Experimental discovery of Weyl semimetal TaAs

Weyl semimetals are a class of materials that can be regarded as three-dimensional analogs of graphene 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, matching remarkably well with the experimental results, further confirm that TaAs is a Weyl semimetal.

any perturbation respecting the translational symmetry can only shift but not annihilate them (21,22). This is different from topological insulators whose topological properties are protected by the energy gap in the bulk state. Therefore, a WSM can be viewed as a new type of topological non-trivial phase other than the Z 2 topological insulators, making WSMs a good platform for studying and manipulating novel topological quantum states with a promising application potential.
A hallmark of a WSM is the existence of Fermi arcs on the surface (3)(4)(5), which is a direct consequence of separated Weyl nodes with opposite chirality, with the two ending points of the Fermi arc coinciding with the Weyl-node projections on the surface (Fig.   1B). Another unique property of a WSM is the chiral anomaly (23)(24)(25), which implies the apparent violation of charge conservation and leads to interesting transport properties, such as negative magneto-resistance, chiral magnetic effects and anomalous Hall effect (26)(27)(28).
In this work, we report the observation of Fermi arcs on the surface of noncentrosymmetric and nonmagnetic material TaAs using angle-resolved photoemission spectroscopy (ARPES). Unlike the previously proposed WSMs which are usually complex materials tailored by fine tuning methods (29)(30)(31)(32)(33)(34), TaAs is predicted to be a WSM in its natural state (35,36). The removal of the spin degeneracy of the bands is induced by the lack of inversion symmetry in the crystal structure rather than by the breaking of the time reversal symmetry. Such realization of the WSM phase in nonmagnetic materials allows direct observation of the Fermi arcs by ARPES because the complexity caused by a magnetic domain structure is absent.
The crystal structure of TaAs shown in Fig. 1C has the nonsymmorphic space group I4 1 md. Due to the lack of inversion symmetry, first-principles calculations predict that TaAs is a time-reversal invariant three-dimensional (3D) WSM with a dozen pairs of Weyl nodes in the Brillouin zone (BZ) (35,36). To prove this experimentally, we investigate the electronic structure of TaAs single crystals using ARPES. The core level spectrum in Fig. 1E shows the characteristic peaks of Ta and As elements, confirming the chemical composition of TaAs samples. It is important to notice that the As 3d core levels have two sets of spin-orbit doublets, while the Ta 4f core levels have only one set of doublets, suggesting that the cleaved surface is As terminated. The cleaved (001) surfaces in our measurements are very flat at the millimeter scale (Fig. 1, F and G), which is larger than the 30×20 µm 2 spot size of the incident light in our ARPES experiments and thus a single surface domain can be measured. High-quality ARPES data of highly dispersive and well-defined quasiparticle peaks are obtained (Fig. 1H), enabling us to precisely determine the band structure and the Fermi surface (FS).
To investigate the electronic structure in the 3D BZ, we carried out photon energy dependent ARPES measurements. To our surprise, almost all the observed band dispersions do not show any noticeable change with varying the incident photon energy over a wide range (20 -200 eV) (some examples are shown in Fig. 2, A to E), indicating that they are non-dispersive along k z . To understand the two-dimensionality of the experimental band structure, we carried out first-principles band structure calculations for a (001) oriented seven-unit-cell-thick slab (37) with top and bottom surfaces terminated by As and Ta layers, respectively (Fig. 2, G and H). The experimental band dispersions are remarkably well reproduced by the calculated surface state band structure with the As termination, in agreement with the conclusion from our core level data. The absence of bulk bands can be understood from our calculations that the bulk bands have vanishing spectral weight within the topmost unit cell, where most of the surface-sensitive ARPES signal origins.
The absence of bulk bands in the low-photon-energy ARPES measurements enables us to compare directly the measured surface states and their FSs with the calculated results with great precision. The consistency between calculations and experiments is further confirmed by the overall electronic structure along high-symmetry lines ( It is clear that the a1 arc connects the W2 and W1 nodes and the a5 arc connects two W2 nodes. Such connections are consistent with their topological charges, i.e. ±2 for W1 and ±1 for W2. Furthermore, the mirror Chern number of the mirror plane passing through Γ -Y is 1, which imposes the number of edge states crossing E F to be odd (35). The connection pattern obeys this rule since only the a5 arc crosses Γ -Y one time.
In summary, we have observed Fermi arcs on the (001) surface of TaAs by using ARPES. The surface FS is found to cross a closed k-loop on the (001) surface BZ an odd number of times, which gives a strong evidence for an odd number of Weyl nodes enclosed inside the loop. Our first-principles calculations reproduce almost every detail of the experimental measurements, including the band dispersion and the surface FS. The shape of the Fermi arcs and their connectivity are further identified and clearly shown for the first time. Our study confirms that we have discovered a Weyl semimetal in TaAs.
Note Added: After the completion of this work, we subsequently performed experiments investigating the bulk electronic structure of TaAs and observed the existence of Weyl nodes, another characteristic of Weyl semimetals. The latter observation, which corroborates the finding in this paper, was reported in Ref. [38].
At the time this work was made public through posting on arXiv as eprint arXiv:1502.04684, a similar work, carried out independently by another group, also became public as eprint arXiv:1502.03807. A revised version of that paper was recently published: see Ref. [39].

A1: Sample growth and preparations
High quality TaAs single crystals were grown by the chemical vapor transport method. A polycrystalline sample was filled in a quartz ampoule using iodine as transporting agent of 2mg/cm 3 . After evacuating and sealing, the ampoule was kept at the growth temperature for three weeks. Large polyhedral crystals with dimensions up to 1.5 mm were obtained in a temperature field of ΔT = 1150 °C-1000 °C. The as-grown crystals were characterized by X-ray diffraction using PANalytical diffractometer with Cu Kα radiation at room temperature. The crystal growth orientation is determined by single-crystal X-ray diffraction and the average stoichiometry was determined by energy-dispersive X-ray spectroscopy. TaAs consists of alternating stacking of Ta and As layers and has a NbAs type body-centered-tetragonal structure (40). The corresponding space group is I4 1 md and the lattice parameters are a = b = 3.4348 Å and c = 11.641 Å.
The adjacent TaAs layers are rotated by 90° and shifted by a/2.  (Fig. 2, I and J). We identify three Fermi crossings along Γ -X at k x = 0.35, 0.44 and 0.945 π/a, respectively (Fig. 2, A to E). The first two crossings at k x = 0.35 and 0.44 π/a are clear. There are three bands identified near E F around X . While the outermost band crosses E F at k x = 0.945 π/a, the two inner bands curl down below E F , leading to the feature k x = 0.975 π/a. The calculated bands in Fig. 2G also show that these two inner bands are hole-like but do not cross E F . We identify four Fermi crossings along X -M (Fig. 3, E and F). The first two crossings close to X come from one electron-like band with a bottom just below E F , in agreement with the calculations. The third and fourth ones at k y ~ 0.35 π/a are from two nearly degenerate bands, which are separated along cut C2 at the higher binding energy (Fig. 3, G and H). Along Γ -Y , the bands are similar to those along Γ -X and there are three Fermi crossings. Along Y -M , there are two Fermi crossings (Fig. 3, I and J).

B2: Determination of Fermi arcs topology and connection pattern
As seen from Fig. 4, A to E, there is one Fermi arc noted as a1 connecting W1 and W2 along Γ -Y . Experimentally, a1 and a2 are nearly degenerate (Fig. 4, D and E). To distinguish them, we measured the band dispersion along cut C4 (Fig. 4, G and H), where a1 and a2 are well separated around a binding energy of 0.4 eV. Although the calculated a1 line has relatively smaller weight at the surface around E F , more surface weight is recovered at higher binding energy as shown in Fig. 4H. The horseshoe-like arc a5, connecting the adjacent W1 points with opposite chirality on either side of Γ -Y , is clearly identified in both experiments and calculations. In addition, one can see three other arc-like lines around W1, namely a2, a3, and a4. The a2 and a4 lines are also observed in our ARPES experiments but they are connected to each other, thus revealing their trivial nature. The a3 line, or equivalently b3, which is not seen in experiment (Fig.   4I), is mainly a bulk state. Our calculation along C5 (Fig. 4J), also shows that b3 has small weight at the surface at all binding energy, further supporting its bulk nature. Its spectral weight on the surface is increased slightly only when approaching the surface band b4 near E F . This is the reason why b3 appears in the calculated Fermi surface in Fig.   4F. W2 has a topological charge of 1 and is connected to W1 by the a1 arc. The arc-connecting pattern around W2 is indicated in Fig. 4K. The surface state contributing to the a1 arc crosses E F along C6 and curls down below E F along C7 (Fig. 4, L and M).

B3: Difference of Fermi arcs in Weyl semimetal and Dirac semimetal
Here we draw attention to the difference between a Fermi arc on the surface of a Weyl semimetal and a Fermi arc on the surface of a Dirac semimetal, as in the case of Na 3 Bi (10,12). Since a Dirac node is composed by two "kissing" Weyl nodes with opposite chirality (3,4), it serves as both Fermi arc "source" and "sink" at the same time.
There are always two Fermi arcs connected to one projected Dirac node. Theoretically, these two arcs just touch each other instead of forming a continuing closed Fermi surface pocket (10). However, this raises a serious concern on how to unambiguously identify two touching arcs or one closed Fermi surface pockets in ARPES experiments.