Observation of Weyl nodes and Fermi arcs in TaP

Transcription

1 Observation of Weyl nodes and Fermi arcs in TaP N. Xu 1,2,*, H. M. Weng 3,4,*, B. Q. Lv 1,3, C. Matt 1, J. Park 1, F. Bisti 1, V. N. Strocov 1, D. gawryluk 5, E. Pomjakushina 5, K. Conder 5, N. C. Plumb 1, M. Radovic 1, G. Autès 6,7, O. V. Yazyev 6,7, Z. Fang 3,4, X. Dai 3,4, G. Aeppli 1,2,8, T. Qian 3, J. Mesot 1,2,8, H. Ding 3,4, and M. Shi 1, 1 Swiss Light Source, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland 2 Institute of Condensed Matter Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland 3 Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing , China 4 Collaborative Innovation Center of Quantum Matter, Beijing, China 5 Laboratory for Developments and Methods, Paul Scherrer Institut, CH-5232 Villigen, Switzerland 6 Institute of Theoretical Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland 7 National Center for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland 8 Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland * These authors contributed equally to this work. nan.xu@psi.ch, dingh@iphy.ac.cn, ming.shi@psi.ch Page 1

2 Weyl fermions are two-component spinors described by irreducible representations of the Lorentz group. They are massless with well-defined helicity and move with the speed of light. Although such kind of elementary particles have not been found yet in real space, the charge excitations in a certain class of materials, the Weyl semimetals, are predicted to behave exactly the same as the Weyl fermions, leading to exotic properties like chiral anomaly and quantum anomalous Hall effect. Carrying out angle-resolved photoemission spectroscopy on TaP, a Weyl semimetal candidate, in a wide photon energy range, we observed the pairs of Weyl cones in the bulk electronic states and the unclosed Fermi arcs on the Ta-terminated surface, which fully agree with theoretical calculations. Our results unambiguously establish that TaP is a Weyl semimetal with one type of well-separated Weyl nodes locates at the chemical potential, which guarantee that the exotic low-energy excitations near the Weyl nodes dominate the transport properties, and may lead to novel applications in this nontoxic transition metal monophosphide. Page 2

3 The concept of a three-dimensional Weyl semimetal (WSM) has recently been brought forward as a novel quantum state in which spin non-degenerate band crossings near the chemical potential are topologically unavoidable [1, 2]. The band crossing points, - the Weyl nodes, always appear in pair(s), and the low-energy excitations near the Weyl nodes are dispersing linearly in three-dimensional momentum space, which can be described by a reduced two-component massless Dirac equation [3]. An isolated Weyl node is a sink or source of Berry curvature, which can be viewed as a magnetic monopole in momentum space, and the chirality corresponds to its topological charge [4, 5]. WSM is also a topologically non-trivial metallic phase of matter with the Fermi surface of surface states forming arcs, which is distinct from that of topological insulators, extending the classification of topological phases beyond insulators. WSM state needs no additional symmetry protections other than translational symmetry in the crystal, which is much more robust than the topological insulator state or other topological semimetal states [6-13]. In addition to the Fermi arcs of the surface states, the Weyl nodes in the bulk electronic structure are predicted to cause various unusual transport phenomena, such as negative magneto-resistivity [14-16] due to chiral anomaly [17-19], non-local quantum oscillation [20] and quantum anomalous Hall effect [5], which have good potential for device applications. In searching WSMs a number of magnetic materials, e.g. R 2 Ir 2 O 7 [1], HgCr 2 Se 4 [5], Hg 1-x-y Cd x Mn y Te [21], have been proposed, in which the spin degeneracy of the crossing bands is lifted because of time reversal symmetry breaking. However, due to the complex magnetic domain structure and the interplay between external magnetic field and magnetization, the WSM phase has not yet been realized experimentally in these proposed materials. Recently, a theoretical breakthrough has predicted that the WSM with twelve pairs of Weyl nodes in the Brillouin zone (BZ) can be realized in the nonmagnetic and non-centrosymmetric transition metal monoarsenides family [22, 23]. In contrast to the slow progress on identifying the WSM properties in the proposed magnetic materials [1, 5, 21, 24-33], some key features of WSMs are experimentally observed in some of these monoarsenides compounds, including Fermi arcs [34-36] and the negative magneto-resistivity [14-17]. In particular, the predicted Weyl nodes in the bulk electronic structure of TaAs have been observed directly by angle-resolved photoemission spectroscopy (ARPES) [37]. However, Page 3

4 eight pairs of Weyl nodes in TaAs, which are well-separated in momentum space, are 21 mev below the chemical potential [37]. Although in TaAs the other four pairs are in the vicinity of the chemical potential, in each pair the Weyl nodes with opposite chirality are very close to each other, which can be easily annihilated into Dirac fermions with scattering process and lose their chirality. Therefore, the transport properties of this type of Weyl nodes in TaAs are easily dominated by non-topological phenomena (such as the negative magneto-resistance is saturated in high magnetic field). The realization of WSMs with well-separated Weyl nodes sitting at chemical potential is critical for examining the transport theories based on Weyl fermions, and potentially it is important for the application of the exotic properties of WSM states. Moreover, until now the Fermi arcs of the surface states were only observed on the As- terminated surface [34-36], the experimental evidence for the counterpart arcs on the other side, which are needed for forming a closed Fermi surface loop, are still missing. Here, we present the experimental realization of the WSM state in a transition metal monophosphide TaP. In the bulk states two types of Weyl nodes are observed. One type of Weyl nodes, which are well-separated in momentum space, locate at the Fermi level ensuring the exotic low-energy excitations near the Weyl nodes dominate the transport properties. The other is below the Fermi level that enables us to investigate both upper and lower parts of the Weyl cone while the only lower part of the cone has been observed in TaAs [37]. In the surface states we observed the Fermi arcs originating from the Ta-terminated surface, that have not been obtained in TaAs, as well as the P-terminated one. Therefore the realization of WSM states in an arsenide-free material TaP, with well-separated Weyl nodes sitting at the chemical potential, provides great opportunities not only for revealing fundamental physics of the WSM state but also for practical applications. TaP has a body-centred-tetragonal structure without inversion symmetry (space group I4 1 md), as depicted in Fig. 1a. The lattice parameters obtained from our x-ray diffraction measurement at room temperature are a = b = Å and c = Å, consistent with the values reported previously [38]. Ab initio calculations predict that there are twelve pairs of Weyl nodes in the Brillouin zone (BZ) (Fig. 1b), the eight pairs locate at k z ~ ±0.6 π/c (named W1) where c = c/2 and the other four pairs sit in the k z = 0 plane (W2) [22]. The bulk electronic structure of TaP was characterized by Page 4

5 a soft x-ray ARPES experiment, which can dramatically enhance the bulk sensitivity and k z resolution. Figure 1c presents the ARPES spectra in the k y -k z plane (the shadow plane in Fig. 1b), acquired with hν = ev. Both the Fermi surface (FS) and the band disperses along k z show a periodicity of 2π/c, indicating their bulk origin. The experimentally determined energy bands are in good agreement with the bulk band structure calculated with spin-orbit coupling (SOC), as shown in Figs. 1d-e. Due to the absence of inversion symmetry and the strong SOC in TaP, the spin degeneracy is lifted and the bulk states split into two bands, which are clearly observed in the ARPES results and band calculations (Fig. 1d). Figure 1f illustrates the band structure near a pair of Weyl nodes where the color of spheres represents the chirality. The energy bands near Weyl nodes disperse linearly in all the directions in momentum space and satisfy following conditions. (1) The band in the k x -k y plane containing a pair of the Weyl nodes has a double-dirac-cone dispersion, as depicted in Fig. 1h. (2) Along the cut passing through a pair of Weyl nodes (cut x in Fig. 1f), two spin non-degenerated bands cross each other twice and disperse linearly near the crossing points (Fig. 1g). (3) The band along a cut perpendicular to cut x (cut y or cut z in Fig. 1f) passes through one Weyl node and exhibits a single Dirac cone dispersion, seen in Fig. 1g. With the above conditions, we have identified the Weyl nodes W1 and determined their location in the k space. Figures 2a-b show that the FS splits into two small pockets sitting aside the k x/y = 0 plane, which is fully consistent with the band structure of Weyl nodes (Fig. 1h). The ARPES intensity and the corresponding curvature plots along cut x (passing through two Weyl nodes) are shown in Figs. 2c-d where the measured energy bands are in very good agreement with those obtained from the first-principles calculations. Two bands cross each other twice with the Weyl nodes at k x = ±0.03 π/a. The band between two Weyl points is enhanced with photons of 478 ev (Figs. 2e-f) due to the matrix element effect. The band structures along cut y /cut z are also remarkably consistent with the calculations, i.e. with the Weyl nodes locating at k y = 0.54 π/a and k z = 0.58 π/c, as seen from Figs. 2g-j. Within the experimental precision the Weyl nodes W1 locate at the chemical potential in TaP, which guarantees that the exotic transport phenomena related to the low excitations near the Weyl nodes such as negative magnetoresistance, chiral magnetic effects, and quantum anomalous Hall effect dominate overall transport. It makes TaP promising to Page 5

6 examine some of new transport theories proposed for Weyl fermions. The other type of Weyl nodes (W2) locating at the k z = 0 plane has been identified. Figure 3b shows the FS map recorded with hν = 455 ev, corresponding to k z = 0. Because the chemical potential is ~15 mev above the Weyl points of W2, the FS shows a single pocket at the middle points of the BZ boundary, in contrast to the FS of W1 that forms two small pockets slightly off the mirror plane. W2 below the chemical potential enable us to observe the whole band dispersions near the Weyl nodes, including the upper branches of Dirac cones that are unoccupied in TaAs/NbAs and accordingly unattainable with ARPES. As seen from Figs. 3d-g, the band structures passing through W2 along cut x and cut y are in excellent agreement with our calculations, forming a double Dirac cone dispersion in the k x -k y plane as shown in Fig. 3c. With a smaller Fermi velocity a Dirac cone dispersion is also observed along out-of-plane (k z ), as shown in Figs. 2h-i. The full consistency between the experimental results and the first-principles calculations unambiguously establishes two types of Weyl nodes W1 and W2 in TaP, and in the unit of (π/a, π/a, π/c ) they locate at (±0.03, ±0.54, ±0.58) and (±0.01, ±1.03, 0), respectively. In a WSM open Fermi arcs are expected to appear on certain surfaces, with their loci overlapping with the projection of the bulk Weyl nodes. Because of its surface sensitivity, ARPES with vacuum ultra-violet light (VUV-ARPES) is an ideal tool to investigate the Fermi arcs. Comparison between angle-integrated core level spectra taken with soft x-ray and VUV light reveals that Ta- and P-terminated surface states coexist. Two additional P-2p peaks appearing in the spectrum taken with VUV light (Fig. 4b), indicate the P-terminated surface states. The broadening of the peak originating from Ta-4f in the VUV spectrum and the different peak positions (Fig. 4c) indicate an additional component corresponding to the Ta-4f state of the Ta-terminated surface states. The FS acquired with hν = 50 ev (Fig. 4e) is very different from the bulk FS shown in Figs. 2 and 3. No dependence of the FS on the incident photon energy (Fig. 4d) confirms that the FS originates from the surface states. The 2D FSs (Fig 4e) and the band structure (Fig. 4i) measured with VUV light agree remarkably with the calculated FS and band dispersions of the surface states on the Ta-terminated (001) surface (Fig. 4g). Our calculation reveals that on the Ta-terminated surface along the Γ-X direction the Fermi arcs between the pairs of W2 or W1 nodes are very short, Page 6

7 thus it is difficult to resolve them. On the other hand, along the Γ-Y direction the Fermi arcs connect the W1 in different BZ (Ta 3-4 in Fig. 4g). This type of unclosed FS is directly observed by our ARPES measurements as marked as Ta 3-4 in Fig. 4e, with the Fermi arcs terminating at the projection of the Weyl nodes on the surface. At a higher binding energy (E B = -0.1 ev), the loci of the Fermi arcs separate more from each other, which is consistent with the dispersion of the bulk Weyl cones (Fig. 4f). The intensity of the surface states associated with the P-terminated surface is weak. Only the most pronounced feature, a pair of well-degenerated hole pockets centered at the Γ point, is visible in the FS map (Fig. 4e) and in the band structure (Fig. 4i). The observation of the Fermi arcs ending at the surface projection of the bulk Weyl nodes further confirms WSM state in TaP. In addition, we observed the missing Fermi arcs on the Ta-termination, revealing that Fermi arcs on opposite surfaces form a closed Fermi surface loop through the bulk Weyl nodes. In summary, we have identified pairs of Weyl nodes in the bulk states of TaP. The observation of Fermi arcs originating from the Ta-terminated surface, which end at the projections of the Weyl nodes on the surface, further confirms WSM states in TaP. Our observations are consistent with first-principles band calculations. The well-separated Weyl nodes W1 locating at the chemical potential in an arsenide-free WSM TaP, guarantee that exotic low-energy excitations near the Weyl nodes dominate the transport properties, thus make TaP as an ideal platform for revealing fundamental physics of the WSM state and for practical applications. Note: After we finished the manuscript we became aware of a posted preprint (ref. [42]) which reports that the magneto-resistivity in TaP is not saturated at high magnetic field and it is highly sensitive to the angle between the magnetic field and the current direction. The experimental result is fully consistent with our observation of well-separated W1 at E F. Methods Sample synthesis. Single crystals of TaP have been grown by a chemical vapor transport in a temperature gradient 850C 950 C, using 0.6 g of polycrystalline TaP as a source and iodine as a transport agent with a concentration of 12.2 mg/cm 3. Page 7

8 Polycrystalline TaP was synthesised by a solid state reaction using elemental niobium and red phosphorus of a minimum purity %. The respective amounts of starting reagents were mixed and pressed into pellets in the He-glove box, and annealed in the evacuated quartz ampule at C for 60 hours. The laboratory X-ray diffraction measurements, which were done at room temperature using Cu Ka radiation on Brucker D8 diffractometer, have proven that the obtained crystals are a phase pure compound with the tetragonal structure (space group I41/amd (N 141)). Angle-resolved photoemission spectroscopy. Clean surfaces for ARPES measurements were obtained by cleaving TaP samples in situ in a vacuum better than Torr. VUV-ARPES measurements were performed at the Surface and Interface (SIS) beamline at SLS with a Scienta R4000 analyser. Soft X-ray ARPES measurements were performed at the Advanced Resonant Spectroscopies (ADRESS) beamline at Swiss Light Source (SLS) with a SPECS analyser [39], and data were collected using circular-polarized light with an overall energy resolution on the order of mev at T = 10 K. Calculation Methods. First-principles calculations were performed using the OpenMX [40] software package. The pseudo atomic orbital basis set with Ta9.0-s2p2d2f1 and P9.0-s2p2d1 is taken. The pseudo-potentials for Ta and P are generated with the exchange-correlation functional within generalized gradient approximation parameterized by Perdew, Burke and Ernzerhof [41]. The sampling of BZ ( k-grid) has been used. The setting of these parameters has been tested to describe the electronic structure accurately. The experimental lattice constants a = b = Å, c = Å and atomic sites have been used in calculations. Acknowledgements We acknowledge the help in plotting figures from Weilu Zhang. This work was supported by the Sino-Swiss Science and Technology Cooperation (No. IZLCZ ), and the Swiss National Science Foundation (No ), the Ministry of Science and Technology of China (No. 2013CB921700, No. 2015CB921300, No. 2011CBA00108, and No. 2011CBA001000), the National Natural Science Foundation of China (No , No , No , and No ), the Chinese Academy of Sciences (No. XDB ). G.A. Page 8

9 and O.V.Y. acknowledges support by the Swiss NSF (grant No. PP00P2_133552), ERC project TopoMat (grant No ) and NCCR-MARVEL. Page 9

10 References [1] Xiangang Wan, Ari M. Turner, Ashvin Vishwanath, and Sergey Y. Savrasov. Topological semimetal and fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, (2011). [2] Leon Balents. Weyl electrons kiss. Physics 4, 36 (2011). [3] H. Weyl. Elektron und gravitation. Z. Phys. 56, (1929). [4] Z. Fang, N. Nagaosa, K. S. Takahashi, A. Asamitsu, R. Mathieu, T. Ogasawara, H. Yamada, M. Kawasaki, Y. Tokura, and K. Terakura, The Anomalous Hall Effect and Magnetic Monopoles in Momentum Space, Science 302, 92 (2003). [5] Gang Xu, Hongming Weng, Zhijun Wang, Xi Dai, and Zhong Fang. Chern semimetal and the quantized anomalous hall effect in HgCr 2 Se 4. Phys. Rev. Lett. 107, (2011). [6] Zhijun Wang, Yan Sun, Xing-Qiu Chen, Cesare Franchini, Gang Xu, Hongming Weng, Xi Dai, and Zhong Fang. Dirac semimetal and topological phase transitions in A 3 Bi (A=Na, K, Rb). Phys. Rev. B 85, (2012). [7] Zhijun Wang, Hongming Weng, Quansheng Wu, Xi Dai, and Zhong Fang. Three-dimensional Dirac Semimetal and Quantum Transport in Cd 3 As 2. Phys. Rev. B 88, (2013). [8] Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, Discovery of a Three-Dimensional Topological Dirac Semimetal, Na 3 Bi, Science 343, 864 (2014). [9] Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S. K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, A stable three-dimensional topological Dirac semimetal Cd 3 As 2, Nat. Mater. 13, 677 (2014). [10] M. Neupane, S.-Y. Xu, R. Sankar, N. Alidoust, G. Bian, C. Liu, I. Belopolski, T.-R. Chang, H.-T. Jeng, H. Lin, A. Bansil, F. Chou, and M. Z. Hasan, Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd 3 As 2, Nat. Commun. 5 (2014), /ncomms4786. Page 10

11 [11] S. Borisenko, Q. Gibson, D. Evtushinsky, V. Zabolotnyy, B. Bchner, and R. J. Cava, Experimental Realization of a Three-Dimensional Dirac Semimetal, Physical Review Letters 113, (2014). [12] Hongming Weng, Yunye Liang, Qiunan Xu, Rui Yu, Zhong Fang, Xi Dai, and Yoshiyuki Kawazoe, Topological node-line semimetal in three-dimensional graphene networks, Phys. Rev. B 92, (2015). [13] Rui Yu, Hongming Weng, Zhong Fang, Xi Dai, Xiao Hu, Topological Nodal Line Semimetal and Dirac Semimetal State in Antiperovskite Cu 3 PdN, arxiv: [14] X. C. Huang, L. X. Zhang, Y. Long, P. Wang, C. Dong, Z. Yang, H. Liang, M. Xue, Hongming Weng, Z. Fang, X. Dai, G. Chen. Observation of the chiral anomaly induced negative magneto-resistance in 3D Weyl semi-metal TaAs. arxiv: [15] C. Zhang, Z. Yuan, S. Xu, Z. Lin, B. Tong, M. Hassan, J. Wang, C. Zhang, S. Jia, Tantalum Monoarsenide: an Exotic Compensated Semimetal, arxiv: [16] C. Shekhar, A. K. Nayak, Y. Sun, M. Schmidt, M. Nicklas, I. Leermakers, U. Zeitler, W. Schnelle, J. Grin, C. Felser and B. Yan, Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal NbP. arxiv: [17] H. B. Nielsen and Masao Ninomiya. The adler-bell-jackiw anomaly and weyl fermions in a crystal. Physics Letters B 130, 389 (1983). [18] D. T. Son and B. Z. Spivak, Chiral anomaly and classical negative magnetoresistance of weyl metals. Phys. Rev. B 88, (2013). [19] Pavan Hosur and Xiaoliang Qi, Recent developments in transport phenomena in Weyl semimetals. Comptes Rendus Physique 14, 857 (2013). [20] A. C. Potter, I. Kimchi and A. Vishwanath, Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals. Nat. Commun. 5 (2014), /ncomms6161. [21] Daniel Bulmash, Chao-Xing Liu, and Xiao-Liang Qi, Prediction of a weyl semimetal in Hg 1-x-y Cd x Mn y Te. Phys. Rev. B 89, (2014). Page 11

12 [22] Hongming Weng, Chen Fang, Zhong Fang, B. A. Bernevig and X. Dai. Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides. Phys. Rev. X 5, (2015). [23] S. M. Huang et al. An inversion breaking Weyl semimetal state in the TaAs material class. arxiv: [24] A. A. Burkov and Leon Balents. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett., 107, (2011). [25] Gábor B. Halász and Leon Balents. Time-reversal invariant realization of the weyl semimetal phase. Phys. Rev. B 85, (2012). [26] A. A. Zyuzin, Si Wu, and A. A. Burkov. Weyl semimetal with broken time reversal and inversion symmetries. Phys. Rev. B 85, (2012). [27] Ling Lu, Liang Fu, John D Joannopoulos, and Marin Soljaˇcíc, Weyl points and line nodes in gyroid photonic crystals, Nature Photonics 7, 294 (2013). [28] Ling Lu, Zhiyu Wang, Dexin Ye, Lixin Ran, Liang Fu, John D. Joannopoulos, and Marin Soljačić, Experimental observation of Weyl points. arxiv: [29] Tena Dubček, Colin J. Kennedy, Ling Lu, Wolfgang Ketterle, Marin Soljačić, Hrvoje Buljan. Weyl points in three-dimensional optical lattices: synthetic magnetic monopoles in momentum space. Phys. Rev. Lett., 114, (2015). [30] M. Hirayama, R. Okugawa, S. Ishibashi, S. Murakami, and T. Miyake. Weyl Node and Spin Texture in Trigonal Tellurium and Selenium. Phys. Rev. Lett., 114, (2015). [31] Jianpeng Liu and David Vanderbilt. Weyl semimetals from noncentrosymmetric topological insulators. Phys. Rev. B 90, (2014). [32] Bahadur Singh, Ashutosh Sharma, H. Lin, M. Z. Hasan, R. Prasad, and A. Bansil. Topological electronic structure and weyl semimetal in the TlBiSe 2 class of semiconductors, Phys. Rev. B 86, (2012) [33] Tomas Bzdusek, Andreas Ruegg, Manfred Sigrist, Weyl semimetal from spontaneous inversion symmetry breaking in pyrochlore oxides. arxiv: Page 12

13 [34] B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, H. Ding. Discovery of Weyl semimetal TaAs. arxiv: [35] S. Y. Xu et al. Experimental realization of a topological Weyl semimetal phase with Fermi arc surface states in TaAs. arxiv: [36] S. Y. Xu et al. Discovery of Weyl semimetal NbAs. arxiv: [37] B. Q. Lv, N. Xu, H. M. Weng, J. Z. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, C. Matt, F. Bisti, V. N. Strocov, J. Mesot, Z. Fang, X. Dai, T. Qian, M. Shi, and H. Ding, Observation of Weyl nodes in TaAs, arxiv: [38] Boller, H. & Parthe, E. The transposition structure of NbAs and of similar monophosphides and arsenides of niobium and tantalum. Acta Crystallogr. 16, (1963). [39] V. N. Strocov. Intrinsic accuracy in 3-dimensional photoemission band mapping. J. Electron Spectrosc. Relat. Phenom. 130, 65 (2003). [40] [41] J. P. Perdew, K. Burke, and M. Ernzerhof. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996). [42] C. Shekhar, F. Arnold, S. Wu, Y. Sun, M. Schmidt, N. Kumar, A. Grushin, J. H. Bardarson, R. Reis, M. Naumann, M. Baenitz, H. Borrmann, M. Nicklas, E. Hassinger, C. Felser, and B. Yan, Large and unsaturated negative magnetoresistance induced by the chiral anomaly in the Weyl semimetal TaP, arxiv: Page 13

14 Fig. 1. Bulk electronic structure of TaP. a, Crystal structure of TaP. b, Bulk and surface BZ of TaP with high-symmetry points labelled. c, photoemission intensity of the bulk electronic states as a function of energy relative to Fermi level in the k y -k z plane shown as grey plane in b. d, ARPES spectra along the high-symmetry lines Γ-Σ-S-Z-Γ. The calculated bands are overlaid on top for comparison. e, Corresponding energy distribution curves. f, Illustration of a pair of Weyl nodes in 3D momentum space. g, Band structure passing through Weyl node along cut x, cut y and cut z. h, Schematic band dispersions of one pair of Weyl nodes in a 2D plane of the momentum space, k y -k z plane. Page 14

15 Fig. 2. W1 type of Weyl cones in TaP. a, Fermi surface map in the k y -k z plane at k x = 0, the data was acquired with soft X-ray. b, Fermi surface map in the k x -k y plane at k z = ±0.58 π/c, which correspond to hv = 478 and 520 ev as indicated in a. c, Photoemission intensity plot passing through W1 along cut x, acquired with hν = 520 ev. d, Corresponding curvature plot with calculation overlaid on top for comparison. e-f, Same as c-d but with hν = 478 ev. g-h and i-j Same as c-d but along long cut y and cut z, respectively. Page 15

16 Fig. 3. W2 type of Weyl cones in TaP. a, Fermi surface map in the k y -k z plane at k x = 0 acquired with soft X-ray. b, Fermi surface map in the k x -k y plane at k z = 0, which correspond to hv = 455 ev as indicated in a. c, ARPES intensity profile as a function of energy relative to Fermi level in the k x -k y plane containing a pair of Weyl nodes W2. d, Photoemission intensity plot passing through W1 along cut x. e, The corresponding curvature plot of the spectrum in d with the calculation band overlaid on top for comparison. f-g and h-i Same as d-e but along long cut y and cut z, respectively. Page 16

17 Fig. 4. Fermi arc on the Ta terminated (001) surface of TaP. a, Core level spectra taken with hν = 610 ev. The peaks are labeled to the corresponding core levels from Ta and P. b, The comparison of P-2p core level spectrum recorded with VUV light (hν = 210 ev) with that acquired with soft X-ray. The peaks marked as B and S are contributed by photoelectrons from the bulk and topmost P layer, respectively. c, Same as b, but focusing on the Ta 4f 7/2 core level. d, Photon-energy-dependent spectrum acquired with hν = ev. e, Fermi surface map recorded with VUV light (hν = 50 ev). f, ARPES intensity map at E B = -0.1 ev. g-h, The calculated Fermi surface of the surface states on the Ta- and P- terminated (001) surface, respectively. i, ARPES spectra along high symmetry lines acquired with hν = 50 ev. The calculated bands on Ta termination are overlaid for comparison. The surface bands resulting from the Ta-terminated surface are indicated with color lines. The grew arrows indicate the surface states from P-terminated surface. Page 17