d, the counting of the Fermi crossings along the sections (panel (ii)), (panel (iii)) and (panel (i)) yields five, two and zero crossings, respectively. Thus there are a total of seven (an odd number) Fermi crossings along the loop , which confirms the existence of the Fermi arcs on the FS of TaAs (see Supplementary Information for Fermi crossing counting along the loop).
In addition to the unique surface Fermi arcs, we also carried out ARPES measurements (Fig. 4) with high photon energies to investigate the bulk band structure of TaAs. In Fig. 4b, bulk bands with strong k_{z} dispersion can be clearly seen in the k_{y}–k_{z} spectra intensity map (in contrast to the surface αbands in Fig. 2g, h without k_{z} dispersion; see Supplementary Information for futher details), agreeing well with our calculation (overlaid on Fig. 4b, note that the Weyl points are not observed here as they are off the k_{x} = 0 plane, see Fig. 1c, d). Also, the measured dispersions along the highsymmetry directions show good agreement with calculations (Fig. 4c, d).
The excellent agreements between our experiments and calculations allow us to identify the Weyl points predicted as lying at the k_{z} = ±1.16π/c and k_{z} = 0 planes (Fig. 1c), which can be accessed using 189 eV (k_{z} = −1.16π/c in the reduced BZ) and 204 eV (k_{z} = 0 in the reduced BZ) photons, respectively (see Fig. 4b). At each photon energy, we first carried out k_{x}–k_{y} FS mapping (Fig. 4e, g) to locate the inplane momentum positions of the Weyl points, then measured the band dispersions across them (Fig. 4f, h). Indeed, the measured bulk band dispersions in both cases show clear linear dispersions that again match well with our calculations (Fig. 4f, h), confirming the existence of Weyl points in the bulk band structure of TaAs (see Supplementary Information for further details).
The observation of the unique surface Fermi arcs and the bulk Weyl points with linear dispersions, together with the overall agreement of the measurements with the theoretical calculations, establish TaAs as the first TWS experimentally observed. This discovery extends the possibilities for the exploration of other exotic phenomena associated with TWSs and potential applications that would benefit from the ultrahigh mobility and unusually large (and nonsaturating) magnetoresistance in recently discovered 3D semimetals^{25, 26}.
We note that while we were finalizing this manuscript, two other groups also independently studied the compound TaAs (refs 27, 28), and the Weyl points were also observed in a photonic crystal^{29}.
Methods
Sample synthesis.
Precursor polycrystalline TaAs samples were prepared by mixing highpurity (>99.99%) Ta and As elements. The mixture was sealed into a quartz tube under high vacuum, which was again sealed into another evacuated tube for extra protection. First, the vessel was heated to 600 °C at the rate of 50 °C h^{−1}, then, after 10 h of soaking, it was slowly heated to 1,050 °C at the rate of 30 °C h^{−1} and kept at this temperature for 24 h. Finally the vessel was cooled down to room temperature.
From the polycrystalline precursor, the single crystals were grown using the chemical vapour transport method in a twozone furnace. The polycrystalline TaAs powder and 0.46 mg cm^{−3} of iodine were loaded into a 24mmdiameter quartz tube and sealed under vacuum. The charged part of the tube was kept at 1,150 °C and the other end at 1,000 °C for three weeks. The resulting crystals can be as large as 0.5–1 mm in size.
Angleresolved photoemission spectroscopy.
ARPES measurements were performed at beamline 10.0.1 of the Advanced Light Source (ALS) at the Lawrence Berkeley National Laboratory and BL I05 of the Diamond Light Source (DLS). The measurement pressure was kept below 3 × 10^{−11}/9 × 10^{−11} torr in the two facilities, and data were recorded by Scienta R4000 analysers at a 10 K sample temperature. The total convolved energy and angle resolutions were 16 meV and 0.2°, respectively. A fresh surface of TaAs for the ARPES measurement was obtained by cleaving the TaAs sample in situ along its natural (001) cleavage plane.
Local density approximation (LDA) calculations.
Electronic structures were calculated using the densityfunctional theory (DFT) method which is implemented in the Vienna ab initio simulation package (VASP; ref. 30). The core electrons were represented by the projected augmented wave method^{31}. The exchange–correlation was considered in the generalized gradient approximation (GGA; ref. 32) and spin–orbital coupling (SOC) was included selfconsistently. The energy cutoff was set to be 300 eV for the planewave basis. Experimental lattice parameters were used in the construction of a slab model with a thickness of seven unit cells to simulate a surface, in which the top and bottom surface are terminated by As and Ta, respectively. The positions of the outermost four atomic layers were fully optimized in determining the surface atomic relaxation. The surface band structures and the FSs were projected to the first unit cell of the Asterminated side, which fits the experimental band structure well. We adopted 12 × 12 and 400 × 400 kpoint grids in the charge selfconsistent and FS calculations, respectively.
Change history
 Corrected online 03 September 2015
 In the version of this Letter originally published a description of arclike Fermi surfaces in the abstract contained a typographical error. This error has been corrected in the online versions.
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Acknowledgements
Y.L.C. acknowledges the support from the EPSRC (UK) grant EP/K04074X/1 and a DARPA (US) MESO project (no. N660011114105). The Advanced Light Source is operated by the Department of Energy, Office of Basic Energy Science (contract DEAC0205CH11231).
Author information
Author footnotes
These authors contributed equally to this work.
 L. X. Yang,
 Z. K. Liu &
 Y. Sun
Affiliations

State Key Laboratory of Low Dimensional Quantum Physics, Collaborative Innovation Center of Quantum Matter and Department of Physics, Tsinghua University, Beijing 100084, China
 L. X. Yang,
 T. Zhang &
 Y. L. Chen

Physics Department, Oxford University, Oxford OX1 3PU, UK
 L. X. Yang,
 H. Peng,
 H. F. Yang,
 T. Zhang,
 B. Zhou,
 Y. F. Guo,
 M. Rahn,
 D. Prabhakaran &
 Y. L. Chen

Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
 L. X. Yang,
 B. Zhou,
 Y. Zhang,
 Z. Hussain &
 S.K. Mo

Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxfordshire OX11 0QX, UK
 Z. K. Liu &
 Y. L. Chen

School of Physical Science and Technology, ShanghaiTech University, Shanghai 200031, China
 Z. K. Liu,
 B. Yan &
 Y. L. Chen

Max Planck Institute for Chemical Physics of Solids, D01187 Dresden, Germany
 Y. Sun,
 C. Felser &
 B. Yan

State Key Laboratory of Functional Materials for Informatics, SIMIT, Chinese Academy of Sciences, Shanghai 200050, China
 H. F. Yang
Contributions
Y.L.C. conceived the experiments. L.X.Y. and Z.K.L. carried out ARPES measurements with the assistance of H.P., H.F.Y., T.Z., B.Z., Y.Z. and S.K.M. D.P., Y.F.G. and M.R. synthesized and characterized bulk single crystals. B.Y. and Y.S. performed ab initio calculations. All authors contributed to the scientific planning and discussions.
Competing financial interests
The authors declare no competing financial interests.
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L. X. Yang
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